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 | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 203 | 55 | 429 | 0 | 422 | 0 | 0 | 63 | 44 |
N.S. |
1 | 1.35 | 0.37 | 2.86 | 0.00 | 2.81 | 0.00 | 0.00 | 0.42 | 0.29 |
time (sec) |
N/A | 0.441 | 0.040 | 1.570 | 0.000 | 0.161 | 0.000 | 0.000 | 0.164 | 26.475 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 205 | 57 | 431 | 0 | 475 | 0 | 0 | 33 | 44 |
N.S. |
1 | 1.34 | 0.37 | 2.82 | 0.00 | 3.10 | 0.00 | 0.00 | 0.22 | 0.29 |
time (sec) |
N/A | 0.431 | 0.041 | 1.004 | 0.000 | 0.170 | 0.000 | 0.000 | 0.156 | 26.873 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 230 | 57 | 460 | 0 | 525 | 0 | 0 | 98 | 44 |
N.S. |
1 | 1.29 | 0.32 | 2.58 | 0.00 | 2.95 | 0.00 | 0.00 | 0.55 | 0.25 |
time (sec) |
N/A | 0.544 | 0.049 | 1.033 | 0.000 | 0.186 | 0.000 | 0.000 | 0.156 | 26.792 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.213 | 0.065 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.212 | 0.050 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.189 | 0.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.205 | 0.050 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 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 | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.206 | 0.046 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 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 | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.220 | 0.064 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 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 | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.219 | 0.062 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.191 | 0.051 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 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 | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.222 | 0.060 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 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 | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.218 | 0.060 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 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 | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.215 | 0.060 | 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 | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.214 | 0.054 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.187 | 0.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.214 | 0.054 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.212 | 0.049 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 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 | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.224 | 0.055 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.223 | 0.053 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.190 | 0.042 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.219 | 0.050 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-1) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.218 | 0.046 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 73 | 57 | 0 | 0 | 144 | 0 | 0 | 19 | 44 |
N.S. |
1 | 0.57 | 0.45 | 0.00 | 0.00 | 1.12 | 0.00 | 0.00 | 0.15 | 0.34 |
time (sec) |
N/A | 0.297 | 0.049 | 0.000 | 0.000 | 0.134 | 0.000 | 0.000 | 0.169 | 26.631 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 221 | 57 | 0 | 0 | 267 | 0 | 0 | 19 | 44 |
N.S. |
1 | 1.36 | 0.35 | 0.00 | 0.00 | 1.64 | 0.00 | 0.00 | 0.12 | 0.27 |
time (sec) |
N/A | 0.368 | 0.049 | 0.000 | 0.000 | 0.112 | 0.000 | 0.000 | 0.177 | 26.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 247 | 57 | 0 | 0 | 322 | 0 | 0 | 19 | 44 |
N.S. |
1 | 1.31 | 0.30 | 0.00 | 0.00 | 1.71 | 0.00 | 0.00 | 0.10 | 0.23 |
time (sec) |
N/A | 0.450 | 0.062 | 0.000 | 0.000 | 0.129 | 0.000 | 0.000 | 0.164 | 26.997 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 101 | 57 | 0 | 0 | 197 | 0 | 0 | 19 | 44 |
N.S. |
1 | 0.65 | 0.37 | 0.00 | 0.00 | 1.27 | 0.00 | 0.00 | 0.12 | 0.28 |
time (sec) |
N/A | 0.393 | 0.063 | 0.000 | 0.000 | 0.110 | 0.000 | 0.000 | 0.167 | 26.546 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 101 | 57 | 0 | 0 | 195 | 0 | 0 | 19 | 44 |
N.S. |
1 | 0.65 | 0.37 | 0.00 | 0.00 | 1.26 | 0.00 | 0.00 | 0.12 | 0.28 |
time (sec) |
N/A | 0.389 | 0.057 | 0.000 | 0.000 | 0.097 | 0.000 | 0.000 | 0.162 | 27.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 73 | 57 | 0 | 0 | 152 | 0 | 0 | 19 | 44 |
N.S. |
1 | 0.57 | 0.45 | 0.00 | 0.00 | 1.19 | 0.00 | 0.00 | 0.15 | 0.34 |
time (sec) |
N/A | 0.300 | 0.034 | 0.000 | 0.000 | 0.093 | 0.000 | 0.000 | 0.167 | 26.885 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 221 | 55 | 0 | 0 | 266 | 0 | 0 | 19 | 44 |
N.S. |
1 | 1.35 | 0.34 | 0.00 | 0.00 | 1.62 | 0.00 | 0.00 | 0.12 | 0.27 |
time (sec) |
N/A | 0.343 | 0.032 | 0.000 | 0.000 | 0.096 | 0.000 | 0.000 | 0.174 | 26.535 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 247 | 55 | 0 | 0 | 323 | 0 | 0 | 19 | 44 |
N.S. |
1 | 1.31 | 0.29 | 0.00 | 0.00 | 1.71 | 0.00 | 0.00 | 0.10 | 0.23 |
time (sec) |
N/A | 0.450 | 0.039 | 0.000 | 0.000 | 0.116 | 0.000 | 0.000 | 0.157 | 27.195 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 101 | 57 | 0 | 0 | 189 | 0 | 0 | 19 | 44 |
N.S. |
1 | 0.65 | 0.37 | 0.00 | 0.00 | 1.22 | 0.00 | 0.00 | 0.12 | 0.28 |
time (sec) |
N/A | 0.396 | 0.039 | 0.000 | 0.000 | 0.099 | 0.000 | 0.000 | 0.166 | 26.597 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F | B |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 101 | 57 | 0 | 0 | 219 | 0 | 0 | 19 | 44 |
N.S. |
1 | 0.65 | 0.37 | 0.00 | 0.00 | 1.41 | 0.00 | 0.00 | 0.12 | 0.28 |
time (sec) |
N/A | 0.398 | 0.040 | 0.000 | 0.000 | 0.099 | 0.000 | 0.000 | 0.175 | 27.459 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 0 | 0 | 18 | 0 | 0 | 11 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.12 | 0.00 | 0.00 | 0.69 | 0.62 |
time (sec) |
N/A | 0.182 | 0.015 | 0.000 | 0.000 | 0.080 | 0.000 | 0.000 | 0.162 | 26.198 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 0 | 0 | 10 | 0 | 0 | 11 | 94 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.62 | 0.00 | 0.00 | 0.69 | 5.88 |
time (sec) |
N/A | 0.183 | 0.020 | 0.000 | 0.000 | 0.069 | 0.000 | 0.000 | 0.178 | 26.227 |
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 | 80 | 80 | 79 | 0 | 0 | 0 | 0 | 0 | 19 | 71 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.89 |
time (sec) |
N/A | 0.239 | 0.119 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 27.764 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 82 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.246 | 0.131 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 85 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.238 | 0.084 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 85 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.244 | 0.105 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 69 | 55 | 87 | 77 | 70 | 2040 | 248 | 23 | 132 |
N.S. |
1 | 0.93 | 0.74 | 1.18 | 1.04 | 0.95 | 27.57 | 3.35 | 0.31 | 1.78 |
time (sec) |
N/A | 0.260 | 0.361 | 5.835 | 0.038 | 0.099 | 4.316 | 0.135 | 0.184 | 26.982 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 48 | 48 | 50 | 53 | 46 | 525 | 118 | 23 | 62 |
N.S. |
1 | 0.96 | 0.96 | 1.00 | 1.06 | 0.92 | 10.50 | 2.36 | 0.46 | 1.24 |
time (sec) |
N/A | 0.244 | 0.097 | 3.721 | 0.036 | 0.090 | 1.212 | 0.123 | 0.169 | 26.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 25 | 25 | 24 | 24 | 56 | 24 | 26 | 25 |
N.S. |
1 | 1.00 | 1.04 | 1.04 | 1.00 | 1.00 | 2.33 | 1.00 | 1.08 | 1.04 |
time (sec) |
N/A | 0.193 | 0.011 | 8.793 | 0.032 | 0.084 | 0.344 | 0.124 | 0.232 | 25.847 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 51 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.221 | 0.027 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 51 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.229 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 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 | 68 | 68 | 63 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.236 | 0.063 | 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 | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 63 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.243 | 0.057 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 63 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.206 | 0.048 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 63 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.225 | 0.056 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 63 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.224 | 0.052 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 78 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.241 | 0.159 | 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 | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 75 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.235 | 0.077 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 75 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.234 | 0.081 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 78 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.244 | 0.103 | 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 | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 78 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.238 | 0.100 | 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 | A | A | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 70 | 83 | 87 | 78 | 84 | 2451 | 249 | 23 | 132 |
N.S. |
1 | 0.92 | 1.09 | 1.14 | 1.03 | 1.11 | 32.25 | 3.28 | 0.30 | 1.74 |
time (sec) |
N/A | 0.253 | 0.696 | 6.385 | 0.038 | 0.082 | 4.448 | 0.133 | 0.190 | 26.891 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 49 | 50 | 52 | 52 | 50 | 688 | 117 | 23 | 65 |
N.S. |
1 | 0.98 | 1.00 | 1.04 | 1.04 | 1.00 | 13.76 | 2.34 | 0.46 | 1.30 |
time (sec) |
N/A | 0.242 | 0.399 | 3.116 | 0.036 | 0.102 | 1.251 | 0.127 | 0.241 | 0.510 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 26 | 26 | 25 | 25 | 60 | 25 | 27 | 26 |
N.S. |
1 | 1.00 | 1.04 | 1.04 | 1.00 | 1.00 | 2.40 | 1.00 | 1.08 | 1.04 |
time (sec) |
N/A | 0.195 | 0.013 | 6.727 | 0.026 | 0.080 | 0.346 | 0.117 | 0.156 | 0.182 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 52 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.220 | 0.305 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 154 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 3.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.232 | 1.525 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 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 | 49 | 49 | 244 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 4.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.227 | 2.086 | 0.000 | 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 | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 68 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.231 | 0.496 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 68 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.226 | 0.318 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 64 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.204 | 0.056 | 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 | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 80 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.225 | 0.583 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 82 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.224 | 0.523 | 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 | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 158 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 2.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.242 | 0.962 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 76 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.237 | 0.578 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 82 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.232 | 0.498 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 82 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.08 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.233 | 0.658 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 79 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.243 | 0.647 | 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 | A | B | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 78 | 58 | 265 | 63 | 56 | 0 | 100 | 21 | 0 |
N.S. |
1 | 0.92 | 0.68 | 3.12 | 0.74 | 0.66 | 0.00 | 1.18 | 0.25 | 0.00 |
time (sec) |
N/A | 0.252 | 0.921 | 12.404 | 0.036 | 0.100 | 0.000 | 0.134 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 58 | 48 | 253 | 50 | 46 | 0 | 77 | 21 | 0 |
N.S. |
1 | 0.92 | 0.76 | 4.02 | 0.79 | 0.73 | 0.00 | 1.22 | 0.33 | 0.00 |
time (sec) |
N/A | 0.241 | 0.548 | 1.174 | 0.034 | 0.078 | 0.000 | 0.134 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 40 | 36 | 243 | 35 | 34 | 0 | 53 | 21 | 0 |
N.S. |
1 | 0.98 | 0.88 | 5.93 | 0.85 | 0.83 | 0.00 | 1.29 | 0.51 | 0.00 |
time (sec) |
N/A | 0.234 | 0.482 | 1.418 | 0.035 | 0.075 | 0.000 | 0.133 | 0.167 | 0.000 |
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 | 18 | 18 | 18 | 17 | 23 | 23 | 0 | 22 | 19 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 1.28 | 1.28 | 0.00 | 1.22 | 1.06 | 1.28 |
time (sec) |
N/A | 0.197 | 0.196 | 1.631 | 0.032 | 0.094 | 0.000 | 0.133 | 0.180 | 0.219 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 51 | 73 | 151 | 72 | 265 | 0 | 61 | 19 | 0 |
N.S. |
1 | 0.88 | 1.26 | 2.60 | 1.24 | 4.57 | 0.00 | 1.05 | 0.33 | 0.00 |
time (sec) |
N/A | 0.234 | 0.474 | 2.838 | 0.113 | 0.141 | 0.000 | 0.134 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 90 | 95 | 462 | 106 | 373 | 0 | 98 | 21 | 0 |
N.S. |
1 | 0.97 | 1.02 | 4.97 | 1.14 | 4.01 | 0.00 | 1.05 | 0.23 | 0.00 |
time (sec) |
N/A | 0.267 | 0.920 | 3.157 | 0.112 | 0.144 | 0.000 | 0.133 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 131 | 107 | 309 | 138 | 457 | 0 | 127 | 21 | 0 |
N.S. |
1 | 1.07 | 0.87 | 2.51 | 1.12 | 3.72 | 0.00 | 1.03 | 0.17 | 0.00 |
time (sec) |
N/A | 0.481 | 1.251 | 2.805 | 0.112 | 0.144 | 0.000 | 0.134 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 133 | 73 | 117 | 0 | 106 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.08 | 0.59 | 0.95 | 0.00 | 0.86 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 1.076 | 0.554 | 12.168 | 0.000 | 0.093 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 100 | 61 | 105 | 0 | 94 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.05 | 0.64 | 1.11 | 0.00 | 0.99 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.768 | 0.443 | 4.645 | 0.000 | 0.111 | 0.000 | 0.000 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 51 | 96 | 0 | 83 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.76 | 1.43 | 0.00 | 1.24 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.559 | 0.371 | 2.477 | 0.000 | 0.107 | 0.000 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 77 | 0 | 57 | 0 | 0 | 12 | 35 |
N.S. |
1 | 1.00 | 1.00 | 2.03 | 0.00 | 1.50 | 0.00 | 0.00 | 0.32 | 0.92 |
time (sec) |
N/A | 0.392 | 0.060 | 2.174 | 0.000 | 0.087 | 0.000 | 0.000 | 0.171 | 0.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 47 | 87 | 0 | 98 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.76 | 1.40 | 0.00 | 1.58 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.565 | 0.463 | 3.028 | 0.000 | 0.089 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 63 | 105 | 0 | 148 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.66 | 1.11 | 0.00 | 1.56 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.780 | 0.561 | 3.582 | 0.000 | 0.094 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 128 | 73 | 117 | 0 | 187 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.04 | 0.59 | 0.95 | 0.00 | 1.52 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 1.037 | 0.972 | 4.845 | 0.000 | 0.131 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 76 | 52 | 255 | 72 | 54 | 0 | 98 | 28 | 0 |
N.S. |
1 | 0.92 | 0.63 | 3.07 | 0.87 | 0.65 | 0.00 | 1.18 | 0.34 | 0.00 |
time (sec) |
N/A | 0.416 | 0.648 | 6.644 | 0.035 | 0.093 | 0.000 | 0.138 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 58 | 42 | 247 | 55 | 43 | 0 | 75 | 28 | 0 |
N.S. |
1 | 0.92 | 0.67 | 3.92 | 0.87 | 0.68 | 0.00 | 1.19 | 0.44 | 0.00 |
time (sec) |
N/A | 0.405 | 0.412 | 1.372 | 0.035 | 0.079 | 0.000 | 0.141 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 40 | 30 | 236 | 37 | 31 | 0 | 46 | 28 | 0 |
N.S. |
1 | 0.98 | 0.73 | 5.76 | 0.90 | 0.76 | 0.00 | 1.12 | 0.68 | 0.00 |
time (sec) |
N/A | 0.396 | 0.375 | 1.302 | 0.036 | 0.108 | 0.000 | 0.132 | 0.199 | 0.000 |
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 | 18 | 18 | 18 | 17 | 23 | 18 | 0 | 25 | 26 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 1.28 | 1.00 | 0.00 | 1.39 | 1.44 | 1.00 |
time (sec) |
N/A | 0.319 | 0.179 | 0.465 | 0.034 | 0.092 | 0.000 | 0.133 | 0.200 | 25.890 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 71 | 85 | 208 | 87 | 298 | 0 | 75 | 26 | 0 |
N.S. |
1 | 0.92 | 1.10 | 2.70 | 1.13 | 3.87 | 0.00 | 0.97 | 0.34 | 0.00 |
time (sec) |
N/A | 0.415 | 0.528 | 2.175 | 0.117 | 0.121 | 0.000 | 0.134 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F(-1) | A | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 110 | 97 | 295 | 123 | 407 | 0 | 127 | 28 | 0 |
N.S. |
1 | 0.97 | 0.86 | 2.61 | 1.09 | 3.60 | 0.00 | 1.12 | 0.25 | 0.00 |
time (sec) |
N/A | 0.459 | 1.111 | 2.335 | 0.120 | 0.147 | 0.000 | 0.136 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 132 | 70 | 229 | 0 | 108 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.03 | 0.55 | 1.79 | 0.00 | 0.84 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.137 | 0.687 | 7.043 | 0.000 | 0.100 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 99 | 60 | 213 | 0 | 98 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.01 | 0.61 | 2.17 | 0.00 | 1.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.778 | 0.484 | 4.794 | 0.000 | 0.093 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 48 | 193 | 0 | 85 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 0.73 | 2.92 | 0.00 | 1.29 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.574 | 0.349 | 2.537 | 0.000 | 0.093 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 48 | 184 | 0 | 84 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.73 | 2.79 | 0.00 | 1.27 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.533 | 0.086 | 2.197 | 0.000 | 0.121 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 95 | 57 | 159 | 0 | 113 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.06 | 0.63 | 1.77 | 0.00 | 1.26 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.746 | 0.498 | 3.041 | 0.000 | 0.088 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 128 | 77 | 169 | 0 | 167 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.03 | 0.62 | 1.36 | 0.00 | 1.35 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.010 | 0.639 | 4.049 | 0.000 | 0.112 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 78 | 52 | 264 | 66 | 70 | 0 | 100 | 32 | 0 |
N.S. |
1 | 0.92 | 0.61 | 3.11 | 0.78 | 0.82 | 0.00 | 1.18 | 0.38 | 0.00 |
time (sec) |
N/A | 0.412 | 1.098 | 5.460 | 0.037 | 0.101 | 0.000 | 0.138 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 58 | 42 | 254 | 52 | 57 | 0 | 74 | 32 | 0 |
N.S. |
1 | 0.92 | 0.67 | 4.03 | 0.83 | 0.90 | 0.00 | 1.17 | 0.51 | 0.00 |
time (sec) |
N/A | 0.396 | 0.774 | 1.862 | 0.061 | 0.121 | 0.000 | 0.134 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 40 | 32 | 260 | 36 | 42 | 0 | 49 | 32 | 50 |
N.S. |
1 | 0.98 | 0.78 | 6.34 | 0.88 | 1.02 | 0.00 | 1.20 | 0.78 | 1.22 |
time (sec) |
N/A | 0.393 | 0.529 | 50.892 | 0.035 | 0.099 | 0.000 | 0.128 | 0.197 | 26.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 17 | 23 | 28 | 0 | 33 | 30 | 39 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 1.15 | 1.40 | 0.00 | 1.65 | 1.50 | 1.95 |
time (sec) |
N/A | 0.332 | 0.160 | 3.941 | 0.039 | 0.079 | 0.000 | 0.140 | 0.204 | 25.995 |