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 | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 201 | 99 | 0 | 0 | 161 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.04 | 0.51 | 0.00 | 0.00 | 0.83 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.620 | 0.045 | 0.000 | 0.000 | 0.083 | 0.000 | 0.000 | 200.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 282 | 116 | 0 | 0 | 266 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.14 | 0.47 | 0.00 | 0.00 | 1.07 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.866 | 0.141 | 0.000 | 0.000 | 0.083 | 0.000 | 0.000 | 200.025 | 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 | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 271 | 62 | 0 | 0 | 258 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.22 | 0.28 | 0.00 | 0.00 | 1.16 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.814 | 0.037 | 0.000 | 0.000 | 0.086 | 0.000 | 0.000 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 239 | 55 | 0 | 0 | 249 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.22 | 0.28 | 0.00 | 0.00 | 1.27 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.731 | 0.026 | 0.000 | 0.000 | 0.087 | 0.000 | 0.000 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 205 | 35 | 0 | 0 | 243 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.28 | 0.22 | 0.00 | 0.00 | 1.52 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.690 | 0.054 | 0.000 | 0.000 | 0.085 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 232 | 83 | 0 | 0 | 282 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.34 | 0.48 | 0.00 | 0.00 | 1.63 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.785 | 0.035 | 0.000 | 0.000 | 0.080 | 0.000 | 0.000 | 200.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 79 | 55 | 0 | 0 | 130 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.10 | 0.76 | 0.00 | 0.00 | 1.81 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.409 | 0.022 | 0.000 | 0.000 | 0.083 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 111 | 69 | 0 | 0 | 148 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.01 | 0.63 | 0.00 | 0.00 | 1.35 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.448 | 0.028 | 0.000 | 0.000 | 0.083 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 143 | 78 | 0 | 0 | 157 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.03 | 0.56 | 0.00 | 0.00 | 1.13 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.521 | 0.030 | 0.000 | 0.000 | 0.081 | 0.000 | 0.000 | 200.044 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 175 | 86 | 0 | 0 | 165 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.04 | 0.51 | 0.00 | 0.00 | 0.98 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.559 | 0.039 | 0.000 | 0.000 | 0.085 | 0.000 | 0.000 | 200.024 | 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 | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 282 | 116 | 0 | 0 | 262 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.14 | 0.47 | 0.00 | 0.00 | 1.06 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.862 | 0.143 | 0.000 | 0.000 | 0.084 | 0.000 | 0.000 | 200.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 222 | 271 | 62 | 0 | 0 | 254 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.22 | 0.28 | 0.00 | 0.00 | 1.14 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.808 | 0.038 | 0.000 | 0.000 | 0.080 | 0.000 | 0.000 | 200.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 239 | 56 | 0 | 0 | 246 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.22 | 0.29 | 0.00 | 0.00 | 1.26 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.757 | 0.027 | 0.000 | 0.000 | 0.084 | 0.000 | 0.000 | 200.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 205 | 150 | 0 | 0 | 237 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.27 | 0.93 | 0.00 | 0.00 | 1.47 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.674 | 0.259 | 0.000 | 0.000 | 0.083 | 0.000 | 0.000 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 232 | 83 | 0 | 0 | 282 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.33 | 0.48 | 0.00 | 0.00 | 1.62 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.773 | 0.037 | 0.000 | 0.000 | 0.081 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 79 | 55 | 0 | 0 | 124 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.08 | 0.75 | 0.00 | 0.00 | 1.70 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.397 | 0.020 | 0.000 | 0.000 | 0.084 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 111 | 70 | 0 | 0 | 145 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.01 | 0.64 | 0.00 | 0.00 | 1.32 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.432 | 0.030 | 0.000 | 0.000 | 0.081 | 0.000 | 0.000 | 200.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 143 | 78 | 0 | 0 | 153 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.03 | 0.56 | 0.00 | 0.00 | 1.10 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.516 | 0.031 | 0.000 | 0.000 | 0.084 | 0.000 | 0.000 | 200.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 173 | 86 | 0 | 0 | 161 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.03 | 0.51 | 0.00 | 0.00 | 0.96 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.560 | 0.039 | 0.000 | 0.000 | 0.088 | 0.000 | 0.000 | 200.029 | 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 | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 272 | 314 | 79 | 0 | 0 | 302 | 0 | 0 | 82 | 0 |
N.S. |
1 | 1.15 | 0.29 | 0.00 | 0.00 | 1.11 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.899 | 0.052 | 0.000 | 0.000 | 0.117 | 0.000 | 0.000 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 297 | 70 | 0 | 0 | 294 | 0 | 0 | 82 | 0 |
N.S. |
1 | 1.21 | 0.28 | 0.00 | 0.00 | 1.20 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.866 | 0.050 | 0.000 | 0.000 | 0.143 | 0.000 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 266 | 64 | 0 | 0 | 286 | 0 | 0 | 243 | 0 |
N.S. |
1 | 1.21 | 0.29 | 0.00 | 0.00 | 1.30 | 0.00 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 0.819 | 0.031 | 0.000 | 0.000 | 0.148 | 0.000 | 0.000 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 232 | 33 | 0 | 0 | 275 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.25 | 0.18 | 0.00 | 0.00 | 1.48 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.710 | 0.083 | 0.000 | 0.000 | 0.123 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 253 | 90 | 0 | 0 | 364 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.30 | 0.46 | 0.00 | 0.00 | 1.87 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.831 | 0.086 | 0.000 | 0.000 | 0.134 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 105 | 55 | 0 | 0 | 170 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.11 | 0.58 | 0.00 | 0.00 | 1.79 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.438 | 0.024 | 0.000 | 0.000 | 0.122 | 0.000 | 0.000 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 137 | 70 | 0 | 0 | 192 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.01 | 0.51 | 0.00 | 0.00 | 1.41 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.459 | 0.031 | 0.000 | 0.000 | 0.131 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 169 | 78 | 0 | 0 | 200 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.02 | 0.47 | 0.00 | 0.00 | 1.21 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.551 | 0.035 | 0.000 | 0.000 | 0.124 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 201 | 86 | 0 | 0 | 208 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.04 | 0.44 | 0.00 | 0.00 | 1.07 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.615 | 0.045 | 0.000 | 0.000 | 0.122 | 0.000 | 0.000 | 200.034 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 244 | 59 | 0 | 0 | 208 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.26 | 0.30 | 0.00 | 0.00 | 1.07 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.759 | 0.041 | 0.000 | 0.000 | 0.114 | 0.000 | 0.000 | 0.324 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 218 | 49 | 0 | 0 | 203 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.25 | 0.28 | 0.00 | 0.00 | 1.17 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.649 | 0.023 | 0.000 | 0.000 | 0.119 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 193 | 39 | 0 | 0 | 197 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.30 | 0.26 | 0.00 | 0.00 | 1.32 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.620 | 0.061 | 0.000 | 0.000 | 0.082 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 361 | 74 | 0 | 0 | 369 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.44 | 0.29 | 0.00 | 0.00 | 1.47 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.848 | 0.035 | 0.000 | 0.000 | 0.084 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 208 | 50 | 0 | 0 | 234 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.35 | 0.32 | 0.00 | 0.00 | 1.52 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.562 | 0.016 | 0.000 | 0.000 | 0.098 | 0.000 | 0.000 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 236 | 60 | 0 | 0 | 253 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.28 | 0.33 | 0.00 | 0.00 | 1.38 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.590 | 0.021 | 0.000 | 0.000 | 0.137 | 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(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 141 | 59 | 0 | 0 | 159 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.07 | 0.45 | 0.00 | 0.00 | 1.20 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.419 | 0.037 | 0.000 | 0.000 | 0.115 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 117 | 46 | 0 | 0 | 154 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.04 | 0.41 | 0.00 | 0.00 | 1.38 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.373 | 0.018 | 0.000 | 0.000 | 0.124 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 92 | 87 | 0 | 0 | 146 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.10 | 1.04 | 0.00 | 0.00 | 1.74 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.336 | 0.168 | 0.000 | 0.000 | 0.114 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 74 | 0 | 0 | 158 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.55 | 0.00 | 0.00 | 1.17 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.391 | 0.033 | 0.000 | 0.000 | 0.114 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 93 | 45 | 0 | 0 | 152 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.09 | 0.53 | 0.00 | 0.00 | 1.79 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.370 | 0.016 | 0.000 | 0.000 | 0.115 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 121 | 57 | 0 | 0 | 166 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.04 | 0.49 | 0.00 | 0.00 | 1.43 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.390 | 0.018 | 0.000 | 0.000 | 0.118 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | C | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 499 | 655 | 70 | 0 | 0 | 467 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.31 | 0.14 | 0.00 | 0.00 | 0.94 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.431 | 0.049 | 0.000 | 0.000 | 0.126 | 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 | C | F | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 473 | 623 | 56 | 0 | 0 | 459 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.32 | 0.12 | 0.00 | 0.00 | 0.97 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 1.325 | 0.025 | 0.000 | 0.000 | 0.137 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | C | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 445 | 589 | 48 | 0 | 0 | 419 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.32 | 0.11 | 0.00 | 0.00 | 0.94 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.260 | 0.071 | 0.000 | 0.000 | 0.129 | 0.000 | 0.000 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | C | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 560 | 820 | 83 | 0 | 0 | 577 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.46 | 0.15 | 0.00 | 0.00 | 1.03 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.834 | 0.046 | 0.000 | 0.000 | 0.145 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 284 | 58 | 0 | 0 | 318 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.33 | 0.27 | 0.00 | 0.00 | 1.49 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.713 | 0.021 | 0.000 | 0.000 | 0.141 | 0.000 | 0.000 | 200.032 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 316 | 73 | 0 | 0 | 355 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.25 | 0.29 | 0.00 | 0.00 | 1.40 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.761 | 0.026 | 0.000 | 0.000 | 0.112 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 50 | 511 | 0 | 0 | 0 | 0 | 494 | 0 |
N.S. |
1 | 1.00 | 0.83 | 8.52 | 0.00 | 0.00 | 0.00 | 0.00 | 8.23 | 0.00 |
time (sec) |
N/A | 0.410 | 0.032 | 0.293 | 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 | C | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 27 | 205 | 0 | 0 | 109 | 0 | 77 | 0 |
N.S. |
1 | 1.00 | 0.59 | 4.46 | 0.00 | 0.00 | 2.37 | 0.00 | 1.67 | 0.00 |
time (sec) |
N/A | 0.350 | 0.013 | 0.145 | 0.000 | 0.000 | 1.722 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 28 | 146 | 0 | 0 | 129 | 0 | 73 | 0 |
N.S. |
1 | 1.00 | 0.60 | 3.11 | 0.00 | 0.00 | 2.74 | 0.00 | 1.55 | 0.00 |
time (sec) |
N/A | 0.361 | 0.014 | 0.131 | 0.000 | 0.000 | 1.833 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 51 | 403 | 0 | 0 | 0 | 0 | 493 | 0 |
N.S. |
1 | 1.00 | 0.85 | 6.72 | 0.00 | 0.00 | 0.00 | 0.00 | 8.22 | 0.00 |
time (sec) |
N/A | 0.400 | 0.028 | 0.271 | 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 | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 172 | 93 | 149 | 0 | 0 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.35 | 0.73 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.993 | 0.125 | 0.092 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 71 | 71 | 0 | 0 | 102 | 0 | 46 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.85 | 0.00 | 0.00 | 1.21 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.433 | 0.068 | 0.079 | 0.000 | 0.000 | 1.641 | 0.000 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 32 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.417 | 0.053 | 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 | C | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 172 | 56 | 0 | 0 | 0 | 0 | 0 | 73 | 0 |
N.S. |
1 | 1.37 | 0.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.961 | 0.091 | 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 | 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 | 36 | 36 | 0 | 0 | 0 | 0 | 0 | 0 | 361 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 10.03 | 0.00 |
time (sec) |
N/A | 0.355 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 16.694 | 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 | 36 | 36 | 0 | 0 | 0 | 0 | 0 | 0 | 279 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 7.75 | 0.00 |
time (sec) |
N/A | 0.350 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.523 | 0.000 |
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 | 36 | 36 | 0 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.11 | 0.00 |
time (sec) |
N/A | 0.350 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.526 | 0.000 |
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 | 36 | 36 | 0 | 0 | 0 | 0 | 0 | 0 | 777 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 21.58 | 0.00 |
time (sec) |
N/A | 0.346 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.595 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 0 | 0 | 0 | 0 | 0 | 0 | 358 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 9.94 | 0.00 |
time (sec) |
N/A | 0.338 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.190 | 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 | 33 | 33 | 0 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.336 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 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 | 33 | 33 | 0 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.330 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.326 | 0.000 |
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 | 36 | 36 | 0 | 0 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.343 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.269 | 0.000 |
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 | 40 | 40 | 0 | 0 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.349 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 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 | 183 | 161 | 182 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 0.88 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.534 | 0.206 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.147 | 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 | 138 | 147 | 96 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.07 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.480 | 0.056 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 99 | 86 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.05 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.390 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 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 | 60 | 65 | 46 | 0 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.08 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.332 | 0.047 | 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 | 111 | 111 | 95 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.429 | 0.032 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.241 | 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 | 67 | 67 | 65 | 0 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.370 | 0.022 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 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 | 105 | 105 | 91 | 0 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.424 | 0.034 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 150 | 101 | 0 | 0 | 0 | 0 | 0 | 122 | 0 |
N.S. |
1 | 1.02 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.486 | 0.051 | 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 | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 122 | 75 | 91 | 118 | 92 | 189 | 78 | 101 | 128 |
N.S. |
1 | 1.13 | 0.69 | 0.84 | 1.09 | 0.85 | 1.75 | 0.72 | 0.94 | 1.19 |
time (sec) |
N/A | 0.473 | 0.121 | 0.167 | 0.107 | 0.078 | 1.259 | 0.134 | 0.159 | 22.740 |
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 | 83 | 88 | 67 | 83 | 95 | 82 | 146 | 66 | 82 | 105 |
N.S. |
1 | 1.06 | 0.81 | 1.00 | 1.14 | 0.99 | 1.76 | 0.80 | 0.99 | 1.27 |
time (sec) |
N/A | 0.435 | 0.111 | 0.122 | 0.109 | 0.075 | 0.923 | 0.155 | 0.161 | 0.036 |
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 | 61 | 56 | 59 | 75 | 72 | 70 | 129 | 54 | 63 | 82 |
N.S. |
1 | 0.92 | 0.97 | 1.23 | 1.18 | 1.15 | 2.11 | 0.89 | 1.03 | 1.34 |
time (sec) |
N/A | 0.369 | 0.108 | 0.115 | 0.111 | 0.077 | 1.178 | 0.133 | 0.165 | 0.042 |
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 | 33 | 33 | 30 | 45 | 27 | 47 | 80 | 30 | 25 | 37 |
N.S. |
1 | 1.00 | 0.91 | 1.36 | 0.82 | 1.42 | 2.42 | 0.91 | 0.76 | 1.12 |
time (sec) |
N/A | 0.340 | 0.021 | 0.178 | 0.105 | 0.071 | 1.048 | 0.145 | 0.151 | 0.044 |
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 | 41 | 46 | 74 | 40 | 62 | 0 | 53 | 45 | 71 |
N.S. |
1 | 0.95 | 1.07 | 1.72 | 0.93 | 1.44 | 0.00 | 1.23 | 1.05 | 1.65 |
time (sec) |
N/A | 0.402 | 0.038 | 0.104 | 0.110 | 0.076 | 0.000 | 0.123 | 0.161 | 0.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 29 | 33 | 73 | 60 | 0 | 66 | 71 | 32 |
N.S. |
1 | 1.00 | 0.91 | 1.03 | 2.28 | 1.88 | 0.00 | 2.06 | 2.22 | 1.00 |
time (sec) |
N/A | 0.355 | 0.017 | 0.115 | 0.103 | 0.074 | 0.000 | 0.146 | 0.159 | 22.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 63 | 35 | 40 | 126 | 89 | 0 | 145 | 142 | 183 |
N.S. |
1 | 0.97 | 0.54 | 0.62 | 1.94 | 1.37 | 0.00 | 2.23 | 2.18 | 2.82 |
time (sec) |
N/A | 0.401 | 0.028 | 0.140 | 0.131 | 0.076 | 0.000 | 0.140 | 0.166 | 22.667 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 43 | 49 | 189 | 116 | 0 | 199 | 72 | 49 |
N.S. |
1 | 1.00 | 0.44 | 0.51 | 1.95 | 1.20 | 0.00 | 2.05 | 0.74 | 0.51 |
time (sec) |
N/A | 0.453 | 0.032 | 0.156 | 0.142 | 0.079 | 0.000 | 0.127 | 0.164 | 22.796 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 131 | 51 | 57 | 264 | 144 | 0 | 321 | 29 | 57 |
N.S. |
1 | 1.02 | 0.40 | 0.44 | 2.05 | 1.12 | 0.00 | 2.49 | 0.22 | 0.44 |
time (sec) |
N/A | 0.489 | 0.042 | 0.194 | 0.121 | 0.077 | 0.000 | 0.160 | 200.026 | 22.781 |
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 | 37 | 35 | 23 | 45 | 59 | 59 | 66 | 59 | 44 | 59 |
N.S. |
1 | 0.95 | 0.62 | 1.22 | 1.59 | 1.59 | 1.78 | 1.59 | 1.19 | 1.59 |
time (sec) |
N/A | 0.384 | 0.026 | 0.086 | 0.030 | 0.063 | 0.052 | 0.119 | 0.168 | 22.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 35 | 32 | 29 | 37 | 37 | 36 | 37 | 28 | 37 |
N.S. |
1 | 0.95 | 0.86 | 0.78 | 1.00 | 1.00 | 0.97 | 1.00 | 0.76 | 1.00 |
time (sec) |
N/A | 0.389 | 0.021 | 0.078 | 0.028 | 0.068 | 0.037 | 0.121 | 0.156 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 35 | 30 | 29 | 37 | 37 | 37 | 37 | 28 | 37 |
N.S. |
1 | 0.95 | 0.81 | 0.78 | 1.00 | 1.00 | 1.00 | 1.00 | 0.76 | 1.00 |
time (sec) |
N/A | 0.383 | 0.020 | 0.078 | 0.030 | 0.064 | 0.041 | 0.136 | 0.157 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 16 | 16 | 15 | 17 | 17 | 15 | 17 | 16 | 15 |
N.S. |
1 | 0.84 | 0.84 | 0.79 | 0.89 | 0.89 | 0.79 | 0.89 | 0.84 | 0.79 |
time (sec) |
N/A | 0.351 | 0.013 | 0.072 | 0.032 | 0.064 | 0.035 | 0.118 | 0.153 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 26 | 26 | 10 | 11 | 11 | 10 | 11 | 9 | 9 |
N.S. |
1 | 1.73 | 1.73 | 0.67 | 0.73 | 0.73 | 0.67 | 0.73 | 0.60 | 0.60 |
time (sec) |
N/A | 0.272 | 0.012 | 0.065 | 0.031 | 0.059 | 0.027 | 0.118 | 0.157 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 29 | 25 | 28 | 29 | 28 | 20 | 30 | 36 | 28 |
N.S. |
1 | 0.94 | 0.81 | 0.90 | 0.94 | 0.90 | 0.65 | 0.97 | 1.16 | 0.90 |
time (sec) |
N/A | 0.372 | 0.024 | 0.075 | 0.030 | 0.065 | 0.090 | 0.140 | 0.163 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 25 | 13 | 25 | 25 | 22 | 32 | 32 | 12 |
N.S. |
1 | 1.00 | 1.92 | 1.00 | 1.92 | 1.92 | 1.69 | 2.46 | 2.46 | 0.92 |
time (sec) |
N/A | 0.328 | 0.012 | 0.076 | 0.027 | 0.061 | 0.118 | 0.124 | 0.153 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 35 | 23 | 21 | 47 | 47 | 48 | 21 | 37 | 21 |
N.S. |
1 | 0.95 | 0.62 | 0.57 | 1.27 | 1.27 | 1.30 | 0.57 | 1.00 | 0.57 |
time (sec) |
N/A | 0.378 | 0.020 | 0.079 | 0.026 | 0.068 | 0.142 | 0.118 | 0.162 | 0.075 |
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 | 37 | 35 | 23 | 21 | 57 | 57 | 61 | 21 | 45 | 21 |
N.S. |
1 | 0.95 | 0.62 | 0.57 | 1.54 | 1.54 | 1.65 | 0.57 | 1.22 | 0.57 |
time (sec) |
N/A | 0.383 | 0.020 | 0.080 | 0.037 | 0.065 | 0.170 | 0.141 | 0.155 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 80 | 75 | 91 | 164 | 93 | 173 | 78 | 101 | 128 |
N.S. |
1 | 0.96 | 0.90 | 1.10 | 1.98 | 1.12 | 2.08 | 0.94 | 1.22 | 1.54 |
time (sec) |
N/A | 0.409 | 0.120 | 0.262 | 0.108 | 0.080 | 7.606 | 0.144 | 0.159 | 0.035 |
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 | 59 | 59 | 44 | 68 | 77 | 65 | 109 | 48 | 49 | 64 |
N.S. |
1 | 1.00 | 0.75 | 1.15 | 1.31 | 1.10 | 1.85 | 0.81 | 0.83 | 1.08 |
time (sec) |
N/A | 0.373 | 0.033 | 0.139 | 0.111 | 0.081 | 1.944 | 0.162 | 0.160 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 56 | 59 | 75 | 118 | 71 | 119 | 54 | 63 | 82 |
N.S. |
1 | 0.92 | 0.97 | 1.23 | 1.93 | 1.16 | 1.95 | 0.89 | 1.03 | 1.34 |
time (sec) |
N/A | 0.382 | 0.097 | 0.136 | 0.110 | 0.081 | 5.432 | 0.141 | 0.159 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 64 | 48 | 62 | 85 | 52 | 88 | 38 | 42 | 58 |
N.S. |
1 | 1.21 | 0.91 | 1.17 | 1.60 | 0.98 | 1.66 | 0.72 | 0.79 | 1.09 |
time (sec) |
N/A | 0.391 | 0.050 | 0.120 | 0.108 | 0.074 | 3.647 | 0.154 | 0.150 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 69 | 45 | 186 | 89 | 94 | 0 | 79 | 101 | 114 |
N.S. |
1 | 0.93 | 0.61 | 2.51 | 1.20 | 1.27 | 0.00 | 1.07 | 1.36 | 1.54 |
time (sec) |
N/A | 0.419 | 0.051 | 0.164 | 0.107 | 0.075 | 0.000 | 0.136 | 0.162 | 22.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 29 | 35 | 146 | 89 | 0 | 83 | 117 | 34 |
N.S. |
1 | 1.00 | 0.91 | 1.09 | 4.56 | 2.78 | 0.00 | 2.59 | 3.66 | 1.06 |
time (sec) |
N/A | 0.362 | 0.022 | 0.174 | 0.036 | 0.079 | 0.000 | 0.164 | 0.161 | 22.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 63 | 34 | 40 | 216 | 116 | 0 | 199 | 72 | 299 |
N.S. |
1 | 0.97 | 0.52 | 0.62 | 3.32 | 1.78 | 0.00 | 3.06 | 1.11 | 4.60 |
time (sec) |
N/A | 0.404 | 0.052 | 0.172 | 0.038 | 0.085 | 0.000 | 0.137 | 0.158 | 22.481 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 43 | 49 | 327 | 145 | 0 | 253 | 31 | 492 |
N.S. |
1 | 1.00 | 0.44 | 0.51 | 3.37 | 1.49 | 0.00 | 2.61 | 0.32 | 5.07 |
time (sec) |
N/A | 0.455 | 0.048 | 0.208 | 0.038 | 0.080 | 0.000 | 0.147 | 200.022 | 22.545 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 131 | 51 | 57 | 462 | 171 | 0 | 509 | 308 | 604 |
N.S. |
1 | 1.02 | 0.40 | 0.44 | 3.58 | 1.33 | 0.00 | 3.95 | 2.39 | 4.68 |
time (sec) |
N/A | 0.506 | 0.117 | 0.263 | 0.043 | 0.099 | 0.000 | 0.188 | 0.168 | 22.498 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 48 | 31 | 45 | 59 | 59 | 63 | 59 | 44 | 59 |
N.S. |
1 | 0.91 | 0.58 | 0.85 | 1.11 | 1.11 | 1.19 | 1.11 | 0.83 | 1.11 |
time (sec) |
N/A | 0.407 | 0.050 | 0.092 | 0.030 | 0.066 | 0.051 | 0.114 | 0.151 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 26 | 26 | 23 | 28 | 28 | 29 | 28 | 24 | 24 |
N.S. |
1 | 0.81 | 0.81 | 0.72 | 0.88 | 0.88 | 0.91 | 0.88 | 0.75 | 0.75 |
time (sec) |
N/A | 0.368 | 0.034 | 0.072 | 0.025 | 0.061 | 0.045 | 0.112 | 0.154 | 22.592 |