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 | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 174 | 338 | 253 | 0 | 423 | 0 | 0 | 55 | 0 |
N.S. |
1 | 1.03 | 2.00 | 1.50 | 0.00 | 2.50 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.754 | 20.608 | 3.310 | 0.000 | 0.127 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 165 | 340 | 264 | 0 | 984 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.04 | 2.14 | 1.66 | 0.00 | 6.19 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.768 | 20.658 | 1.326 | 0.000 | 0.222 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 182 | 340 | 258 | 0 | 997 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.04 | 1.94 | 1.47 | 0.00 | 5.70 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.799 | 20.758 | 1.247 | 0.000 | 0.209 | 0.000 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 185 | 338 | 267 | 0 | 991 | 0 | 0 | 55 | 0 |
N.S. |
1 | 1.04 | 1.90 | 1.50 | 0.00 | 5.57 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.776 | 20.744 | 1.277 | 0.000 | 0.207 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 176 | 342 | 255 | 0 | 994 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.04 | 2.01 | 1.50 | 0.00 | 5.85 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.792 | 20.696 | 1.274 | 0.000 | 0.255 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 316 | 316 | 348 | 0 | 0 | 0 | 0 | 0 | 73 | 0 |
N.S. |
1 | 1.00 | 1.10 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.181 | 11.756 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 325 | 399 | 0 | 0 | 0 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.00 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 1.145 | 11.555 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 333 | 334 | 400 | 0 | 0 | 0 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.00 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.141 | 10.652 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 329 | 329 | 401 | 0 | 0 | 0 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.151 | 11.554 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 265 | 265 | 380 | 900 | 0 | 390 | 0 | 0 | 96 | 0 |
N.S. |
1 | 1.00 | 1.43 | 3.40 | 0.00 | 1.47 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.943 | 11.762 | 0.437 | 0.000 | 0.419 | 0.000 | 0.000 | 0.142 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 207 | 258 | 0 | 82 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 1.43 | 1.78 | 0.00 | 0.57 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.716 | 10.446 | 2.458 | 0.000 | 0.158 | 0.000 | 0.000 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 160 | 209 | 253 | 0 | 83 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.31 | 1.58 | 0.00 | 0.52 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.765 | 10.556 | 2.426 | 0.000 | 0.147 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 163 | 207 | 262 | 0 | 245 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 1.27 | 1.61 | 0.00 | 1.50 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.734 | 10.562 | 2.324 | 0.000 | 0.161 | 0.000 | 0.000 | 0.137 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 209 | 249 | 0 | 248 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 1.34 | 1.60 | 0.00 | 1.59 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.747 | 10.477 | 2.373 | 0.000 | 0.146 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 275 | 336 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.069 | 11.592 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 283 | 388 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.078 | 11.403 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.139 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 292 | 389 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 1.092 | 10.806 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 288 | 288 | 389 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 1.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.088 | 11.153 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 246 | 372 | 892 | 0 | 350 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.00 | 1.51 | 3.63 | 0.00 | 1.42 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.929 | 11.305 | 0.380 | 0.000 | 0.198 | 0.000 | 0.000 | 0.139 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 31 | 42 | 0 | 44 | 0 | 0 | 26 | 205 |
N.S. |
1 | 1.00 | 1.35 | 1.83 | 0.00 | 1.91 | 0.00 | 0.00 | 1.13 | 8.91 |
time (sec) |
N/A | 0.341 | 1.147 | 0.517 | 0.000 | 0.150 | 0.000 | 0.000 | 0.150 | 0.226 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 33 | 49 | 0 | 47 | 0 | 0 | 26 | 221 |
N.S. |
1 | 1.00 | 1.22 | 1.81 | 0.00 | 1.74 | 0.00 | 0.00 | 0.96 | 8.19 |
time (sec) |
N/A | 0.338 | 1.123 | 0.461 | 0.000 | 0.119 | 0.000 | 0.000 | 0.165 | 21.874 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 21 | 75 | 0 | 40 | 0 | 0 | 26 | 205 |
N.S. |
1 | 1.00 | 0.84 | 3.00 | 0.00 | 1.60 | 0.00 | 0.00 | 1.04 | 8.20 |
time (sec) |
N/A | 0.326 | 1.158 | 0.589 | 0.000 | 0.140 | 0.000 | 0.000 | 0.152 | 22.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 23 | 79 | 0 | 38 | 0 | 0 | 26 | 221 |
N.S. |
1 | 1.00 | 0.92 | 3.16 | 0.00 | 1.52 | 0.00 | 0.00 | 1.04 | 8.84 |
time (sec) |
N/A | 0.338 | 1.158 | 0.618 | 0.000 | 0.138 | 0.000 | 0.000 | 0.156 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 48 | 0 | 0 | 0 | 0 | 0 | 96 | 65 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.92 | 1.30 |
time (sec) |
N/A | 0.446 | 3.407 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 22.720 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 50 | 0 | 0 | 0 | 0 | 0 | 97 | 67 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.87 | 1.29 |
time (sec) |
N/A | 0.460 | 3.394 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 22.666 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 51 | 0 | 0 | 592 | 0 | 0 | 99 | 74 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 11.17 | 0.00 | 0.00 | 1.87 | 1.40 |
time (sec) |
N/A | 0.452 | 3.393 | 0.000 | 0.000 | 0.611 | 0.000 | 0.000 | 0.216 | 25.199 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 51 | 0 | 0 | 641 | 0 | 0 | 99 | 78 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 12.09 | 0.00 | 0.00 | 1.87 | 1.47 |
time (sec) |
N/A | 0.457 | 3.321 | 0.000 | 0.000 | 0.715 | 0.000 | 0.000 | 0.196 | 25.628 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 44 | 503 | 0 | 294 | 0 | 0 | 46 | 67 |
N.S. |
1 | 1.00 | 0.96 | 10.93 | 0.00 | 6.39 | 0.00 | 0.00 | 1.00 | 1.46 |
time (sec) |
N/A | 0.417 | 1.566 | 0.627 | 0.000 | 0.168 | 0.000 | 0.000 | 0.154 | 23.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 273 | 246 | 0 | 61 | 0 | 0 | 52 | 327 |
N.S. |
1 | 1.00 | 1.96 | 1.77 | 0.00 | 0.44 | 0.00 | 0.00 | 0.37 | 2.35 |
time (sec) |
N/A | 0.608 | 20.425 | 0.464 | 0.000 | 0.096 | 0.000 | 0.000 | 0.168 | 22.691 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 271 | 246 | 0 | 66 | 0 | 0 | 60 | 359 |
N.S. |
1 | 1.00 | 1.77 | 1.61 | 0.00 | 0.43 | 0.00 | 0.00 | 0.39 | 2.35 |
time (sec) |
N/A | 0.665 | 20.370 | 0.403 | 0.000 | 0.101 | 0.000 | 0.000 | 0.152 | 22.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 269 | 246 | 0 | 55 | 0 | 0 | 54 | 327 |
N.S. |
1 | 1.00 | 1.72 | 1.58 | 0.00 | 0.35 | 0.00 | 0.00 | 0.35 | 2.10 |
time (sec) |
N/A | 0.616 | 20.343 | 0.431 | 0.000 | 0.131 | 0.000 | 0.000 | 0.176 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 275 | 246 | 0 | 57 | 0 | 0 | 52 | 359 |
N.S. |
1 | 1.00 | 1.83 | 1.64 | 0.00 | 0.38 | 0.00 | 0.00 | 0.35 | 2.39 |
time (sec) |
N/A | 0.661 | 20.381 | 0.503 | 0.000 | 0.111 | 0.000 | 0.000 | 0.158 | 21.674 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 297 | 292 | 438 | 0 | 0 | 0 | 0 | 0 | 92 | 0 |
N.S. |
1 | 0.98 | 1.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.989 | 11.653 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 299 | 447 | 0 | 0 | 0 | 0 | 0 | 92 | 0 |
N.S. |
1 | 0.98 | 1.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.980 | 11.478 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 313 | 308 | 448 | 0 | 0 | 0 | 0 | 0 | 96 | 0 |
N.S. |
1 | 0.98 | 1.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 1.019 | 11.542 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 310 | 305 | 441 | 0 | 0 | 0 | 0 | 0 | 95 | 0 |
N.S. |
1 | 0.98 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 1.025 | 11.730 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 221 | 384 | 521 | 0 | 396 | 0 | 0 | 96 | 0 |
N.S. |
1 | 1.00 | 1.74 | 2.36 | 0.00 | 1.79 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.895 | 10.933 | 0.422 | 0.000 | 0.243 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 193 | 240 | 0 | 51 | 0 | 0 | 25 | 207 |
N.S. |
1 | 1.00 | 1.50 | 1.86 | 0.00 | 0.40 | 0.00 | 0.00 | 0.19 | 1.60 |
time (sec) |
N/A | 0.600 | 10.258 | 0.439 | 0.000 | 0.104 | 0.000 | 0.000 | 0.152 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 195 | 240 | 0 | 54 | 0 | 0 | 29 | 224 |
N.S. |
1 | 1.00 | 1.34 | 1.66 | 0.00 | 0.37 | 0.00 | 0.00 | 0.20 | 1.54 |
time (sec) |
N/A | 0.623 | 10.218 | 0.366 | 0.000 | 0.139 | 0.000 | 0.000 | 0.163 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 148 | 193 | 240 | 0 | 47 | 0 | 0 | 25 | 208 |
N.S. |
1 | 1.00 | 1.30 | 1.62 | 0.00 | 0.32 | 0.00 | 0.00 | 0.17 | 1.41 |
time (sec) |
N/A | 0.605 | 10.225 | 0.547 | 0.000 | 0.130 | 0.000 | 0.000 | 0.145 | 22.756 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 195 | 240 | 0 | 45 | 0 | 0 | 25 | 223 |
N.S. |
1 | 1.00 | 1.39 | 1.71 | 0.00 | 0.32 | 0.00 | 0.00 | 0.18 | 1.59 |
time (sec) |
N/A | 0.626 | 10.258 | 0.490 | 0.000 | 0.139 | 0.000 | 0.000 | 0.154 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 260 | 369 | 0 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.946 | 11.347 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 268 | 371 | 0 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 1.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.972 | 10.626 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 277 | 277 | 372 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.951 | 10.669 | 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 | C | F | F | F(-1) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 273 | 372 | 0 | 0 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 1.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.967 | 10.753 | 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 | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 202 | 295 | 509 | 0 | 356 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.00 | 1.46 | 2.52 | 0.00 | 1.76 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.853 | 10.537 | 0.373 | 0.000 | 0.164 | 0.000 | 0.000 | 0.140 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 49 | 130 | 0 | 202 | 0 | 0 | 186 | 0 |
N.S. |
1 | 1.00 | 1.17 | 3.10 | 0.00 | 4.81 | 0.00 | 0.00 | 4.43 | 0.00 |
time (sec) |
N/A | 0.426 | 1.890 | 1.841 | 0.000 | 0.176 | 0.000 | 0.000 | 0.365 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 49 | 133 | 0 | 204 | 0 | 0 | 207 | 0 |
N.S. |
1 | 1.00 | 1.07 | 2.89 | 0.00 | 4.43 | 0.00 | 0.00 | 4.50 | 0.00 |
time (sec) |
N/A | 0.433 | 1.877 | 1.702 | 0.000 | 0.141 | 0.000 | 0.000 | 0.352 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 47 | 130 | 0 | 46 | 0 | 0 | 196 | 0 |
N.S. |
1 | 1.00 | 1.07 | 2.95 | 0.00 | 1.05 | 0.00 | 0.00 | 4.45 | 0.00 |
time (sec) |
N/A | 0.406 | 1.822 | 1.704 | 0.000 | 0.171 | 0.000 | 0.000 | 0.558 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 51 | 134 | 0 | 54 | 0 | 0 | 188 | 0 |
N.S. |
1 | 1.00 | 1.16 | 3.05 | 0.00 | 1.23 | 0.00 | 0.00 | 4.27 | 0.00 |
time (sec) |
N/A | 0.400 | 1.846 | 1.701 | 0.000 | 0.114 | 0.000 | 0.000 | 0.357 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 84 | 0 | 0 | 1240 | 0 | 0 | 583 | 0 |
N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 17.97 | 0.00 | 0.00 | 8.45 | 0.00 |
time (sec) |
N/A | 0.562 | 7.471 | 0.000 | 0.000 | 0.967 | 0.000 | 0.000 | 0.536 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 84 | 0 | 0 | 1294 | 0 | 0 | 599 | 0 |
N.S. |
1 | 1.00 | 1.18 | 0.00 | 0.00 | 18.23 | 0.00 | 0.00 | 8.44 | 0.00 |
time (sec) |
N/A | 0.560 | 7.591 | 0.000 | 0.000 | 0.990 | 0.000 | 0.000 | 0.548 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 85 | 0 | 0 | 1245 | 0 | 0 | 608 | 0 |
N.S. |
1 | 1.00 | 1.18 | 0.00 | 0.00 | 17.29 | 0.00 | 0.00 | 8.44 | 0.00 |
time (sec) |
N/A | 0.546 | 7.506 | 0.000 | 0.000 | 0.908 | 0.000 | 0.000 | 0.544 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 87 | 0 | 0 | 1303 | 0 | 0 | 586 | 0 |
N.S. |
1 | 1.00 | 1.21 | 0.00 | 0.00 | 18.10 | 0.00 | 0.00 | 8.14 | 0.00 |
time (sec) |
N/A | 0.512 | 7.451 | 0.000 | 0.000 | 0.936 | 0.000 | 0.000 | 0.517 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 663 | 0 | 0 | 1273 | 0 | 0 | 583 | 0 |
N.S. |
1 | 1.00 | 9.08 | 0.00 | 0.00 | 17.44 | 0.00 | 0.00 | 7.99 | 0.00 |
time (sec) |
N/A | 0.564 | 10.912 | 0.000 | 0.000 | 0.574 | 0.000 | 0.000 | 0.527 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 648 | 0 | 0 | 1330 | 0 | 0 | 599 | 0 |
N.S. |
1 | 1.00 | 8.64 | 0.00 | 0.00 | 17.73 | 0.00 | 0.00 | 7.99 | 0.00 |
time (sec) |
N/A | 0.584 | 10.930 | 0.000 | 0.000 | 0.535 | 0.000 | 0.000 | 0.641 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 649 | 0 | 0 | 1278 | 0 | 0 | 608 | 0 |
N.S. |
1 | 1.00 | 8.54 | 0.00 | 0.00 | 16.82 | 0.00 | 0.00 | 8.00 | 0.00 |
time (sec) |
N/A | 0.574 | 10.871 | 0.000 | 0.000 | 0.564 | 0.000 | 0.000 | 0.853 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 666 | 0 | 0 | 1339 | 0 | 0 | 586 | 0 |
N.S. |
1 | 1.00 | 8.76 | 0.00 | 0.00 | 17.62 | 0.00 | 0.00 | 7.71 | 0.00 |
time (sec) |
N/A | 0.562 | 10.987 | 0.000 | 0.000 | 0.532 | 0.000 | 0.000 | 0.864 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 49 | 132 | 0 | 46 | 0 | 0 | 186 | 0 |
N.S. |
1 | 1.00 | 1.17 | 3.14 | 0.00 | 1.10 | 0.00 | 0.00 | 4.43 | 0.00 |
time (sec) |
N/A | 0.397 | 1.909 | 1.658 | 0.000 | 0.157 | 0.000 | 0.000 | 0.545 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 49 | 135 | 0 | 54 | 0 | 0 | 207 | 0 |
N.S. |
1 | 1.00 | 1.07 | 2.93 | 0.00 | 1.17 | 0.00 | 0.00 | 4.50 | 0.00 |
time (sec) |
N/A | 0.410 | 1.859 | 1.660 | 0.000 | 0.113 | 0.000 | 0.000 | 0.490 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 47 | 132 | 0 | 202 | 0 | 0 | 196 | 0 |
N.S. |
1 | 1.00 | 1.07 | 3.00 | 0.00 | 4.59 | 0.00 | 0.00 | 4.45 | 0.00 |
time (sec) |
N/A | 0.398 | 1.850 | 1.592 | 0.000 | 0.138 | 0.000 | 0.000 | 0.753 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 51 | 136 | 0 | 204 | 0 | 0 | 188 | 0 |
N.S. |
1 | 1.00 | 1.16 | 3.09 | 0.00 | 4.64 | 0.00 | 0.00 | 4.27 | 0.00 |
time (sec) |
N/A | 0.390 | 1.898 | 1.565 | 0.000 | 0.127 | 0.000 | 0.000 | 0.352 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 84 | 0 | 0 | 1236 | 0 | 0 | 583 | 0 |
N.S. |
1 | 1.00 | 1.22 | 0.00 | 0.00 | 17.91 | 0.00 | 0.00 | 8.45 | 0.00 |
time (sec) |
N/A | 0.521 | 7.946 | 0.000 | 0.000 | 0.987 | 0.000 | 0.000 | 0.540 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 84 | 0 | 0 | 1288 | 0 | 0 | 599 | 0 |
N.S. |
1 | 1.00 | 1.18 | 0.00 | 0.00 | 18.14 | 0.00 | 0.00 | 8.44 | 0.00 |
time (sec) |
N/A | 0.542 | 7.631 | 0.000 | 0.000 | 0.869 | 0.000 | 0.000 | 0.533 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 85 | 0 | 0 | 1239 | 0 | 0 | 608 | 0 |
N.S. |
1 | 1.00 | 1.18 | 0.00 | 0.00 | 17.21 | 0.00 | 0.00 | 8.44 | 0.00 |
time (sec) |
N/A | 0.545 | 7.694 | 0.000 | 0.000 | 0.911 | 0.000 | 0.000 | 0.532 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 87 | 0 | 0 | 1299 | 0 | 0 | 586 | 0 |
N.S. |
1 | 1.00 | 1.21 | 0.00 | 0.00 | 18.04 | 0.00 | 0.00 | 8.14 | 0.00 |
time (sec) |
N/A | 0.515 | 7.930 | 0.000 | 0.000 | 0.909 | 0.000 | 0.000 | 0.521 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 667 | 0 | 0 | 1270 | 0 | 0 | 583 | 0 |
N.S. |
1 | 1.00 | 9.14 | 0.00 | 0.00 | 17.40 | 0.00 | 0.00 | 7.99 | 0.00 |
time (sec) |
N/A | 0.526 | 10.875 | 0.000 | 0.000 | 0.545 | 0.000 | 0.000 | 0.529 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 649 | 0 | 0 | 1324 | 0 | 0 | 599 | 0 |
N.S. |
1 | 1.00 | 8.65 | 0.00 | 0.00 | 17.65 | 0.00 | 0.00 | 7.99 | 0.00 |
time (sec) |
N/A | 0.566 | 11.016 | 0.000 | 0.000 | 0.540 | 0.000 | 0.000 | 0.544 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 650 | 0 | 0 | 1273 | 0 | 0 | 608 | 0 |
N.S. |
1 | 1.00 | 8.55 | 0.00 | 0.00 | 16.75 | 0.00 | 0.00 | 8.00 | 0.00 |
time (sec) |
N/A | 0.559 | 10.964 | 0.000 | 0.000 | 0.536 | 0.000 | 0.000 | 0.570 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 670 | 0 | 0 | 1335 | 0 | 0 | 586 | 0 |
N.S. |
1 | 1.00 | 8.82 | 0.00 | 0.00 | 17.57 | 0.00 | 0.00 | 7.71 | 0.00 |
time (sec) |
N/A | 0.551 | 10.846 | 0.000 | 0.000 | 0.522 | 0.000 | 0.000 | 0.567 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 269 | 245 | 0 | 51 | 0 | 0 | 96 | 0 |
N.S. |
1 | 1.00 | 1.86 | 1.69 | 0.00 | 0.35 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.661 | 20.653 | 1.553 | 0.000 | 0.108 | 0.000 | 0.000 | 0.353 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 267 | 245 | 0 | 207 | 0 | 0 | 96 | 0 |
N.S. |
1 | 1.00 | 1.84 | 1.69 | 0.00 | 1.43 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.697 | 20.405 | 1.648 | 0.000 | 0.117 | 0.000 | 0.000 | 0.353 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 173 | 291 | 260 | 0 | 716 | 0 | 0 | 226 | 0 |
N.S. |
1 | 1.00 | 1.68 | 1.50 | 0.00 | 4.14 | 0.00 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.741 | 20.532 | 1.081 | 0.000 | 0.247 | 0.000 | 0.000 | 0.466 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 184 | 291 | 259 | 0 | 735 | 0 | 0 | 252 | 0 |
N.S. |
1 | 0.98 | 1.56 | 1.39 | 0.00 | 3.93 | 0.00 | 0.00 | 1.35 | 0.00 |
time (sec) |
N/A | 0.809 | 20.608 | 1.027 | 0.000 | 0.374 | 0.000 | 0.000 | 0.692 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 187 | 289 | 257 | 0 | 723 | 0 | 0 | 240 | 0 |
N.S. |
1 | 0.98 | 1.52 | 1.35 | 0.00 | 3.81 | 0.00 | 0.00 | 1.26 | 0.00 |
time (sec) |
N/A | 0.775 | 20.592 | 1.109 | 0.000 | 0.240 | 0.000 | 0.000 | 0.912 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 183 | 293 | 258 | 0 | 724 | 0 | 0 | 231 | 0 |
N.S. |
1 | 1.00 | 1.60 | 1.41 | 0.00 | 3.96 | 0.00 | 0.00 | 1.26 | 0.00 |
time (sec) |
N/A | 0.769 | 20.482 | 1.066 | 0.000 | 0.165 | 0.000 | 0.000 | 0.608 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 332 | 332 | 456 | 0 | 0 | 7008 | 0 | 0 | 879 | 0 |
N.S. |
1 | 1.00 | 1.37 | 0.00 | 0.00 | 21.11 | 0.00 | 0.00 | 2.65 | 0.00 |
time (sec) |
N/A | 1.224 | 11.587 | 0.000 | 0.000 | 26.410 | 0.000 | 0.000 | 1.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 336 | 336 | 466 | 0 | 0 | 7063 | 0 | 0 | 905 | 0 |
N.S. |
1 | 1.00 | 1.39 | 0.00 | 0.00 | 21.02 | 0.00 | 0.00 | 2.69 | 0.00 |
time (sec) |
N/A | 1.261 | 11.989 | 0.000 | 0.000 | 26.893 | 0.000 | 0.000 | 0.985 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 345 | 345 | 467 | 0 | 0 | 7009 | 0 | 0 | 917 | 0 |
N.S. |
1 | 1.00 | 1.35 | 0.00 | 0.00 | 20.32 | 0.00 | 0.00 | 2.66 | 0.00 |
time (sec) |
N/A | 1.230 | 11.382 | 0.000 | 0.000 | 27.382 | 0.000 | 0.000 | 0.798 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 345 | 345 | 459 | 0 | 0 | 7078 | 0 | 0 | 885 | 0 |
N.S. |
1 | 1.00 | 1.33 | 0.00 | 0.00 | 20.52 | 0.00 | 0.00 | 2.57 | 0.00 |
time (sec) |
N/A | 1.216 | 11.592 | 0.000 | 0.000 | 26.860 | 0.000 | 0.000 | 0.806 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 177 | 209 | 255 | 0 | 58 | 0 | 0 | 115 | 0 |
N.S. |
1 | 1.30 | 1.54 | 1.88 | 0.00 | 0.43 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.728 | 10.425 | 1.623 | 0.000 | 0.116 | 0.000 | 0.000 | 0.339 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 193 | 232 | 255 | 0 | 69 | 0 | 0 | 128 | 0 |
N.S. |
1 | 1.27 | 1.53 | 1.68 | 0.00 | 0.45 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.803 | 10.587 | 1.559 | 0.000 | 0.138 | 0.000 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 187 | 230 | 253 | 0 | 213 | 0 | 0 | 122 | 0 |
N.S. |
1 | 1.14 | 1.40 | 1.54 | 0.00 | 1.30 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.795 | 10.912 | 1.588 | 0.000 | 0.152 | 0.000 | 0.000 | 0.456 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 179 | 211 | 253 | 0 | 217 | 0 | 0 | 118 | 0 |
N.S. |
1 | 1.15 | 1.35 | 1.62 | 0.00 | 1.39 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.787 | 10.660 | 1.503 | 0.000 | 0.157 | 0.000 | 0.000 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 164 | 225 | 253 | 0 | 214 | 0 | 0 | 115 | 0 |
N.S. |
1 | 1.12 | 1.53 | 1.72 | 0.00 | 1.46 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.771 | 10.939 | 1.612 | 0.000 | 0.139 | 0.000 | 0.000 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 295 | 445 | 0 | 0 | 1288 | 0 | 0 | 436 | 0 |
N.S. |
1 | 1.06 | 1.60 | 0.00 | 0.00 | 4.63 | 0.00 | 0.00 | 1.57 | 0.00 |
time (sec) |
N/A | 1.158 | 11.992 | 0.000 | 0.000 | 0.967 | 0.000 | 0.000 | 0.460 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 286 | 303 | 454 | 0 | 0 | 1354 | 0 | 0 | 449 | 0 |
N.S. |
1 | 1.06 | 1.59 | 0.00 | 0.00 | 4.73 | 0.00 | 0.00 | 1.57 | 0.00 |
time (sec) |
N/A | 1.185 | 11.673 | 0.000 | 0.000 | 0.859 | 0.000 | 0.000 | 0.452 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 282 | 319 | 455 | 0 | 0 | 1295 | 0 | 0 | 455 | 0 |
N.S. |
1 | 1.13 | 1.61 | 0.00 | 0.00 | 4.59 | 0.00 | 0.00 | 1.61 | 0.00 |
time (sec) |
N/A | 1.231 | 11.646 | 0.000 | 0.000 | 0.891 | 0.000 | 0.000 | 0.453 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 315 | 448 | 0 | 0 | 1348 | 0 | 0 | 440 | 0 |
N.S. |
1 | 1.13 | 1.61 | 0.00 | 0.00 | 4.85 | 0.00 | 0.00 | 1.58 | 0.00 |
time (sec) |
N/A | 1.216 | 11.981 | 0.000 | 0.000 | 0.878 | 0.000 | 0.000 | 0.454 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 317 | 297 | 214 | 275 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.94 | 0.68 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.845 | 10.807 | 0.515 | 0.000 | 0.000 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 329 | 302 | 235 | 264 | 0 | 0 | 0 | 0 | 101 | 0 |
N.S. |
1 | 0.92 | 0.71 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 1.766 | 10.892 | 0.562 | 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 | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 325 | 300 | 233 | 273 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.92 | 0.72 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.544 | 10.240 | 0.521 | 0.000 | 0.000 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 321 | 299 | 233 | 266 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.93 | 0.73 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.672 | 10.873 | 0.498 | 0.000 | 0.000 | 0.000 | 0.000 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 358 | 309 | 213 | 275 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.86 | 0.59 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.702 | 10.694 | 0.475 | 0.000 | 0.000 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 346 | 301 | 235 | 268 | 0 | 0 | 0 | 0 | 100 | 0 |
N.S. |
1 | 0.87 | 0.68 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.661 | 10.827 | 0.429 | 0.000 | 0.000 | 0.000 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-1) | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 342 | 299 | 233 | 277 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 0.87 | 0.68 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.474 | 10.232 | 0.451 | 0.000 | 0.000 | 0.000 | 0.000 | 200.037 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 362 | 311 | 233 | 266 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 0.86 | 0.64 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.670 | 10.779 | 0.428 | 0.000 | 0.000 | 0.000 | 0.000 | 200.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 39 | 90 | 0 | 33 | 56 | 0 | 65 | 334 |
N.S. |
1 | 1.00 | 0.31 | 0.72 | 0.00 | 0.26 | 0.45 | 0.00 | 0.52 | 2.67 |
time (sec) |
N/A | 0.448 | 10.040 | 0.515 | 0.000 | 0.134 | 2.482 | 0.000 | 0.145 | 0.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 40 | 101 | 0 | 36 | 99 | 0 | 75 | 373 |
N.S. |
1 | 1.00 | 0.29 | 0.73 | 0.00 | 0.26 | 0.71 | 0.00 | 0.54 | 2.68 |
time (sec) |
N/A | 0.464 | 10.042 | 0.507 | 0.000 | 0.156 | 4.144 | 0.000 | 0.158 | 23.410 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 142 | 58 | 132 | 0 | 52 | 94 | 0 | 85 | 334 |
N.S. |
1 | 1.00 | 0.41 | 0.93 | 0.00 | 0.37 | 0.66 | 0.00 | 0.60 | 2.35 |
time (sec) |
N/A | 0.467 | 10.057 | 0.843 | 0.000 | 0.132 | 4.273 | 0.000 | 0.146 | 0.106 |