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 | B | F | F | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 281 | 194 | 712 | 0 | 0 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.15 | 0.79 | 2.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.489 | 3.109 | 6.958 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 271 | 171 | 485 | 0 | 1343 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.20 | 0.76 | 2.16 | 0.00 | 5.97 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.484 | 2.042 | 4.274 | 0.000 | 0.170 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 254 | 175 | 549 | 0 | 1394 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.16 | 0.80 | 2.51 | 0.00 | 6.37 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.457 | 2.045 | 4.168 | 0.000 | 0.167 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 228 | 172 | 547 | 0 | 1531 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.01 | 0.76 | 2.43 | 0.00 | 6.80 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 1.159 | 1.390 | 1.200 | 0.000 | 0.193 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 290 | 351 | 245 | 1082 | 0 | 1746 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.21 | 0.84 | 3.73 | 0.00 | 6.02 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.570 | 4.343 | 6.391 | 0.000 | 0.213 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 228 | 0 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 1.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.314 | 1.672 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 211 | 191 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.02 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.380 | 0.498 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.007 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 117 | 120 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.94 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.285 | 0.234 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 67 | 0 | 0 | 0 | 0 | 0 | 151 | 64 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.25 | 0.96 |
time (sec) |
N/A | 0.232 | 0.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 36.525 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.259 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.257 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 199 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 2.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.271 | 1.048 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 195 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 2.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.268 | 0.899 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 145 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 1.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.238 | 0.639 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.269 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | C | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 208 | 203 | 264 | 210 | 3216 | 0 | 238 | 25 | 229 |
N.S. |
1 | 0.95 | 0.93 | 1.21 | 0.96 | 14.68 | 0.00 | 1.09 | 0.11 | 1.05 |
time (sec) |
N/A | 0.483 | 0.305 | 1.496 | 0.109 | 0.797 | 0.000 | 0.438 | 0.177 | 35.728 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 155 | 139 | 106 | 159 | 1049 | 0 | 163 | 25 | 153 |
N.S. |
1 | 0.93 | 0.83 | 0.63 | 0.95 | 6.28 | 0.00 | 0.98 | 0.15 | 0.92 |
time (sec) |
N/A | 0.434 | 0.182 | 0.596 | 0.115 | 0.758 | 0.000 | 0.433 | 0.175 | 35.697 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 135 | 116 | 48 | 121 | 401 | 184 | 141 | 90 | 123 |
N.S. |
1 | 0.94 | 0.81 | 0.33 | 0.84 | 2.78 | 1.28 | 0.98 | 0.62 | 0.85 |
time (sec) |
N/A | 0.338 | 0.063 | 0.467 | 0.107 | 0.133 | 2.424 | 0.389 | 0.160 | 35.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | C | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 290 | 276 | 268 | 300 | 288 | 4396 | 0 | 335 | 76 | 600 |
N.S. |
1 | 0.95 | 0.92 | 1.03 | 0.99 | 15.16 | 0.00 | 1.16 | 0.26 | 2.07 |
time (sec) |
N/A | 0.614 | 0.262 | 0.957 | 0.122 | 0.885 | 0.000 | 0.425 | 0.184 | 35.636 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | C | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 385 | 365 | 362 | 372 | 470 | 10135 | 0 | 531 | 25 | 898 |
N.S. |
1 | 0.95 | 0.94 | 0.97 | 1.22 | 26.32 | 0.00 | 1.38 | 0.06 | 2.33 |
time (sec) |
N/A | 0.740 | 2.575 | 1.902 | 0.119 | 1.736 | 0.000 | 0.409 | 0.190 | 36.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 767 | 767 | 300 | 121 | 0 | 23437 | 0 | 0 | 25 | 2338 |
N.S. |
1 | 1.00 | 0.39 | 0.16 | 0.00 | 30.56 | 0.00 | 0.00 | 0.03 | 3.05 |
time (sec) |
N/A | 1.734 | 0.643 | 2.001 | 0.000 | 3.461 | 0.000 | 0.000 | 0.175 | 38.763 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 484 | 484 | 231 | 83 | 0 | 8236 | 0 | 0 | 25 | 951 |
N.S. |
1 | 1.00 | 0.48 | 0.17 | 0.00 | 17.02 | 0.00 | 0.00 | 0.05 | 1.96 |
time (sec) |
N/A | 0.957 | 0.413 | 0.964 | 0.000 | 1.274 | 0.000 | 0.000 | 0.182 | 37.910 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 245 | 126 | 83 | 0 | 25429 | 0 | 0 | 16 | 609 |
N.S. |
1 | 1.00 | 0.51 | 0.34 | 0.00 | 103.79 | 0.00 | 0.00 | 0.07 | 2.49 |
time (sec) |
N/A | 0.501 | 0.050 | 0.424 | 0.000 | 1.054 | 0.000 | 0.000 | 0.168 | 37.405 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | C | F | F | F | B |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 0 | 432 | 162 | 0 | 59362 | 0 | 0 | 25 | 19737 |
N.S. |
1 | 0.00 | 1.44 | 0.54 | 0.00 | 198.54 | 0.00 | 0.00 | 0.08 | 66.01 |
time (sec) |
N/A | 0.000 | 0.591 | 2.395 | 0.000 | 3.275 | 0.000 | 0.000 | 0.189 | 39.545 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F(-2) | C | F | F | F | B |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1093 | 0 | 679 | 291 | 0 | 85064 | 0 | 0 | 0 | 323390 |
N.S. |
1 | 0.00 | 0.62 | 0.27 | 0.00 | 77.83 | 0.00 | 0.00 | 0.00 | 295.87 |
time (sec) |
N/A | 0.000 | 2.275 | 4.721 | 0.000 | 11.051 | 0.000 | 0.000 | 0.340 | 47.758 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | C | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 284 | 284 | 439 | 311 | 263 | 3624 | 0 | 287 | 0 | 384 |
N.S. |
1 | 1.00 | 1.55 | 1.10 | 0.93 | 12.76 | 0.00 | 1.01 | 0.00 | 1.35 |
time (sec) |
N/A | 0.570 | 3.456 | 3.513 | 0.112 | 1.215 | 0.000 | 0.434 | 0.506 | 0.397 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | C | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 239 | 258 | 284 | 213 | 2255 | 0 | 235 | 0 | 203 |
N.S. |
1 | 1.03 | 1.11 | 1.22 | 0.91 | 9.68 | 0.00 | 1.01 | 0.00 | 0.87 |
time (sec) |
N/A | 0.511 | 1.054 | 1.420 | 0.117 | 0.919 | 0.000 | 0.393 | 0.294 | 35.817 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 177 | 184 | 153 | 163 | 665 | 0 | 176 | 41 | 172 |
N.S. |
1 | 0.88 | 0.92 | 0.76 | 0.82 | 3.32 | 0.00 | 0.88 | 0.20 | 0.86 |
time (sec) |
N/A | 0.418 | 0.835 | 1.226 | 0.109 | 0.145 | 0.000 | 0.394 | 0.187 | 0.356 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 170 | 152 | 134 | 155 | 655 | 617 | 169 | 239 | 165 |
N.S. |
1 | 0.97 | 0.86 | 0.76 | 0.88 | 3.72 | 3.51 | 0.96 | 1.36 | 0.94 |
time (sec) |
N/A | 0.367 | 0.536 | 1.071 | 0.110 | 0.148 | 92.038 | 0.415 | 0.185 | 35.636 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | C | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 616 | 561 | 564 | 389 | 483 | 10855 | 0 | 581 | 0 | 980 |
N.S. |
1 | 0.91 | 0.92 | 0.63 | 0.78 | 17.62 | 0.00 | 0.94 | 0.00 | 1.59 |
time (sec) |
N/A | 0.936 | 4.997 | 2.510 | 0.113 | 2.234 | 0.000 | 0.403 | 0.499 | 36.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | C | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 776 | 715 | 724 | 483 | 788 | 15989 | 0 | 843 | 0 | 1605 |
N.S. |
1 | 0.92 | 0.93 | 0.62 | 1.02 | 20.60 | 0.00 | 1.09 | 0.00 | 2.07 |
time (sec) |
N/A | 1.223 | 6.498 | 5.548 | 0.127 | 6.432 | 0.000 | 0.435 | 2.944 | 36.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | C | N/A | F(-2) | C | N/A | N/A | N/A | B |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 394 | 241 | 0 | 9984 | 22 | 3 | 5459 | 2431 |
N.S. |
1 | 1.00 | 17.13 | 10.48 | 0.00 | 434.09 | 0.96 | 0.13 | 237.35 | 105.70 |
time (sec) |
N/A | 0.218 | 1.049 | 1.988 | 0.000 | 8.865 | 140.691 | 3.345 | 0.307 | 37.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | C | N/A | F(-2) | C | N/A | N/A | N/A | B |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 273 | 175 | 0 | 36403 | 22 | 3 | 41 | 1648 |
N.S. |
1 | 1.00 | 11.87 | 7.61 | 0.00 | 1582.74 | 0.96 | 0.13 | 1.78 | 71.65 |
time (sec) |
N/A | 0.222 | 0.933 | 2.348 | 0.000 | 2.853 | 119.448 | 3.159 | 0.202 | 37.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | C | N/A | F(-2) | C | N/A | N/A | N/A | B |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 502 | 349 | 0 | 70185 | 15 | 3 | 32 | 1567 |
N.S. |
1 | 1.00 | 35.86 | 24.93 | 0.00 | 5013.21 | 1.07 | 0.21 | 2.29 | 111.93 |
time (sec) |
N/A | 0.189 | 0.764 | 3.155 | 0.000 | 7.644 | 85.567 | 3.140 | 0.193 | 38.991 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | C | N/A | F(-2) | C | F(-1) | N/A | N/A | B |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 845 | 398 | 0 | 102913 | 0 | 3 | 47824 | 3148 |
N.S. |
1 | 1.00 | 36.74 | 17.30 | 0.00 | 4474.48 | 0.00 | 0.13 | 2079.30 | 136.87 |
time (sec) |
N/A | 0.224 | 2.534 | 7.599 | 0.000 | 40.607 | 0.000 | 3.077 | 1.208 | 41.902 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | C | N/A | F(-2) | C | F(-1) | N/A | N/A | B |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 1158 | 525 | 0 | 133123 | 0 | 3 | 225974 | 4657 |
N.S. |
1 | 1.00 | 50.35 | 22.83 | 0.00 | 5787.96 | 0.00 | 0.13 | 9824.96 | 202.48 |
time (sec) |
N/A | 0.224 | 2.477 | 12.033 | 0.000 | 127.922 | 0.000 | 3.096 | 42.232 | 46.296 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 123 | 207 | 178 | 177 | 1429 | 0 | 376 | 29 | 1931 |
N.S. |
1 | 0.94 | 1.58 | 1.36 | 1.35 | 10.91 | 0.00 | 2.87 | 0.22 | 14.74 |
time (sec) |
N/A | 0.372 | 0.315 | 3.136 | 0.113 | 0.303 | 0.000 | 0.395 | 0.205 | 0.750 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 108 | 189 | 152 | 158 | 1041 | 0 | 322 | 29 | 1097 |
N.S. |
1 | 0.96 | 1.67 | 1.35 | 1.40 | 9.21 | 0.00 | 2.85 | 0.26 | 9.71 |
time (sec) |
N/A | 0.352 | 0.235 | 1.618 | 0.117 | 0.205 | 0.000 | 0.421 | 0.205 | 0.548 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 96 | 160 | 136 | 121 | 631 | 0 | 288 | 29 | 489 |
N.S. |
1 | 1.01 | 1.68 | 1.43 | 1.27 | 6.64 | 0.00 | 3.03 | 0.31 | 5.15 |
time (sec) |
N/A | 0.299 | 0.097 | 0.831 | 0.108 | 0.157 | 0.000 | 0.403 | 0.198 | 35.843 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 69 | 54 | 48 | 100 | 161 | 129 | 232 | 64 | 40 |
N.S. |
1 | 0.97 | 0.76 | 0.68 | 1.41 | 2.27 | 1.82 | 3.27 | 0.90 | 0.56 |
time (sec) |
N/A | 0.246 | 0.030 | 0.528 | 0.114 | 0.108 | 2.342 | 0.358 | 0.196 | 35.524 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 112 | 184 | 185 | 167 | 1329 | 0 | 384 | 77 | 3891 |
N.S. |
1 | 0.96 | 1.57 | 1.58 | 1.43 | 11.36 | 0.00 | 3.28 | 0.66 | 33.26 |
time (sec) |
N/A | 0.340 | 0.221 | 1.168 | 0.111 | 0.201 | 0.000 | 0.418 | 0.187 | 37.942 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 164 | 255 | 241 | 244 | 2529 | 0 | 496 | 29 | 7758 |
N.S. |
1 | 1.09 | 1.69 | 1.60 | 1.62 | 16.75 | 0.00 | 3.28 | 0.19 | 51.38 |
time (sec) |
N/A | 0.403 | 1.233 | 2.412 | 0.111 | 0.529 | 0.000 | 0.395 | 0.214 | 39.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 200 | 200 | 224 | 0 | 2433 | 0 | 836 | 29 | 8773 |
N.S. |
1 | 1.10 | 1.10 | 1.23 | 0.00 | 13.37 | 0.00 | 4.59 | 0.16 | 48.20 |
time (sec) |
N/A | 0.516 | 1.456 | 4.112 | 0.000 | 0.735 | 0.000 | 0.886 | 0.197 | 37.907 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 162 | 194 | 179 | 0 | 1751 | 0 | 995 | 29 | 3088 |
N.S. |
1 | 1.05 | 1.25 | 1.15 | 0.00 | 11.30 | 0.00 | 6.42 | 0.19 | 19.92 |
time (sec) |
N/A | 0.436 | 1.006 | 2.174 | 0.000 | 0.443 | 0.000 | 0.749 | 0.200 | 37.851 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 131 | 171 | 148 | 0 | 1197 | 0 | 906 | 29 | 4299 |
N.S. |
1 | 1.03 | 1.35 | 1.17 | 0.00 | 9.43 | 0.00 | 7.13 | 0.23 | 33.85 |
time (sec) |
N/A | 0.403 | 0.616 | 0.999 | 0.000 | 0.275 | 0.000 | 0.758 | 0.191 | 37.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 161 | 158 | 73 | 0 | 541 | 0 | 560 | 29 | 1409 |
N.S. |
1 | 1.29 | 1.26 | 0.58 | 0.00 | 4.33 | 0.00 | 4.48 | 0.23 | 11.27 |
time (sec) |
N/A | 0.312 | 0.635 | 0.786 | 0.000 | 0.205 | 0.000 | 0.717 | 0.183 | 36.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 137 | 175 | 166 | 0 | 2589 | 0 | 1211 | 29 | 2832 |
N.S. |
1 | 0.96 | 1.23 | 1.17 | 0.00 | 18.23 | 0.00 | 8.53 | 0.20 | 19.94 |
time (sec) |
N/A | 0.383 | 0.913 | 1.639 | 0.000 | 0.398 | 0.000 | 0.775 | 0.207 | 37.389 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 153 | 205 | 230 | 0 | 4113 | 0 | 2183 | 0 | 4664 |
N.S. |
1 | 0.95 | 1.27 | 1.43 | 0.00 | 25.55 | 0.00 | 13.56 | 0.00 | 28.97 |
time (sec) |
N/A | 0.490 | 1.422 | 2.654 | 0.000 | 0.632 | 0.000 | 0.904 | 0.264 | 37.970 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 193 | 253 | 311 | 0 | 5587 | 0 | 3106 | 0 | 6534 |
N.S. |
1 | 0.95 | 1.24 | 1.52 | 0.00 | 27.39 | 0.00 | 15.23 | 0.00 | 32.03 |
time (sec) |
N/A | 0.526 | 1.925 | 3.949 | 0.000 | 1.122 | 0.000 | 0.902 | 0.357 | 38.932 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 37 | 0 | 25 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.61 | 0.00 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.216 | 7.268 | 1.168 | 1.612 | 0.428 | 0.000 | 1.014 | 0.193 | 42.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 199 | 141 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.01 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.417 | 0.188 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 138 | 106 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.99 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.309 | 0.065 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 67 | 0 | 0 | 0 | 0 | 0 | 151 | 64 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.25 | 0.96 |
time (sec) |
N/A | 0.237 | 0.021 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 35.812 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 156 | 0 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.363 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 234 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.444 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 37 | 0 | 25 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.61 | 0.00 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.225 | 3.859 | 1.584 | 2.572 | 0.107 | 0.000 | 0.980 | 0.216 | 36.740 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 37 | 0 | 25 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.61 | 0.00 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.222 | 5.078 | 1.547 | 1.653 | 0.096 | 0.000 | 0.995 | 0.184 | 36.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 16 | 28 | 0 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 2.00 | 0.00 | 1.14 | 1.14 | 1.14 |
time (sec) |
N/A | 0.187 | 1.260 | 0.808 | 0.766 | 0.095 | 0.000 | 0.635 | 0.177 | 35.780 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 37 | 0 | 25 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.61 | 0.00 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.218 | 4.794 | 1.285 | 1.670 | 0.117 | 0.000 | 1.377 | 0.195 | 37.958 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 37 | 0 | 25 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.61 | 0.00 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.221 | 7.907 | 1.345 | 2.851 | 0.148 | 0.000 | 0.977 | 0.187 | 38.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 25 | 0 | 25 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.00 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.226 | 5.514 | 0.422 | 3.243 | 0.097 | 0.000 | 6.138 | 0.171 | 36.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 221 | 155 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.98 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.409 | 0.263 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 146 | 114 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.99 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.344 | 0.106 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 69 | 0 | 0 | 0 | 0 | 0 | 153 | 70 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.22 | 1.01 |
time (sec) |
N/A | 0.240 | 0.028 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 36.559 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 23 | 21 | 23 | 23 | 0 | 23 | 23 | 25 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.00 | 1.10 | 1.10 | 1.19 |
time (sec) |
N/A | 0.214 | 4.159 | 0.581 | 1.964 | 0.092 | 0.000 | 0.525 | 0.168 | 35.798 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 25 | 0 | 25 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.00 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.221 | 8.390 | 0.606 | 2.059 | 0.089 | 0.000 | 0.554 | 0.177 | 35.789 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 25 | 0 | 25 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.00 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.224 | 11.212 | 0.851 | 5.513 | 0.090 | 0.000 | 12.866 | 0.180 | 35.883 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 25 | 22 | 25 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.96 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.220 | 9.392 | 0.619 | 3.711 | 0.102 | 56.412 | 10.775 | 0.172 | 34.749 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 14 | 16 | 16 | 14 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.14 | 1.00 | 1.14 | 1.14 | 1.14 |
time (sec) |
N/A | 0.185 | 2.249 | 0.244 | 1.794 | 0.113 | 5.329 | 3.253 | 0.178 | 35.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 25 | 0 | 25 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.00 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.221 | 5.236 | 0.576 | 2.138 | 0.090 | 0.000 | 3.252 | 0.173 | 34.874 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 23 | 25 | 25 | 0 | 25 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.00 | 1.09 | 1.09 | 1.09 |
time (sec) |
N/A | 0.222 | 8.602 | 0.618 | 2.220 | 0.088 | 0.000 | 3.464 | 0.174 | 34.841 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 139 | 113 | 114 | 273 | 179 | 0 | 218 | 1041 | 115 |
N.S. |
1 | 1.09 | 0.88 | 0.89 | 2.13 | 1.40 | 0.00 | 1.70 | 8.13 | 0.90 |
time (sec) |
N/A | 0.337 | 0.343 | 4.660 | 0.037 | 0.286 | 0.000 | 0.555 | 0.314 | 34.806 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 102 | 78 | 83 | 159 | 118 | 0 | 152 | 689 | 90 |
N.S. |
1 | 1.09 | 0.83 | 0.88 | 1.69 | 1.26 | 0.00 | 1.62 | 7.33 | 0.96 |
time (sec) |
N/A | 0.307 | 0.298 | 2.346 | 0.035 | 0.163 | 0.000 | 0.644 | 0.245 | 34.766 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 69 | 52 | 58 | 82 | 78 | 0 | 91 | 374 | 52 |
N.S. |
1 | 1.08 | 0.81 | 0.91 | 1.28 | 1.22 | 0.00 | 1.42 | 5.84 | 0.81 |
time (sec) |
N/A | 0.269 | 0.119 | 1.244 | 0.032 | 0.117 | 0.000 | 0.592 | 0.198 | 34.655 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 47 | 37 | 42 | 43 | 37 | 0 | 53 | 128 | 28 |
N.S. |
1 | 1.09 | 0.86 | 0.98 | 1.00 | 0.86 | 0.00 | 1.23 | 2.98 | 0.65 |
time (sec) |
N/A | 0.224 | 0.042 | 0.809 | 0.032 | 0.096 | 0.000 | 0.513 | 0.186 | 34.730 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 39 | 38 | 54 | 37 | 35 | 0 | 38 | 116 | 41 |
N.S. |
1 | 1.03 | 1.00 | 1.42 | 0.97 | 0.92 | 0.00 | 1.00 | 3.05 | 1.08 |
time (sec) |
N/A | 0.222 | 0.030 | 0.993 | 0.027 | 0.096 | 0.000 | 0.504 | 0.183 | 34.755 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 58 | 50 | 101 | 56 | 91 | 0 | 68 | 316 | 69 |
N.S. |
1 | 0.92 | 0.79 | 1.60 | 0.89 | 1.44 | 0.00 | 1.08 | 5.02 | 1.10 |
time (sec) |
N/A | 0.269 | 0.159 | 1.831 | 0.027 | 0.107 | 0.000 | 0.522 | 0.185 | 34.712 |
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 | 89 | 81 | 72 | 161 | 92 | 198 | 0 | 108 | 521 | 103 |
N.S. |
1 | 0.91 | 0.81 | 1.81 | 1.03 | 2.22 | 0.00 | 1.21 | 5.85 | 1.16 |
time (sec) |
N/A | 0.287 | 0.594 | 3.628 | 0.033 | 0.138 | 0.000 | 0.668 | 0.207 | 34.821 |
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 | 121 | 110 | 100 | 253 | 137 | 371 | 0 | 154 | 743 | 138 |
N.S. |
1 | 0.91 | 0.83 | 2.09 | 1.13 | 3.07 | 0.00 | 1.27 | 6.14 | 1.14 |
time (sec) |
N/A | 0.309 | 0.308 | 7.536 | 0.036 | 0.193 | 0.000 | 0.582 | 0.201 | 35.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 109 | 147 | 120 | 180 | 602 | 0 | 543 | 2952 | 141 |
N.S. |
1 | 0.91 | 1.22 | 1.00 | 1.50 | 5.02 | 0.00 | 4.52 | 24.60 | 1.18 |
time (sec) |
N/A | 0.320 | 4.890 | 6.547 | 0.113 | 0.132 | 0.000 | 0.743 | 2.524 | 34.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 89 | 111 | 121 | 130 | 472 | 0 | 330 | 2081 | 112 |
N.S. |
1 | 0.92 | 1.14 | 1.25 | 1.34 | 4.87 | 0.00 | 3.40 | 21.45 | 1.15 |
time (sec) |
N/A | 0.296 | 1.262 | 3.279 | 0.113 | 0.119 | 0.000 | 0.753 | 1.028 | 34.634 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 69 | 75 | 78 | 85 | 366 | 0 | 170 | 1290 | 83 |
N.S. |
1 | 0.93 | 1.01 | 1.05 | 1.15 | 4.95 | 0.00 | 2.30 | 17.43 | 1.12 |
time (sec) |
N/A | 0.284 | 0.605 | 1.726 | 0.111 | 0.108 | 0.000 | 0.765 | 0.411 | 34.689 |
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 | 53 | 51 | 53 | 51 | 51 | 300 | 0 | 66 | 582 | 53 |
N.S. |
1 | 0.96 | 1.00 | 0.96 | 0.96 | 5.66 | 0.00 | 1.25 | 10.98 | 1.00 |
time (sec) |
N/A | 0.242 | 0.403 | 0.980 | 0.113 | 0.103 | 0.000 | 0.591 | 0.412 | 34.669 |
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 | 52 | 50 | 52 | 55 | 50 | 290 | 0 | 85 | 559 | 44 |
N.S. |
1 | 0.96 | 1.00 | 1.06 | 0.96 | 5.58 | 0.00 | 1.63 | 10.75 | 0.85 |
time (sec) |
N/A | 0.244 | 0.600 | 1.365 | 0.106 | 0.101 | 0.000 | 0.685 | 0.193 | 34.644 |
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 | 71 | 74 | 72 | 79 | 76 | 402 | 0 | 120 | 1013 | 64 |
N.S. |
1 | 1.04 | 1.01 | 1.11 | 1.07 | 5.66 | 0.00 | 1.69 | 14.27 | 0.90 |
time (sec) |
N/A | 0.261 | 0.671 | 2.593 | 0.113 | 0.102 | 0.000 | 0.610 | 0.200 | 34.729 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 98 | 101 | 115 | 111 | 576 | 0 | 171 | 1480 | 82 |
N.S. |
1 | 1.02 | 1.05 | 1.20 | 1.16 | 6.00 | 0.00 | 1.78 | 15.42 | 0.85 |
time (sec) |
N/A | 0.281 | 1.390 | 5.381 | 0.114 | 0.111 | 0.000 | 0.710 | 0.217 | 35.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 122 | 135 | 155 | 154 | 834 | 0 | 238 | 1969 | 100 |
N.S. |
1 | 1.04 | 1.15 | 1.32 | 1.32 | 7.13 | 0.00 | 2.03 | 16.83 | 0.85 |
time (sec) |
N/A | 0.296 | 3.670 | 10.400 | 0.109 | 0.123 | 0.000 | 0.757 | 0.227 | 37.898 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 70 | 42 | 49 | 69 | 47 | 0 | 128 | 27 | 326 |
N.S. |
1 | 1.09 | 0.66 | 0.77 | 1.08 | 0.73 | 0.00 | 2.00 | 0.42 | 5.09 |
time (sec) |
N/A | 0.358 | 0.241 | 0.711 | 0.037 | 0.085 | 0.000 | 0.828 | 0.180 | 40.341 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 49 | 29 | 28 | 46 | 34 | 0 | 37 | 27 | 69 |
N.S. |
1 | 1.29 | 0.76 | 0.74 | 1.21 | 0.89 | 0.00 | 0.97 | 0.71 | 1.82 |
time (sec) |
N/A | 0.344 | 0.146 | 0.572 | 0.035 | 0.086 | 0.000 | 0.653 | 0.185 | 0.698 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 21 | 20 | 17 | 0 | 37 | 25 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.05 | 0.89 | 0.00 | 1.95 | 1.32 | 1.05 |
time (sec) |
N/A | 0.289 | 0.045 | 0.448 | 0.115 | 0.078 | 0.000 | 0.573 | 0.168 | 34.742 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 52 | 47 | 54 | 70 | 57 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.04 | 0.94 | 1.08 | 1.40 | 1.14 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.312 | 0.097 | 0.647 | 0.109 | 0.092 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 90 | 97 | 102 | 99 | 88 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.03 | 1.11 | 1.17 | 1.14 | 1.01 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.350 | 1.656 | 0.705 | 0.114 | 0.093 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 102 | 75 | 157 | 1955 | 87 | 0 | 234 | 27 | 0 |
N.S. |
1 | 0.78 | 0.58 | 1.21 | 15.04 | 0.67 | 0.00 | 1.80 | 0.21 | 0.00 |
time (sec) |
N/A | 0.427 | 0.299 | 0.659 | 0.882 | 0.097 | 0.000 | 0.517 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 71 | 55 | 131 | 827 | 77 | 0 | 197 | 27 | 0 |
N.S. |
1 | 0.76 | 0.59 | 1.39 | 8.80 | 0.82 | 0.00 | 2.10 | 0.29 | 0.00 |
time (sec) |
N/A | 0.384 | 0.239 | 0.618 | 0.219 | 0.093 | 0.000 | 0.603 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 40 | 40 | 96 | 73 | 55 | 0 | 127 | 27 | 0 |
N.S. |
1 | 0.70 | 0.70 | 1.68 | 1.28 | 0.96 | 0.00 | 2.23 | 0.47 | 0.00 |
time (sec) |
N/A | 0.373 | 0.060 | 0.571 | 0.164 | 0.093 | 0.000 | 0.481 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 38 | 35 | 42 | 42 | 42 | 0 | 0 | 27 | 88 |
N.S. |
1 | 0.67 | 0.61 | 0.74 | 0.74 | 0.74 | 0.00 | 0.00 | 0.47 | 1.54 |
time (sec) |
N/A | 0.403 | 0.083 | 0.566 | 0.110 | 0.081 | 0.000 | 0.000 | 0.189 | 37.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 54 | 47 | 75 | 57 | 66 | 0 | 0 | 27 | 364 |
N.S. |
1 | 0.59 | 0.52 | 0.82 | 0.63 | 0.73 | 0.00 | 0.00 | 0.30 | 4.00 |
time (sec) |
N/A | 0.409 | 0.092 | 0.635 | 0.134 | 0.087 | 0.000 | 0.000 | 0.183 | 39.456 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 62 | 67 | 85 | 68 | 86 | 0 | 0 | 27 | 555 |
N.S. |
1 | 0.50 | 0.54 | 0.69 | 0.55 | 0.69 | 0.00 | 0.00 | 0.22 | 4.48 |
time (sec) |
N/A | 0.420 | 0.224 | 0.658 | 0.119 | 0.085 | 0.000 | 0.000 | 0.184 | 55.796 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 72 | 43 | 48 | 69 | 50 | 0 | 67 | 43 | 486 |
N.S. |
1 | 1.11 | 0.66 | 0.74 | 1.06 | 0.77 | 0.00 | 1.03 | 0.66 | 7.48 |
time (sec) |
N/A | 0.355 | 0.204 | 0.506 | 0.036 | 0.102 | 0.000 | 0.551 | 0.187 | 45.617 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 51 | 31 | 38 | 46 | 40 | 0 | 54 | 43 | 100 |
N.S. |
1 | 1.21 | 0.74 | 0.90 | 1.10 | 0.95 | 0.00 | 1.29 | 1.02 | 2.38 |
time (sec) |
N/A | 0.344 | 0.150 | 0.479 | 0.034 | 0.078 | 0.000 | 0.505 | 0.173 | 39.832 |