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 | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 147 | 170 | 135 | 146 | 0 | 366 | 168 | 209 | 165 |
N.S. |
1 | 1.16 | 0.92 | 0.99 | 0.00 | 2.49 | 1.14 | 1.42 | 1.12 |
time (sec) |
N/A | 0.265 | 0.133 | 2.521 | 0.000 | 0.307 | 105.720 | 0.273 | 10.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 133 | 102 | 112 | 0 | 254 | 122 | 134 | 121 |
N.S. |
1 | 1.17 | 0.89 | 0.98 | 0.00 | 2.23 | 1.07 | 1.18 | 1.06 |
time (sec) |
N/A | 0.239 | 0.172 | 2.858 | 0.000 | 0.361 | 5.403 | 0.283 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 96 | 83 | 76 | 0 | 191 | 90 | 83 | 67 |
N.S. |
1 | 1.16 | 1.00 | 0.92 | 0.00 | 2.30 | 1.08 | 1.00 | 0.81 |
time (sec) |
N/A | 0.213 | 0.095 | 3.267 | 0.000 | 0.381 | 1.756 | 0.280 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 65 | 48 | 0 | 155 | 58 | 49 | 49 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.00 | 2.38 | 0.89 | 0.75 | 0.75 |
time (sec) |
N/A | 0.187 | 0.046 | 3.401 | 0.000 | 0.393 | 1.367 | 0.273 | 10.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 91 | 88 | 0 | 261 | 92 | 89 | 75 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 0.00 | 2.87 | 1.01 | 0.98 | 0.82 |
time (sec) |
N/A | 0.222 | 0.111 | 2.943 | 0.000 | 0.364 | 2.056 | 0.301 | 10.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 136 | 111 | 117 | 0 | 461 | 124 | 140 | 127 |
N.S. |
1 | 1.13 | 0.92 | 0.98 | 0.00 | 3.84 | 1.03 | 1.17 | 1.06 |
time (sec) |
N/A | 0.248 | 0.204 | 3.029 | 0.000 | 0.528 | 2.245 | 0.285 | 0.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 153 | 181 | 145 | 146 | 0 | 783 | 160 | 217 | 171 |
N.S. |
1 | 1.18 | 0.95 | 0.95 | 0.00 | 5.12 | 1.05 | 1.42 | 1.12 |
time (sec) |
N/A | 0.274 | 0.232 | 2.797 | 0.000 | 0.391 | 6.230 | 0.276 | 0.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 186 | 226 | 189 | 175 | 0 | 1157 | 0 | 310 | 213 |
N.S. |
1 | 1.22 | 1.02 | 0.94 | 0.00 | 6.22 | 0.00 | 1.67 | 1.15 |
time (sec) |
N/A | 0.300 | 0.268 | 3.035 | 0.000 | 0.388 | 0.000 | 0.278 | 10.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 210 | 246 | 246 | 257 | 0 | 788 | 0 | 422 | 443 |
N.S. |
1 | 1.17 | 1.17 | 1.22 | 0.00 | 3.75 | 0.00 | 2.01 | 2.11 |
time (sec) |
N/A | 0.309 | 0.433 | 4.055 | 0.000 | 0.300 | 0.000 | 0.295 | 9.821 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 209 | 191 | 204 | 0 | 586 | 0 | 312 | 290 |
N.S. |
1 | 1.17 | 1.07 | 1.15 | 0.00 | 3.29 | 0.00 | 1.75 | 1.63 |
time (sec) |
N/A | 0.282 | 0.329 | 3.527 | 0.000 | 0.328 | 0.000 | 0.283 | 9.713 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 172 | 146 | 151 | 0 | 420 | 0 | 218 | 200 |
N.S. |
1 | 1.19 | 1.01 | 1.05 | 0.00 | 2.92 | 0.00 | 1.51 | 1.39 |
time (sec) |
N/A | 0.261 | 0.303 | 4.034 | 0.000 | 0.338 | 0.000 | 0.270 | 9.750 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 135 | 110 | 129 | 0 | 282 | 0 | 142 | 140 |
N.S. |
1 | 1.21 | 0.98 | 1.15 | 0.00 | 2.52 | 0.00 | 1.27 | 1.25 |
time (sec) |
N/A | 0.237 | 0.264 | 3.976 | 0.000 | 0.311 | 0.000 | 0.293 | 0.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 93 | 75 | 0 | 309 | 0 | 94 | 81 |
N.S. |
1 | 1.00 | 0.99 | 0.80 | 0.00 | 3.29 | 0.00 | 1.00 | 0.86 |
time (sec) |
N/A | 0.206 | 0.187 | 3.853 | 0.000 | 0.314 | 0.000 | 0.276 | 9.718 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 100 | 82 | 0 | 353 | 0 | 111 | 97 |
N.S. |
1 | 1.00 | 0.99 | 0.81 | 0.00 | 3.50 | 0.00 | 1.10 | 0.96 |
time (sec) |
N/A | 0.218 | 0.171 | 27.440 | 0.000 | 0.362 | 0.000 | 0.273 | 9.752 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 146 | 118 | 100 | 0 | 502 | 0 | 171 | 155 |
N.S. |
1 | 1.14 | 0.92 | 0.78 | 0.00 | 3.92 | 0.00 | 1.34 | 1.21 |
time (sec) |
N/A | 0.248 | 0.319 | 7.643 | 0.000 | 0.387 | 0.000 | 0.269 | 9.794 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 158 | 191 | 156 | 153 | 0 | 881 | 0 | 253 | 200 |
N.S. |
1 | 1.21 | 0.99 | 0.97 | 0.00 | 5.58 | 0.00 | 1.60 | 1.27 |
time (sec) |
N/A | 0.278 | 0.313 | 2.663 | 0.000 | 0.378 | 0.000 | 0.284 | 10.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 192 | 236 | 200 | 183 | 0 | 1331 | 0 | 340 | 244 |
N.S. |
1 | 1.23 | 1.04 | 0.95 | 0.00 | 6.93 | 0.00 | 1.77 | 1.27 |
time (sec) |
N/A | 0.298 | 0.403 | 2.819 | 0.000 | 0.465 | 0.000 | 0.290 | 10.125 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 222 | 250 | 250 | 235 | 0 | 858 | 0 | 418 | 430 |
N.S. |
1 | 1.13 | 1.13 | 1.06 | 0.00 | 3.86 | 0.00 | 1.88 | 1.94 |
time (sec) |
N/A | 0.311 | 0.610 | 10.363 | 0.000 | 0.654 | 0.000 | 0.289 | 10.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 186 | 213 | 207 | 180 | 0 | 638 | 0 | 303 | 319 |
N.S. |
1 | 1.15 | 1.11 | 0.97 | 0.00 | 3.43 | 0.00 | 1.63 | 1.72 |
time (sec) |
N/A | 0.285 | 0.522 | 9.706 | 0.000 | 0.342 | 0.000 | 0.275 | 10.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 152 | 176 | 149 | 164 | 0 | 440 | 0 | 203 | 240 |
N.S. |
1 | 1.16 | 0.98 | 1.08 | 0.00 | 2.89 | 0.00 | 1.34 | 1.58 |
time (sec) |
N/A | 0.258 | 0.489 | 11.841 | 0.000 | 0.334 | 0.000 | 0.301 | 0.172 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 135 | 118 | 101 | 0 | 492 | 0 | 133 | 171 |
N.S. |
1 | 1.04 | 0.91 | 0.78 | 0.00 | 3.78 | 0.00 | 1.02 | 1.32 |
time (sec) |
N/A | 0.233 | 0.361 | 9.783 | 0.000 | 0.327 | 0.000 | 0.289 | 9.957 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 142 | 131 | 113 | 0 | 565 | 0 | 155 | 166 |
N.S. |
1 | 0.99 | 0.91 | 0.78 | 0.00 | 3.92 | 0.00 | 1.08 | 1.15 |
time (sec) |
N/A | 0.246 | 0.437 | 9.732 | 0.000 | 0.350 | 0.000 | 0.277 | 0.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 158 | 125 | 129 | 0 | 654 | 0 | 175 | 177 |
N.S. |
1 | 1.08 | 0.86 | 0.88 | 0.00 | 4.48 | 0.00 | 1.20 | 1.21 |
time (sec) |
N/A | 0.252 | 0.280 | 10.960 | 0.000 | 0.333 | 0.000 | 0.290 | 10.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 176 | 203 | 157 | 152 | 0 | 897 | 0 | 269 | 251 |
N.S. |
1 | 1.15 | 0.89 | 0.86 | 0.00 | 5.10 | 0.00 | 1.53 | 1.43 |
time (sec) |
N/A | 0.286 | 0.507 | 2.648 | 0.000 | 0.370 | 0.000 | 0.275 | 10.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 208 | 248 | 202 | 180 | 0 | 1353 | 0 | 340 | 296 |
N.S. |
1 | 1.19 | 0.97 | 0.87 | 0.00 | 6.50 | 0.00 | 1.63 | 1.42 |
time (sec) |
N/A | 0.306 | 0.577 | 2.559 | 0.000 | 0.400 | 0.000 | 0.276 | 10.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 244 | 293 | 257 | 209 | 0 | 2007 | 0 | 433 | 344 |
N.S. |
1 | 1.20 | 1.05 | 0.86 | 0.00 | 8.23 | 0.00 | 1.77 | 1.41 |
time (sec) |
N/A | 0.341 | 0.864 | 2.963 | 0.000 | 1.033 | 0.000 | 0.293 | 10.309 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 295 | 317 | 187 | 233 | 296 | 315 | 0 | 1092 | 346 |
N.S. |
1 | 1.07 | 0.63 | 0.79 | 1.00 | 1.07 | 0.00 | 3.70 | 1.17 |
time (sec) |
N/A | 0.471 | 0.122 | 2.902 | 0.220 | 0.457 | 0.000 | 0.320 | 10.586 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 233 | 248 | 131 | 158 | 211 | 230 | 0 | 750 | 256 |
N.S. |
1 | 1.06 | 0.56 | 0.68 | 0.91 | 0.99 | 0.00 | 3.22 | 1.10 |
time (sec) |
N/A | 0.401 | 0.095 | 2.459 | 0.232 | 0.373 | 0.000 | 0.304 | 10.303 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 179 | 88 | 100 | 140 | 159 | 0 | 469 | 180 |
N.S. |
1 | 1.05 | 0.51 | 0.58 | 0.82 | 0.93 | 0.00 | 2.74 | 1.05 |
time (sec) |
N/A | 0.308 | 0.063 | 2.447 | 0.218 | 0.707 | 0.000 | 0.315 | 10.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 110 | 55 | 59 | 83 | 102 | 0 | 252 | 121 |
N.S. |
1 | 1.01 | 0.50 | 0.54 | 0.76 | 0.94 | 0.00 | 2.31 | 1.11 |
time (sec) |
N/A | 0.238 | 0.041 | 2.738 | 0.212 | 0.331 | 0.000 | 0.282 | 10.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 37 | 40 | 18 | 57 | 0 | 91 | 49 |
N.S. |
1 | 1.00 | 0.77 | 0.83 | 0.38 | 1.19 | 0.00 | 1.90 | 1.02 |
time (sec) |
N/A | 0.174 | 0.015 | 2.987 | 0.219 | 0.312 | 0.000 | 0.295 | 10.117 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 118 | 153 | 0 | 309 | 0 | 235 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.20 | 0.00 | 2.41 | 0.00 | 1.84 | 0.00 |
time (sec) |
N/A | 0.280 | 0.095 | 2.777 | 0.000 | 0.311 | 0.000 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 112 | 153 | 0 | 483 | 0 | 112 | 0 |
N.S. |
1 | 1.00 | 0.87 | 1.19 | 0.00 | 3.74 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.251 | 0.220 | 2.534 | 0.000 | 0.322 | 0.000 | 0.314 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 199 | 194 | 165 | 282 | 0 | 749 | 0 | 228 | 0 |
N.S. |
1 | 0.97 | 0.83 | 1.42 | 0.00 | 3.76 | 0.00 | 1.15 | 0.00 |
time (sec) |
N/A | 0.337 | 0.373 | 2.989 | 0.000 | 0.341 | 0.000 | 0.381 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 264 | 271 | 200 | 447 | 0 | 1115 | 0 | 365 | 0 |
N.S. |
1 | 1.03 | 0.76 | 1.69 | 0.00 | 4.22 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 0.406 | 0.542 | 2.697 | 0.000 | 0.340 | 0.000 | 0.551 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 295 | 317 | 187 | 235 | 373 | 392 | 0 | 2506 | 424 |
N.S. |
1 | 1.07 | 0.63 | 0.80 | 1.26 | 1.33 | 0.00 | 8.49 | 1.44 |
time (sec) |
N/A | 0.484 | 0.142 | 2.460 | 0.244 | 0.409 | 0.000 | 0.546 | 10.792 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 233 | 248 | 132 | 160 | 273 | 292 | 0 | 1756 | 320 |
N.S. |
1 | 1.06 | 0.57 | 0.69 | 1.17 | 1.25 | 0.00 | 7.54 | 1.37 |
time (sec) |
N/A | 0.395 | 0.106 | 2.709 | 0.228 | 0.486 | 0.000 | 0.370 | 10.692 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 179 | 88 | 102 | 189 | 208 | 0 | 1132 | 230 |
N.S. |
1 | 1.05 | 0.51 | 0.60 | 1.11 | 1.22 | 0.00 | 6.62 | 1.35 |
time (sec) |
N/A | 0.315 | 0.072 | 2.860 | 0.214 | 0.401 | 0.000 | 0.338 | 10.497 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 110 | 55 | 61 | 98 | 135 | 0 | 631 | 128 |
N.S. |
1 | 1.01 | 0.50 | 0.56 | 0.90 | 1.24 | 0.00 | 5.79 | 1.17 |
time (sec) |
N/A | 0.240 | 0.051 | 2.492 | 0.221 | 0.392 | 0.000 | 0.309 | 10.486 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 37 | 42 | 43 | 74 | 0 | 254 | 62 |
N.S. |
1 | 1.00 | 0.77 | 0.88 | 0.90 | 1.54 | 0.00 | 5.29 | 1.29 |
time (sec) |
N/A | 0.170 | 0.020 | 2.893 | 0.219 | 0.677 | 0.000 | 0.290 | 10.321 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 181 | 191 | 137 | 265 | 0 | 399 | 0 | 426 | 0 |
N.S. |
1 | 1.06 | 0.76 | 1.46 | 0.00 | 2.20 | 0.00 | 2.35 | 0.00 |
time (sec) |
N/A | 0.343 | 0.169 | 2.806 | 0.000 | 0.326 | 0.000 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 175 | 181 | 142 | 304 | 0 | 411 | 0 | 218 | 0 |
N.S. |
1 | 1.03 | 0.81 | 1.74 | 0.00 | 2.35 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.326 | 0.254 | 2.631 | 0.000 | 0.334 | 0.000 | 0.362 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 184 | 140 | 271 | 0 | 649 | 0 | 208 | 0 |
N.S. |
1 | 0.99 | 0.76 | 1.46 | 0.00 | 3.51 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.308 | 0.382 | 3.094 | 0.000 | 0.318 | 0.000 | 0.385 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 250 | 249 | 198 | 447 | 0 | 967 | 0 | 351 | 0 |
N.S. |
1 | 1.00 | 0.79 | 1.79 | 0.00 | 3.87 | 0.00 | 1.40 | 0.00 |
time (sec) |
N/A | 0.395 | 0.606 | 2.434 | 0.000 | 0.395 | 0.000 | 0.436 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 315 | 326 | 242 | 652 | 0 | 1387 | 0 | 532 | 0 |
N.S. |
1 | 1.03 | 0.77 | 2.07 | 0.00 | 4.40 | 0.00 | 1.69 | 0.00 |
time (sec) |
N/A | 0.481 | 0.900 | 2.811 | 0.000 | 0.367 | 0.000 | 0.515 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 295 | 317 | 197 | 235 | 448 | 467 | 0 | 4241 | 501 |
N.S. |
1 | 1.07 | 0.67 | 0.80 | 1.52 | 1.58 | 0.00 | 14.38 | 1.70 |
time (sec) |
N/A | 0.475 | 0.129 | 2.869 | 0.242 | 0.294 | 0.000 | 0.474 | 11.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 233 | 248 | 142 | 160 | 335 | 354 | 0 | 3022 | 383 |
N.S. |
1 | 1.06 | 0.61 | 0.69 | 1.44 | 1.52 | 0.00 | 12.97 | 1.64 |
time (sec) |
N/A | 0.398 | 0.103 | 2.447 | 0.234 | 0.317 | 0.000 | 0.413 | 10.936 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 179 | 98 | 102 | 217 | 254 | 0 | 1986 | 241 |
N.S. |
1 | 1.05 | 0.57 | 0.60 | 1.27 | 1.49 | 0.00 | 11.61 | 1.41 |
time (sec) |
N/A | 0.311 | 0.070 | 2.987 | 0.225 | 0.314 | 0.000 | 0.371 | 10.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 110 | 65 | 61 | 132 | 169 | 0 | 1138 | 156 |
N.S. |
1 | 1.01 | 0.60 | 0.56 | 1.21 | 1.55 | 0.00 | 10.44 | 1.43 |
time (sec) |
N/A | 0.240 | 0.052 | 2.452 | 0.220 | 0.402 | 0.000 | 0.323 | 10.536 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 37 | 42 | 60 | 91 | 0 | 477 | 79 |
N.S. |
1 | 1.00 | 0.77 | 0.88 | 1.25 | 1.90 | 0.00 | 9.94 | 1.65 |
time (sec) |
N/A | 0.172 | 0.025 | 2.760 | 0.209 | 0.371 | 0.000 | 0.300 | 10.335 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 240 | 254 | 170 | 427 | 0 | 538 | 0 | 644 | 0 |
N.S. |
1 | 1.06 | 0.71 | 1.78 | 0.00 | 2.24 | 0.00 | 2.68 | 0.00 |
time (sec) |
N/A | 0.431 | 0.188 | 2.951 | 0.000 | 0.438 | 0.000 | 0.319 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 233 | 244 | 178 | 511 | 0 | 579 | 0 | 358 | 0 |
N.S. |
1 | 1.05 | 0.76 | 2.19 | 0.00 | 2.48 | 0.00 | 1.54 | 0.00 |
time (sec) |
N/A | 0.405 | 0.332 | 2.544 | 0.000 | 0.399 | 0.000 | 0.436 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 236 | 236 | 184 | 517 | 0 | 562 | 0 | 335 | 0 |
N.S. |
1 | 1.00 | 0.78 | 2.19 | 0.00 | 2.38 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.384 | 0.416 | 3.141 | 0.000 | 0.688 | 0.000 | 0.440 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 236 | 239 | 173 | 433 | 0 | 837 | 0 | 323 | 0 |
N.S. |
1 | 1.01 | 0.73 | 1.83 | 0.00 | 3.55 | 0.00 | 1.37 | 0.00 |
time (sec) |
N/A | 0.385 | 0.622 | 2.492 | 0.000 | 0.358 | 0.000 | 0.493 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 301 | 304 | 245 | 652 | 0 | 1205 | 0 | 506 | 0 |
N.S. |
1 | 1.01 | 0.81 | 2.17 | 0.00 | 4.00 | 0.00 | 1.68 | 0.00 |
time (sec) |
N/A | 0.477 | 1.006 | 2.712 | 0.000 | 0.351 | 0.000 | 0.517 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 366 | 381 | 300 | 900 | 0 | 1687 | 0 | 727 | 0 |
N.S. |
1 | 1.04 | 0.82 | 2.46 | 0.00 | 4.61 | 0.00 | 1.99 | 0.00 |
time (sec) |
N/A | 0.566 | 1.445 | 3.251 | 0.000 | 0.398 | 0.000 | 0.669 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 233 | 248 | 131 | 150 | 192 | 173 | 0 | 393 | 194 |
N.S. |
1 | 1.06 | 0.56 | 0.64 | 0.82 | 0.74 | 0.00 | 1.69 | 0.83 |
time (sec) |
N/A | 0.403 | 0.087 | 2.697 | 0.209 | 0.382 | 0.000 | 0.297 | 10.497 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 179 | 87 | 92 | 122 | 117 | 0 | 247 | 131 |
N.S. |
1 | 1.05 | 0.51 | 0.54 | 0.71 | 0.68 | 0.00 | 1.44 | 0.77 |
time (sec) |
N/A | 0.316 | 0.057 | 2.946 | 0.218 | 0.326 | 0.000 | 0.303 | 10.439 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 110 | 54 | 51 | 65 | 73 | 0 | 142 | 85 |
N.S. |
1 | 1.01 | 0.50 | 0.47 | 0.60 | 0.67 | 0.00 | 1.30 | 0.78 |
time (sec) |
N/A | 0.236 | 0.037 | 2.768 | 0.214 | 0.304 | 0.000 | 0.288 | 10.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 35 | 32 | 18 | 49 | 0 | 68 | 54 |
N.S. |
1 | 1.00 | 0.76 | 0.70 | 0.39 | 1.07 | 0.00 | 1.48 | 1.17 |
time (sec) |
N/A | 0.168 | 0.009 | 2.674 | 0.217 | 0.400 | 0.000 | 0.269 | 10.231 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 97 | 81 | 0 | 235 | 0 | 114 | 0 |
N.S. |
1 | 1.00 | 1.15 | 0.96 | 0.00 | 2.80 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.200 | 0.055 | 3.127 | 0.000 | 0.384 | 0.000 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 135 | 162 | 0 | 558 | 0 | 138 | 0 |
N.S. |
1 | 1.00 | 0.97 | 1.17 | 0.00 | 4.01 | 0.00 | 0.99 | 0.00 |
time (sec) |
N/A | 0.270 | 0.188 | 2.777 | 0.000 | 0.403 | 0.000 | 0.351 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 207 | 216 | 174 | 282 | 0 | 870 | 0 | 254 | 0 |
N.S. |
1 | 1.04 | 0.84 | 1.36 | 0.00 | 4.20 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.342 | 0.252 | 3.003 | 0.000 | 0.378 | 0.000 | 0.400 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 269 | 293 | 195 | 444 | 0 | 1242 | 0 | 393 | 0 |
N.S. |
1 | 1.09 | 0.72 | 1.65 | 0.00 | 4.62 | 0.00 | 1.46 | 0.00 |
time (sec) |
N/A | 0.425 | 0.401 | 2.794 | 0.000 | 0.678 | 0.000 | 0.407 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 175 | 87 | 102 | 79 | 141 | 0 | 243 | 174 |
N.S. |
1 | 1.02 | 0.51 | 0.60 | 0.46 | 0.82 | 0.00 | 1.42 | 1.02 |
time (sec) |
N/A | 0.310 | 0.060 | 2.904 | 0.210 | 0.350 | 0.000 | 0.296 | 10.730 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 106 | 51 | 60 | 36 | 98 | 0 | 139 | 116 |
N.S. |
1 | 1.01 | 0.49 | 0.57 | 0.34 | 0.93 | 0.00 | 1.32 | 1.10 |
time (sec) |
N/A | 0.239 | 0.043 | 2.790 | 0.211 | 0.306 | 0.000 | 0.297 | 10.597 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 35 | 42 | 18 | 74 | 0 | 70 | 82 |
N.S. |
1 | 1.00 | 0.76 | 0.91 | 0.39 | 1.61 | 0.00 | 1.52 | 1.78 |
time (sec) |
N/A | 0.165 | 0.008 | 2.854 | 0.230 | 0.301 | 0.000 | 0.285 | 10.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 115 | 126 | 0 | 500 | 0 | 276 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.91 | 0.00 | 3.60 | 0.00 | 1.99 | 0.00 |
time (sec) |
N/A | 0.287 | 0.082 | 2.648 | 0.000 | 0.318 | 0.000 | 0.300 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 196 | 213 | 141 | 225 | 0 | 764 | 0 | 266 | 0 |
N.S. |
1 | 1.09 | 0.72 | 1.15 | 0.00 | 3.90 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.355 | 0.304 | 2.982 | 0.000 | 0.357 | 0.000 | 0.391 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 269 | 290 | 183 | 374 | 0 | 1140 | 0 | 374 | 0 |
N.S. |
1 | 1.08 | 0.68 | 1.39 | 0.00 | 4.24 | 0.00 | 1.39 | 0.00 |
time (sec) |
N/A | 0.439 | 0.413 | 2.827 | 0.000 | 0.362 | 0.000 | 0.410 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 331 | 367 | 227 | 549 | 0 | 1584 | 0 | 528 | 0 |
N.S. |
1 | 1.11 | 0.69 | 1.66 | 0.00 | 4.79 | 0.00 | 1.60 | 0.00 |
time (sec) |
N/A | 0.527 | 0.747 | 2.865 | 0.000 | 0.665 | 0.000 | 0.485 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 393 | 444 | 282 | 757 | 0 | 2106 | 0 | 726 | 0 |
N.S. |
1 | 1.13 | 0.72 | 1.93 | 0.00 | 5.36 | 0.00 | 1.85 | 0.00 |
time (sec) |
N/A | 0.632 | 1.069 | 2.789 | 0.000 | 1.152 | 0.000 | 0.606 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 108 | 53 | 60 | 50 | 131 | 0 | 110 | 147 |
N.S. |
1 | 1.01 | 0.50 | 0.56 | 0.47 | 1.22 | 0.00 | 1.03 | 1.37 |
time (sec) |
N/A | 0.243 | 0.050 | 2.977 | 0.205 | 0.381 | 0.000 | 0.302 | 10.226 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 37 | 42 | 28 | 107 | 0 | 97 | 110 |
N.S. |
1 | 1.00 | 0.77 | 0.88 | 0.58 | 2.23 | 0.00 | 2.02 | 2.29 |
time (sec) |
N/A | 0.171 | 0.017 | 2.975 | 0.215 | 0.623 | 0.000 | 0.299 | 10.185 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 251 | 273 | 135 | 224 | 0 | 788 | 0 | 396 | 0 |
N.S. |
1 | 1.09 | 0.54 | 0.89 | 0.00 | 3.14 | 0.00 | 1.58 | 0.00 |
time (sec) |
N/A | 0.430 | 0.171 | 2.774 | 0.000 | 0.397 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 257 | 289 | 177 | 423 | 0 | 1236 | 0 | 322 | 0 |
N.S. |
1 | 1.12 | 0.69 | 1.65 | 0.00 | 4.81 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.447 | 0.351 | 2.779 | 0.000 | 0.400 | 0.000 | 0.426 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 329 | 366 | 240 | 658 | 0 | 1778 | 0 | 469 | 0 |
N.S. |
1 | 1.11 | 0.73 | 2.00 | 0.00 | 5.40 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.547 | 0.654 | 2.792 | 0.000 | 0.546 | 0.000 | 0.494 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 395 | 443 | 294 | 920 | 0 | 2388 | 0 | 742 | 0 |
N.S. |
1 | 1.12 | 0.74 | 2.33 | 0.00 | 6.05 | 0.00 | 1.88 | 0.00 |
time (sec) |
N/A | 0.633 | 0.993 | 2.927 | 0.000 | 1.101 | 0.000 | 0.566 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 457 | 520 | 361 | 1215 | 0 | 3078 | 0 | 820 | 0 |
N.S. |
1 | 1.14 | 0.79 | 2.66 | 0.00 | 6.74 | 0.00 | 1.79 | 0.00 |
time (sec) |
N/A | 0.714 | 1.457 | 2.985 | 0.000 | 3.133 | 0.000 | 0.760 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 519 | 597 | 437 | 1543 | 0 | 3874 | 0 | 1056 | 0 |
N.S. |
1 | 1.15 | 0.84 | 2.97 | 0.00 | 7.46 | 0.00 | 2.03 | 0.00 |
time (sec) |
N/A | 0.850 | 2.077 | 2.804 | 0.000 | 6.247 | 0.000 | 0.684 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 52 | 58 | 0 | 144 | 0 | 53 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.12 | 0.00 | 2.77 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.168 | 0.014 | 2.580 | 0.000 | 0.381 | 0.000 | 0.278 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 54 | 63 | 0 | 147 | 0 | 49 | 0 |
N.S. |
1 | 1.00 | 1.02 | 1.19 | 0.00 | 2.77 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.174 | 0.119 | 2.291 | 0.000 | 0.340 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 566 | 604 | 95 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.550 | 0.049 | 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 | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 114 | 436 | 1819 | 1156 | 7164 | 1999 | 1202 |
N.S. |
1 | 1.00 | 0.88 | 3.35 | 13.99 | 8.89 | 55.11 | 15.38 | 9.25 |
time (sec) |
N/A | 0.293 | 0.117 | 2.962 | 0.274 | 0.399 | 2.638 | 0.304 | 10.615 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 79 | 183 | 691 | 479 | 2494 | 805 | 486 |
N.S. |
1 | 1.00 | 0.88 | 2.03 | 7.68 | 5.32 | 27.71 | 8.94 | 5.40 |
time (sec) |
N/A | 0.247 | 0.101 | 2.980 | 0.219 | 0.377 | 1.109 | 0.276 | 10.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 45 | 55 | 174 | 136 | 556 | 219 | 141 |
N.S. |
1 | 1.00 | 0.87 | 1.06 | 3.35 | 2.62 | 10.69 | 4.21 | 2.71 |
time (sec) |
N/A | 0.199 | 0.058 | 4.096 | 0.200 | 0.395 | 0.467 | 0.265 | 9.856 |
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 | 54 | 54 | 54 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.187 | 0.066 | 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 | 61 | 61 | 59 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.190 | 0.074 | 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 | 64 | 64 | 63 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.193 | 0.085 | 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(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 63 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.194 | 0.113 | 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 | 100 | 126 | 107 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.26 | 1.07 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.292 | 0.067 | 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(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 95 | 124 | 112 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.31 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.256 | 0.073 | 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 | 95 | 124 | 112 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.31 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.251 | 0.065 | 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 | 95 | 176 | 94 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.85 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.284 | 0.068 | 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 | 113 | 113 | 96 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.208 | 0.043 | 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 | 93 | 93 | 81 | 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 | 0.240 | 0.052 | 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 | 92 | 120 | 108 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.30 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.252 | 0.062 | 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 | 96 | 124 | 112 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.29 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.251 | 0.066 | 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(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 113 | 116 | 97 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.273 | 0.054 | 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 | 107 | 107 | 95 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.278 | 0.050 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |