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 | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 57 | 64 | 52 | 57 | 54 | 63 | 0 | 52 |
N.S. |
1 | 0.97 | 1.08 | 0.88 | 0.97 | 0.92 | 1.07 | 0.00 | 0.88 |
time (sec) |
N/A | 0.205 | 0.006 | 0.559 | 0.267 | 0.244 | 0.354 | 0.000 | 0.497 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 55 | 61 | 54 | 56 | 59 | 60 | 0 | 54 |
N.S. |
1 | 0.98 | 1.09 | 0.96 | 1.00 | 1.05 | 1.07 | 0.00 | 0.96 |
time (sec) |
N/A | 0.219 | 0.019 | 0.388 | 0.197 | 0.256 | 0.303 | 0.000 | 0.474 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 47 | 53 | 44 | 48 | 47 | 53 | 0 | 44 |
N.S. |
1 | 0.98 | 1.10 | 0.92 | 1.00 | 0.98 | 1.10 | 0.00 | 0.92 |
time (sec) |
N/A | 0.209 | 0.006 | 0.557 | 0.276 | 0.248 | 0.274 | 0.000 | 0.236 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 50 | 46 | 46 | 49 | 49 | 0 | 42 |
N.S. |
1 | 1.00 | 1.11 | 1.02 | 1.02 | 1.09 | 1.09 | 0.00 | 0.93 |
time (sec) |
N/A | 0.211 | 0.012 | 0.383 | 0.199 | 0.240 | 0.251 | 0.000 | 0.404 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 42 | 36 | 37 | 34 | 42 | 0 | 34 |
N.S. |
1 | 1.00 | 1.14 | 0.97 | 1.00 | 0.92 | 1.14 | 0.00 | 0.92 |
time (sec) |
N/A | 0.177 | 0.005 | 0.526 | 0.264 | 0.236 | 0.229 | 0.000 | 0.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 28 | 31 | 33 | 26 | 31 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 1.07 | 1.14 | 0.90 | 1.07 | 0.93 |
time (sec) |
N/A | 0.149 | 0.004 | 0.313 | 0.193 | 0.255 | 0.108 | 0.259 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 35 | 34 | 0 | 0 | 0 | 0 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.80 |
time (sec) |
N/A | 0.199 | 0.005 | 0.480 | 0.000 | 0.000 | 0.000 | 0.000 | 0.314 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 37 | 38 | 39 | 39 | 37 | 37 | 0 | 36 |
N.S. |
1 | 1.06 | 1.09 | 1.11 | 1.11 | 1.06 | 1.06 | 0.00 | 1.03 |
time (sec) |
N/A | 0.184 | 0.005 | 0.303 | 0.179 | 0.251 | 0.270 | 0.000 | 0.349 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 35 | 46 | 39 | 31 | 26 | 37 | 0 | 42 |
N.S. |
1 | 0.95 | 1.24 | 1.05 | 0.84 | 0.70 | 1.00 | 0.00 | 1.14 |
time (sec) |
N/A | 0.178 | 0.006 | 0.481 | 0.264 | 0.242 | 0.229 | 0.000 | 0.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 51 | 54 | 52 | 51 | 50 | 61 | 0 | 46 |
N.S. |
1 | 0.96 | 1.02 | 0.98 | 0.96 | 0.94 | 1.15 | 0.00 | 0.87 |
time (sec) |
N/A | 0.210 | 0.019 | 0.324 | 0.187 | 0.253 | 0.359 | 0.000 | 0.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 46 | 44 | 46 | 41 | 46 | 0 | 42 |
N.S. |
1 | 1.00 | 0.96 | 0.92 | 0.96 | 0.85 | 0.96 | 0.00 | 0.88 |
time (sec) |
N/A | 0.190 | 0.005 | 0.500 | 0.280 | 0.239 | 0.289 | 0.000 | 0.396 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 64 | 60 | 69 | 60 | 62 | 59 | 71 | 0 | 56 |
N.S. |
1 | 0.94 | 1.08 | 0.94 | 0.97 | 0.92 | 1.11 | 0.00 | 0.88 |
time (sec) |
N/A | 0.217 | 0.013 | 0.340 | 0.182 | 0.256 | 0.470 | 0.000 | 0.412 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 198 | 138 | 146 | 163 | 152 | 199 | 0 | 171 |
N.S. |
1 | 1.38 | 0.96 | 1.01 | 1.13 | 1.06 | 1.38 | 0.00 | 1.19 |
time (sec) |
N/A | 1.112 | 0.137 | 1.002 | 0.277 | 0.261 | 0.478 | 0.000 | 0.728 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 170 | 208 | 169 | 266 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.22 | 0.99 | 1.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.075 | 0.602 | 1.991 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 133 | 111 | 118 | 136 | 121 | 155 | 0 | 134 |
N.S. |
1 | 1.19 | 0.99 | 1.05 | 1.21 | 1.08 | 1.38 | 0.00 | 1.20 |
time (sec) |
N/A | 0.711 | 0.100 | 1.024 | 0.298 | 0.254 | 0.383 | 0.000 | 0.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 138 | 151 | 131 | 238 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.95 | 1.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.702 | 0.339 | 1.833 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 75 | 88 | 104 | 83 | 107 | 0 | 88 |
N.S. |
1 | 1.00 | 0.99 | 1.16 | 1.37 | 1.09 | 1.41 | 0.00 | 1.16 |
time (sec) |
N/A | 0.383 | 0.161 | 0.973 | 0.296 | 0.241 | 0.274 | 0.000 | 0.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 97 | 90 | 123 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 1.08 | 1.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.419 | 0.144 | 2.193 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 132 | 157 | 179 | 1002 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.19 | 1.36 | 7.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.654 | 0.189 | 0.743 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 93 | 102 | 270 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 1.24 | 3.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.435 | 0.197 | 2.348 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 76 | 90 | 98 | 98 | 94 | 119 | 0 | 140 |
N.S. |
1 | 0.96 | 1.14 | 1.24 | 1.24 | 1.19 | 1.51 | 0.00 | 1.77 |
time (sec) |
N/A | 0.453 | 0.081 | 0.725 | 0.272 | 0.248 | 0.326 | 0.000 | 2.580 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 137 | 153 | 310 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 1.09 | 2.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.672 | 0.473 | 2.908 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 135 | 128 | 132 | 152 | 135 | 170 | 0 | 171 |
N.S. |
1 | 1.16 | 1.10 | 1.14 | 1.31 | 1.16 | 1.47 | 0.00 | 1.47 |
time (sec) |
N/A | 0.772 | 0.114 | 0.974 | 0.272 | 0.258 | 0.437 | 0.000 | 2.553 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 255 | 525 | 291 | 402 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 2.06 | 1.14 | 1.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.900 | 0.953 | 2.524 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 271 | 370 | 396 | 1185 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.37 | 1.46 | 4.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.384 | 1.124 | 6.276 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 194 | 307 | 225 | 340 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.58 | 1.16 | 1.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.765 | 0.626 | 2.563 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 206 | 225 | 269 | 1088 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.31 | 5.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.394 | 0.680 | 4.188 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 146 | 152 | 276 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 1.16 | 2.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.809 | 0.427 | 2.888 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 134 | 192 | 240 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 1.61 | 2.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.619 | 0.157 | 5.707 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 206 | 239 | 368 | 2026 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 1.79 | 9.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.956 | 0.321 | 0.575 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 116 | 138 | 214 | 1862 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.19 | 1.84 | 16.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.684 | 1.296 | 1.912 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 135 | 176 | 354 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 1.32 | 2.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.829 | 0.376 | 4.621 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 213 | 220 | 305 | 2097 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.43 | 9.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.603 | 1.383 | 6.803 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-1) | F | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 198 | 277 | 265 | 423 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.40 | 1.34 | 2.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.541 | 0.864 | 4.497 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 10 | 8 | 10 | 10 | 7 | 3 | 10 |
N.S. |
1 | 1.00 | 1.25 | 1.00 | 1.25 | 1.25 | 0.88 | 0.38 | 1.25 |
time (sec) |
N/A | 0.154 | 0.742 | 10.581 | 0.255 | 0.231 | 0.269 | 23.919 | 0.293 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 8 | 6 | 8 | 8 | 7 | 3 | 8 |
N.S. |
1 | 1.00 | 1.33 | 1.00 | 1.33 | 1.33 | 1.17 | 0.50 | 1.33 |
time (sec) |
N/A | 0.148 | 0.020 | 4.118 | 0.231 | 0.250 | 0.257 | 21.736 | 0.291 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 3 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 0.30 | 1.20 |
time (sec) |
N/A | 0.162 | 0.514 | 4.589 | 0.238 | 0.233 | 0.368 | 24.442 | 0.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 10 | 8 | 45 | 10 | 8 | 3 | 10 |
N.S. |
1 | 1.00 | 1.25 | 1.00 | 5.62 | 1.25 | 1.00 | 0.38 | 1.25 |
time (sec) |
N/A | 0.156 | 0.715 | 10.509 | 0.258 | 0.234 | 0.310 | 49.107 | 0.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 8 | 6 | 39 | 8 | 8 | 3 | 8 |
N.S. |
1 | 1.00 | 1.33 | 1.00 | 6.50 | 1.33 | 1.33 | 0.50 | 1.33 |
time (sec) |
N/A | 0.147 | 1.095 | 5.540 | 0.234 | 0.251 | 0.298 | 47.802 | 0.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 51 | 12 | 10 | 3 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 5.10 | 1.20 | 1.00 | 0.30 | 1.20 |
time (sec) |
N/A | 0.164 | 1.238 | 4.234 | 0.265 | 0.245 | 0.375 | 49.411 | 0.299 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 8 | 0 | 0 | 10 | 3 | 10 |
N.S. |
1 | 1.00 | 1.20 | 0.80 | 0.00 | 0.00 | 1.00 | 0.30 | 1.00 |
time (sec) |
N/A | 0.152 | 1.483 | 2.086 | 0.000 | 0.000 | 0.400 | 53.543 | 0.307 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 10 | 6 | 0 | 0 | 8 | 3 | 8 |
N.S. |
1 | 1.00 | 1.25 | 0.75 | 0.00 | 0.00 | 1.00 | 0.38 | 1.00 |
time (sec) |
N/A | 0.149 | 1.812 | 1.641 | 0.000 | 0.000 | 0.315 | 53.952 | 0.326 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 10 | 3 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 0.83 | 0.25 | 1.00 |
time (sec) |
N/A | 0.161 | 1.102 | 1.947 | 0.000 | 0.000 | 0.361 | 148.199 | 0.293 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 8 | 0 | 0 | 10 | 3 | 10 |
N.S. |
1 | 1.00 | 1.20 | 0.80 | 0.00 | 0.00 | 1.00 | 0.30 | 1.00 |
time (sec) |
N/A | 0.154 | 0.839 | 1.792 | 0.000 | 0.000 | 1.406 | 81.002 | 0.301 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 10 | 6 | 0 | 0 | 8 | 3 | 8 |
N.S. |
1 | 1.00 | 1.25 | 0.75 | 0.00 | 0.00 | 1.00 | 0.38 | 1.00 |
time (sec) |
N/A | 0.147 | 1.711 | 1.527 | 0.000 | 0.000 | 0.852 | 81.253 | 0.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 10 | 3 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 0.83 | 0.25 | 1.00 |
time (sec) |
N/A | 0.172 | 0.957 | 2.726 | 0.000 | 0.000 | 0.858 | 142.203 | 0.316 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 8 | 0 | 0 | 10 | 3 | 10 |
N.S. |
1 | 1.00 | 1.20 | 0.80 | 0.00 | 0.00 | 1.00 | 0.30 | 1.00 |
time (sec) |
N/A | 0.155 | 0.935 | 1.751 | 0.000 | 0.000 | 0.364 | 70.975 | 0.292 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 10 | 6 | 0 | 0 | 10 | 3 | 8 |
N.S. |
1 | 1.00 | 1.25 | 0.75 | 0.00 | 0.00 | 1.25 | 0.38 | 1.00 |
time (sec) |
N/A | 0.148 | 0.006 | 1.588 | 0.000 | 0.000 | 0.324 | 64.900 | 0.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 12 | 3 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 1.00 | 0.25 | 1.00 |
time (sec) |
N/A | 0.159 | 1.304 | 2.352 | 0.000 | 0.000 | 0.476 | 68.146 | 0.296 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 8 | 0 | 0 | 10 | 3 | 10 |
N.S. |
1 | 1.00 | 1.20 | 0.80 | 0.00 | 0.00 | 1.00 | 0.30 | 1.00 |
time (sec) |
N/A | 0.158 | 1.035 | 1.943 | 0.000 | 0.000 | 0.670 | 249.366 | 0.329 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 10 | 6 | 0 | 0 | 10 | 3 | 8 |
N.S. |
1 | 1.00 | 1.25 | 0.75 | 0.00 | 0.00 | 1.25 | 0.38 | 1.00 |
time (sec) |
N/A | 0.147 | 1.735 | 1.520 | 0.000 | 0.000 | 0.638 | 239.105 | 0.351 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 10 | 0 | 0 | 12 | 3 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 0.00 | 0.00 | 1.00 | 0.25 | 1.00 |
time (sec) |
N/A | 0.158 | 2.338 | 2.635 | 0.000 | 0.000 | 0.909 | 184.339 | 0.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 117 | 128 | 108 | 69 | 86 | 80 | 110 | 86 | 49 |
N.S. |
1 | 1.09 | 0.92 | 0.59 | 0.74 | 0.68 | 0.94 | 0.74 | 0.42 |
time (sec) |
N/A | 0.316 | 0.035 | 0.253 | 0.269 | 0.256 | 1.953 | 0.271 | 0.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 16 | 387 | 44 | 15 | 3 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 24.19 | 2.75 | 0.94 | 0.19 | 1.12 |
time (sec) |
N/A | 0.182 | 4.832 | 2.559 | 3.735 | 0.261 | 7.445 | 72.748 | 0.650 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 16 | 295 | 30 | 15 | 3 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 18.44 | 1.88 | 0.94 | 0.19 | 1.12 |
time (sec) |
N/A | 0.182 | 3.147 | 3.820 | 2.202 | 0.248 | 4.351 | 72.162 | 0.622 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 60 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.214 | 0.041 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 16 | 18 | 18 | 14 | 3 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.88 | 0.19 | 1.12 |
time (sec) |
N/A | 0.179 | 0.346 | 3.526 | 0.268 | 0.245 | 1.260 | 87.381 | 0.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 3 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 0.30 | 1.20 |
time (sec) |
N/A | 0.156 | 0.499 | 1.693 | 0.371 | 0.239 | 1.814 | 80.207 | 0.406 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 16 | 18 | 18 | 15 | 3 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.94 | 0.19 | 1.12 |
time (sec) |
N/A | 0.179 | 0.418 | 4.359 | 0.538 | 0.250 | 155.449 | 79.272 | 0.406 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 53 | 59 | 50 | 54 | 51 | 58 | 60 | 49 |
N.S. |
1 | 0.98 | 1.09 | 0.93 | 1.00 | 0.94 | 1.07 | 1.11 | 0.91 |
time (sec) |
N/A | 0.227 | 0.012 | 0.583 | 0.280 | 0.245 | 29.725 | 0.274 | 0.403 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 52 | 45 | 48 | 51 | 80 | 47 | 44 |
N.S. |
1 | 1.00 | 1.11 | 0.96 | 1.02 | 1.09 | 1.70 | 1.00 | 0.94 |
time (sec) |
N/A | 0.218 | 0.017 | 0.661 | 0.213 | 0.255 | 22.305 | 0.274 | 0.374 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 48 | 41 | 43 | 38 | 48 | 43 | 40 |
N.S. |
1 | 1.00 | 1.12 | 0.95 | 1.00 | 0.88 | 1.12 | 1.00 | 0.93 |
time (sec) |
N/A | 0.198 | 0.008 | 0.734 | 0.288 | 0.229 | 9.849 | 0.267 | 0.353 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 41 | 36 | 38 | 39 | 66 | 40 | 35 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.06 | 1.08 | 1.83 | 1.11 | 0.97 |
time (sec) |
N/A | 0.179 | 0.024 | 0.536 | 0.191 | 0.238 | 5.410 | 0.279 | 0.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 45 | 39 | 63 | 0 | 0 | 0 | 0 | 32 |
N.S. |
1 | 1.15 | 1.00 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.82 |
time (sec) |
N/A | 0.243 | 0.008 | 0.747 | 0.000 | 0.000 | 0.000 | 0.000 | 0.389 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 41 | 44 | 39 | 41 | 43 | 75 | 60 | 38 |
N.S. |
1 | 1.05 | 1.13 | 1.00 | 1.05 | 1.10 | 1.92 | 1.54 | 0.97 |
time (sec) |
N/A | 0.190 | 0.010 | 0.266 | 0.190 | 0.252 | 12.925 | 0.273 | 0.395 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 39 | 48 | 39 | 35 | 30 | 42 | 72 | 41 |
N.S. |
1 | 0.95 | 1.17 | 0.95 | 0.85 | 0.73 | 1.02 | 1.76 | 1.00 |
time (sec) |
N/A | 0.193 | 0.009 | 0.375 | 0.272 | 0.238 | 12.686 | 0.286 | 0.406 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 53 | 60 | 53 | 53 | 54 | 92 | 69 | 50 |
N.S. |
1 | 0.96 | 1.09 | 0.96 | 0.96 | 0.98 | 1.67 | 1.25 | 0.91 |
time (sec) |
N/A | 0.223 | 0.016 | 0.303 | 0.189 | 0.247 | 38.959 | 0.262 | 0.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 161 | 180 | 179 | 121 | 147 | 171 | 153 | 169 | 64 |
N.S. |
1 | 1.12 | 1.11 | 0.75 | 0.91 | 1.06 | 0.95 | 1.05 | 0.40 |
time (sec) |
N/A | 0.389 | 0.068 | 0.869 | 0.289 | 0.257 | 15.270 | 0.329 | 0.400 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 169 | 177 | 118 | 145 | 152 | 143 | 165 | 62 |
N.S. |
1 | 1.06 | 1.11 | 0.74 | 0.91 | 0.96 | 0.90 | 1.04 | 0.39 |
time (sec) |
N/A | 0.382 | 0.056 | 0.535 | 0.277 | 0.261 | 7.490 | 0.337 | 0.452 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 107 | 103 | 127 | 140 | 617 | 149 | 49 |
N.S. |
1 | 1.00 | 0.76 | 0.74 | 0.91 | 1.00 | 4.41 | 1.06 | 0.35 |
time (sec) |
N/A | 0.264 | 0.061 | 0.358 | 0.285 | 0.244 | 4.336 | 0.280 | 0.453 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 143 | 154 | 158 | 107 | 132 | 139 | 121 | 138 | 55 |
N.S. |
1 | 1.08 | 1.10 | 0.75 | 0.92 | 0.97 | 0.85 | 0.97 | 0.38 |
time (sec) |
N/A | 0.360 | 0.074 | 0.349 | 0.276 | 0.251 | 8.534 | 0.289 | 0.240 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | C | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 175 | 177 | 115 | 142 | 170 | 529 | 159 | 63 |
N.S. |
1 | 1.10 | 1.11 | 0.72 | 0.89 | 1.07 | 3.33 | 1.00 | 0.40 |
time (sec) |
N/A | 0.378 | 0.085 | 0.417 | 0.278 | 0.252 | 20.038 | 0.334 | 0.500 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 171 | 177 | 118 | 138 | 163 | 155 | 150 | 63 |
N.S. |
1 | 1.08 | 1.11 | 0.74 | 0.87 | 1.03 | 0.97 | 0.94 | 0.40 |
time (sec) |
N/A | 0.375 | 0.086 | 0.468 | 0.288 | 0.250 | 29.701 | 0.339 | 0.528 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 149 | 121 | 151 | 169 | 137 | 199 | 145 | 150 |
N.S. |
1 | 1.20 | 0.98 | 1.22 | 1.36 | 1.10 | 1.60 | 1.17 | 1.21 |
time (sec) |
N/A | 0.773 | 0.120 | 0.855 | 0.377 | 0.252 | 44.486 | 0.279 | 1.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 154 | 171 | 141 | 333 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.92 | 2.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.792 | 0.364 | 3.561 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 85 | 110 | 126 | 100 | 155 | 100 | 112 |
N.S. |
1 | 1.00 | 0.94 | 1.22 | 1.40 | 1.11 | 1.72 | 1.11 | 1.24 |
time (sec) |
N/A | 0.448 | 0.083 | 1.290 | 0.331 | 0.257 | 16.832 | 0.269 | 0.805 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 113 | 107 | 140 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 1.06 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.475 | 0.152 | 4.438 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 151 | 177 | 201 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 1.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.717 | 0.172 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 97 | 107 | 127 | 339 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 1.31 | 3.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.490 | 0.194 | 3.328 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 86 | 98 | 118 | 110 | 115 | 167 | 0 | 152 |
N.S. |
1 | 0.99 | 1.13 | 1.36 | 1.26 | 1.32 | 1.92 | 0.00 | 1.75 |
time (sec) |
N/A | 0.521 | 0.107 | 0.651 | 0.357 | 0.256 | 22.225 | 0.000 | 0.688 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1393 | 1393 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.556 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1191 | 1191 | 4697 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 3.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.917 | 38.101 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1164 | 1164 | 4697 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 4.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.856 | 35.915 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1360 | 1360 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.265 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 1444 | 1444 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.337 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 149 | 166 | 170 | 399 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 1.14 | 2.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.897 | 0.512 | 4.665 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 154 | 224 | 275 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 1.56 | 1.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.695 | 0.134 | 9.388 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 229 | 267 | 417 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 1.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.040 | 0.301 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 138 | 156 | 239 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 1.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.762 | 0.469 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 149 | 153 | 196 | 465 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.32 | 3.12 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.882 | 0.369 | 4.421 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 406 | 50 | 0 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 22.56 | 2.78 | 0.00 | 1.11 | 1.11 |
time (sec) |
N/A | 0.179 | 2.263 | 0.171 | 3.974 | 0.244 | 0.000 | 0.423 | 0.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 303 | 34 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 16.83 | 1.89 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.183 | 1.467 | 0.176 | 2.349 | 0.247 | 111.972 | 0.521 | 0.320 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 65 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.222 | 0.087 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 20 | 0 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.00 | 1.11 | 1.11 |
time (sec) |
N/A | 0.178 | 0.457 | 0.188 | 0.240 | 0.247 | 0.000 | 0.278 | 0.283 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 124 | 36 | 0 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 6.89 | 2.00 | 0.00 | 1.11 | 1.11 |
time (sec) |
N/A | 0.181 | 0.478 | 0.164 | 0.394 | 0.238 | 0.000 | 0.300 | 0.351 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 53 | 59 | 50 | 54 | 51 | 58 | 60 | 49 |
N.S. |
1 | 0.98 | 1.09 | 0.93 | 1.00 | 0.94 | 1.07 | 1.11 | 0.91 |
time (sec) |
N/A | 0.218 | 0.012 | 0.750 | 0.274 | 0.238 | 129.726 | 0.266 | 0.439 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 52 | 45 | 48 | 51 | 117 | 47 | 44 |
N.S. |
1 | 1.00 | 1.11 | 0.96 | 1.02 | 1.09 | 2.49 | 1.00 | 0.94 |
time (sec) |
N/A | 0.226 | 0.019 | 0.688 | 0.203 | 0.240 | 73.035 | 0.285 | 0.384 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 48 | 41 | 43 | 38 | 48 | 43 | 40 |
N.S. |
1 | 1.00 | 1.12 | 0.95 | 1.00 | 0.88 | 1.12 | 1.00 | 0.93 |
time (sec) |
N/A | 0.204 | 0.010 | 0.816 | 0.267 | 0.251 | 36.158 | 0.265 | 0.384 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 41 | 36 | 38 | 39 | 102 | 40 | 35 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.06 | 1.08 | 2.83 | 1.11 | 0.97 |
time (sec) |
N/A | 0.181 | 0.023 | 0.589 | 0.180 | 0.241 | 20.583 | 0.268 | 0.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 45 | 39 | 63 | 0 | 0 | 0 | 0 | 32 |
N.S. |
1 | 1.15 | 1.00 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.82 |
time (sec) |
N/A | 0.243 | 0.009 | 0.517 | 0.000 | 0.000 | 0.000 | 0.000 | 0.375 |