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 | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 157 | 119 | 87 | 107 | 211 | 122 | 126 | 413 | 113 |
N.S. |
1 | 1.30 | 0.98 | 0.72 | 0.88 | 1.74 | 1.01 | 1.04 | 3.41 | 0.93 |
time (sec) |
N/A | 0.350 | 0.070 | 1.038 | 0.112 | 0.076 | 0.170 | 0.365 | 0.192 | 0.064 |
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 | 24 | 30 | 24 | 20 | 22 | 31 | 19 | 22 | 42 | 19 |
N.S. |
1 | 1.25 | 1.00 | 0.83 | 0.92 | 1.29 | 0.79 | 0.92 | 1.75 | 0.79 |
time (sec) |
N/A | 0.168 | 0.012 | 1.464 | 0.117 | 0.067 | 0.055 | 0.353 | 0.186 | 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 | 39 | 39 | 39 | 32 | 32 | 37 | 42 | 32 | 69 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.82 | 0.95 | 1.08 | 0.82 | 1.77 | 0.87 |
time (sec) |
N/A | 0.174 | 0.020 | 1.011 | 0.123 | 0.076 | 0.067 | 0.395 | 0.209 | 5.374 |
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 | 14 | 20 | 14 | 15 | 14 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 1.43 | 1.00 | 1.07 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.179 | 0.005 | 0.796 | 0.116 | 0.071 | 0.051 | 0.380 | 0.199 | 5.298 |
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 | 33 | 36 | 35 | 27 | 26 | 26 | 39 | 26 | 25 | 30 |
N.S. |
1 | 1.09 | 1.06 | 0.82 | 0.79 | 0.79 | 1.18 | 0.79 | 0.76 | 0.91 |
time (sec) |
N/A | 0.193 | 0.011 | 1.734 | 0.111 | 0.070 | 0.061 | 0.381 | 0.191 | 5.440 |
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 | 58 | 65 | 49 | 42 | 54 | 71 | 61 | 44 | 118 | 53 |
N.S. |
1 | 1.12 | 0.84 | 0.72 | 0.93 | 1.22 | 1.05 | 0.76 | 2.03 | 0.91 |
time (sec) |
N/A | 0.189 | 0.023 | 1.853 | 0.134 | 0.069 | 0.070 | 0.371 | 0.199 | 0.028 |
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 | 40 | 37 | 31 | 30 | 30 | 39 | 30 | 29 | 30 |
N.S. |
1 | 1.08 | 1.00 | 0.84 | 0.81 | 0.81 | 1.05 | 0.81 | 0.78 | 0.81 |
time (sec) |
N/A | 0.184 | 0.009 | 1.957 | 0.112 | 0.071 | 0.056 | 0.360 | 0.187 | 0.027 |
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 | 40 | 37 | 31 | 30 | 30 | 44 | 30 | 29 | 30 |
N.S. |
1 | 1.08 | 1.00 | 0.84 | 0.81 | 0.81 | 1.19 | 0.81 | 0.78 | 0.81 |
time (sec) |
N/A | 0.189 | 0.012 | 1.887 | 0.162 | 0.075 | 0.059 | 0.432 | 0.207 | 0.027 |
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 | 41 | 46 | 41 | 33 | 32 | 32 | 41 | 33 | 31 | 46 |
N.S. |
1 | 1.12 | 1.00 | 0.80 | 0.78 | 0.78 | 1.00 | 0.80 | 0.76 | 1.12 |
time (sec) |
N/A | 0.197 | 0.007 | 1.101 | 0.113 | 0.082 | 0.068 | 0.354 | 0.195 | 5.453 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 122 | 108 | 204 | 0 | 162 | 177 | 202 | 146 | 178 |
N.S. |
1 | 1.17 | 1.04 | 1.96 | 0.00 | 1.56 | 1.70 | 1.94 | 1.40 | 1.71 |
time (sec) |
N/A | 0.460 | 0.098 | 2.353 | 0.000 | 0.099 | 0.472 | 0.418 | 0.286 | 5.505 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 194 | 258 | 113 | 145 | 208 | 0 | 0 | 451 | 177 |
N.S. |
1 | 1.20 | 1.60 | 0.70 | 0.90 | 1.29 | 0.00 | 0.00 | 2.80 | 1.10 |
time (sec) |
N/A | 0.410 | 0.429 | 1.345 | 0.115 | 0.088 | 0.000 | 0.000 | 0.233 | 5.701 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 55 | 46 | 59 | 149 | 326 | 538 | 155 | 58 |
N.S. |
1 | 1.00 | 0.73 | 0.61 | 0.79 | 1.99 | 4.35 | 7.17 | 2.07 | 0.77 |
time (sec) |
N/A | 0.217 | 0.061 | 0.639 | 0.037 | 0.070 | 0.391 | 0.388 | 0.299 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 55 | 46 | 59 | 117 | 94 | 345 | 119 | 58 |
N.S. |
1 | 1.00 | 0.73 | 0.61 | 0.79 | 1.56 | 1.25 | 4.60 | 1.59 | 0.77 |
time (sec) |
N/A | 0.208 | 0.061 | 0.609 | 0.040 | 0.076 | 0.772 | 0.399 | 0.226 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 55 | 46 | 59 | 84 | 94 | 190 | 83 | 58 |
N.S. |
1 | 1.00 | 0.73 | 0.61 | 0.79 | 1.12 | 1.25 | 2.53 | 1.11 | 0.77 |
time (sec) |
N/A | 0.206 | 0.049 | 0.563 | 0.032 | 0.071 | 0.724 | 0.350 | 0.190 | 5.900 |
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 | 73 | 73 | 54 | 46 | 77 | 54 | 102 | 77 | 51 | 58 |
N.S. |
1 | 1.00 | 0.74 | 0.63 | 1.05 | 0.74 | 1.40 | 1.05 | 0.70 | 0.79 |
time (sec) |
N/A | 0.205 | 0.050 | 0.559 | 0.037 | 0.079 | 0.512 | 0.389 | 0.175 | 0.031 |
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 | 71 | 71 | 54 | 47 | 66 | 63 | 94 | 74 | 52 | 58 |
N.S. |
1 | 1.00 | 0.76 | 0.66 | 0.93 | 0.89 | 1.32 | 1.04 | 0.73 | 0.82 |
time (sec) |
N/A | 0.199 | 0.058 | 0.593 | 0.042 | 0.081 | 1.200 | 0.402 | 0.216 | 5.537 |
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 | 71 | 71 | 55 | 46 | 63 | 75 | 252 | 61 | 60 | 58 |
N.S. |
1 | 1.00 | 0.77 | 0.65 | 0.89 | 1.06 | 3.55 | 0.86 | 0.85 | 0.82 |
time (sec) |
N/A | 0.200 | 0.068 | 0.573 | 0.038 | 0.084 | 0.351 | 0.400 | 0.205 | 5.658 |
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 | 73 | 73 | 54 | 48 | 56 | 85 | 376 | 58 | 71 | 52 |
N.S. |
1 | 1.00 | 0.74 | 0.66 | 0.77 | 1.16 | 5.15 | 0.79 | 0.97 | 0.71 |
time (sec) |
N/A | 0.197 | 0.057 | 0.555 | 0.033 | 0.077 | 0.520 | 0.359 | 0.182 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 166 | 173 | 136 | 176 | 365 | 277 | 1411 | 431 | 148 |
N.S. |
1 | 1.00 | 1.04 | 0.82 | 1.06 | 2.20 | 1.67 | 8.50 | 2.60 | 0.89 |
time (sec) |
N/A | 0.317 | 0.153 | 0.934 | 0.034 | 0.075 | 1.171 | 0.317 | 0.185 | 5.535 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 166 | 174 | 136 | 176 | 302 | 277 | 943 | 350 | 148 |
N.S. |
1 | 1.00 | 1.05 | 0.82 | 1.06 | 1.82 | 1.67 | 5.68 | 2.11 | 0.89 |
time (sec) |
N/A | 0.297 | 0.144 | 0.934 | 0.038 | 0.071 | 1.077 | 0.350 | 0.218 | 5.584 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 166 | 172 | 136 | 176 | 237 | 277 | 547 | 269 | 148 |
N.S. |
1 | 1.00 | 1.04 | 0.82 | 1.06 | 1.43 | 1.67 | 3.30 | 1.62 | 0.89 |
time (sec) |
N/A | 0.289 | 0.126 | 0.934 | 0.036 | 0.084 | 0.979 | 0.346 | 0.194 | 0.027 |
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 | 164 | 164 | 172 | 135 | 237 | 176 | 275 | 236 | 192 | 148 |
N.S. |
1 | 1.00 | 1.05 | 0.82 | 1.45 | 1.07 | 1.68 | 1.44 | 1.17 | 0.90 |
time (sec) |
N/A | 0.293 | 0.123 | 0.907 | 0.042 | 0.074 | 0.890 | 0.307 | 0.185 | 0.024 |
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 | 162 | 162 | 171 | 147 | 184 | 185 | 235 | 257 | 194 | 184 |
N.S. |
1 | 1.00 | 1.06 | 0.91 | 1.14 | 1.14 | 1.45 | 1.59 | 1.20 | 1.14 |
time (sec) |
N/A | 0.295 | 0.154 | 0.954 | 0.050 | 0.073 | 5.092 | 0.362 | 0.187 | 5.662 |
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 | 162 | 162 | 170 | 129 | 182 | 197 | 211 | 245 | 201 | 195 |
N.S. |
1 | 1.00 | 1.05 | 0.80 | 1.12 | 1.22 | 1.30 | 1.51 | 1.24 | 1.20 |
time (sec) |
N/A | 0.287 | 0.156 | 0.944 | 0.050 | 0.085 | 5.096 | 0.519 | 0.232 | 0.045 |
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 | 162 | 162 | 172 | 144 | 185 | 206 | 1180 | 239 | 212 | 193 |
N.S. |
1 | 1.00 | 1.06 | 0.89 | 1.14 | 1.27 | 7.28 | 1.48 | 1.31 | 1.19 |
time (sec) |
N/A | 0.291 | 0.151 | 0.981 | 0.040 | 0.099 | 0.616 | 0.357 | 0.216 | 5.676 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 286 | 286 | 397 | 318 | 407 | 727 | 632 | 2883 | 927 | 297 |
N.S. |
1 | 1.00 | 1.39 | 1.11 | 1.42 | 2.54 | 2.21 | 10.08 | 3.24 | 1.04 |
time (sec) |
N/A | 0.475 | 0.415 | 1.072 | 0.036 | 0.081 | 1.553 | 0.407 | 0.179 | 5.758 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 286 | 286 | 396 | 319 | 407 | 619 | 632 | 1970 | 781 | 297 |
N.S. |
1 | 1.00 | 1.38 | 1.12 | 1.42 | 2.16 | 2.21 | 6.89 | 2.73 | 1.04 |
time (sec) |
N/A | 0.422 | 0.407 | 1.170 | 0.043 | 0.078 | 1.367 | 1.082 | 0.181 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 286 | 286 | 396 | 324 | 407 | 512 | 632 | 1177 | 635 | 297 |
N.S. |
1 | 1.00 | 1.38 | 1.13 | 1.42 | 1.79 | 2.21 | 4.12 | 2.22 | 1.04 |
time (sec) |
N/A | 0.414 | 0.316 | 0.990 | 0.042 | 0.073 | 1.306 | 0.379 | 0.216 | 5.755 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 282 | 282 | 396 | 326 | 525 | 408 | 631 | 526 | 493 | 297 |
N.S. |
1 | 1.00 | 1.40 | 1.16 | 1.86 | 1.45 | 2.24 | 1.87 | 1.75 | 1.05 |
time (sec) |
N/A | 0.400 | 0.250 | 0.974 | 0.041 | 0.078 | 1.227 | 0.376 | 0.190 | 5.820 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 280 | 394 | 324 | 415 | 417 | 530 | 639 | 495 | 386 |
N.S. |
1 | 1.00 | 1.41 | 1.16 | 1.48 | 1.49 | 1.89 | 2.28 | 1.77 | 1.38 |
time (sec) |
N/A | 0.420 | 0.357 | 1.039 | 0.041 | 0.085 | 25.506 | 0.374 | 0.195 | 5.610 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 282 | 282 | 395 | 329 | 413 | 429 | 449 | 617 | 502 | 448 |
N.S. |
1 | 1.00 | 1.40 | 1.17 | 1.46 | 1.52 | 1.59 | 2.19 | 1.78 | 1.59 |
time (sec) |
N/A | 0.406 | 0.417 | 1.024 | 0.049 | 0.097 | 24.990 | 0.392 | 0.191 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 278 | 391 | 333 | 413 | 440 | 403 | 611 | 513 | 445 |
N.S. |
1 | 1.00 | 1.41 | 1.20 | 1.49 | 1.58 | 1.45 | 2.20 | 1.85 | 1.60 |
time (sec) |
N/A | 0.411 | 0.357 | 1.025 | 0.037 | 0.087 | 26.489 | 0.428 | 0.231 | 5.810 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 415 | 387 | 504 | 472 | 0 | 6701 | 0 | 1030 | 4862 | 16475 |
N.S. |
1 | 0.93 | 1.21 | 1.14 | 0.00 | 16.15 | 0.00 | 2.48 | 11.72 | 39.70 |
time (sec) |
N/A | 1.035 | 1.936 | 2.623 | 0.000 | 2.002 | 0.000 | 0.420 | 0.668 | 7.749 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 322 | 300 | 364 | 345 | 0 | 2770 | 0 | 797 | 2819 | 8334 |
N.S. |
1 | 0.93 | 1.13 | 1.07 | 0.00 | 8.60 | 0.00 | 2.48 | 8.75 | 25.88 |
time (sec) |
N/A | 0.593 | 1.228 | 1.233 | 0.000 | 0.250 | 0.000 | 0.413 | 0.432 | 6.953 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 233 | 252 | 222 | 0 | 715 | 0 | 445 | 1369 | 709 |
N.S. |
1 | 1.18 | 1.27 | 1.12 | 0.00 | 3.61 | 0.00 | 2.25 | 6.91 | 3.58 |
time (sec) |
N/A | 0.366 | 0.660 | 1.149 | 0.000 | 0.097 | 0.000 | 0.387 | 0.358 | 5.909 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 207 | 198 | 174 | 0 | 2641 | 0 | 414 | 2352 | 4449 |
N.S. |
1 | 1.04 | 0.99 | 0.87 | 0.00 | 13.27 | 0.00 | 2.08 | 11.82 | 22.36 |
time (sec) |
N/A | 0.301 | 0.661 | 1.161 | 0.000 | 0.114 | 0.000 | 0.343 | 0.317 | 0.663 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 310 | 290 | 305 | 297 | 0 | 11293 | 0 | 1492 | 4661 | 23975 |
N.S. |
1 | 0.94 | 0.98 | 0.96 | 0.00 | 36.43 | 0.00 | 4.81 | 15.04 | 77.34 |
time (sec) |
N/A | 0.550 | 0.941 | 1.197 | 0.000 | 0.476 | 0.000 | 0.459 | 2.254 | 8.758 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 414 | 426 | 367 | 419 | 0 | 25912 | 0 | 3302 | 12955 | 58096 |
N.S. |
1 | 1.03 | 0.89 | 1.01 | 0.00 | 62.59 | 0.00 | 7.98 | 31.29 | 140.33 |
time (sec) |
N/A | 0.806 | 1.658 | 1.486 | 0.000 | 3.859 | 0.000 | 0.569 | 25.599 | 10.348 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 602 | 597 | 771 | 644 | 0 | 10077 | 0 | 1785 | 22 | 32541 |
N.S. |
1 | 0.99 | 1.28 | 1.07 | 0.00 | 16.74 | 0.00 | 2.97 | 0.04 | 54.05 |
time (sec) |
N/A | 1.414 | 11.153 | 1.933 | 0.000 | 12.322 | 0.000 | 0.922 | 200.035 | 7.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 445 | 440 | 796 | 542 | 0 | 5256 | 0 | 1398 | 14820 | 21160 |
N.S. |
1 | 0.99 | 1.79 | 1.22 | 0.00 | 11.81 | 0.00 | 3.14 | 33.30 | 47.55 |
time (sec) |
N/A | 0.963 | 7.691 | 1.621 | 0.000 | 0.497 | 0.000 | 0.788 | 13.342 | 8.392 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 363 | 350 | 410 | 454 | 0 | 2396 | 0 | 1193 | 8702 | 5326 |
N.S. |
1 | 0.96 | 1.13 | 1.25 | 0.00 | 6.60 | 0.00 | 3.29 | 23.97 | 14.67 |
time (sec) |
N/A | 0.654 | 3.709 | 1.395 | 0.000 | 0.135 | 0.000 | 0.532 | 12.752 | 9.598 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 283 | 314 | 419 | 0 | 6393 | 0 | 1005 | 13560 | 5740 |
N.S. |
1 | 0.99 | 1.09 | 1.46 | 0.00 | 22.28 | 0.00 | 3.50 | 47.25 | 20.00 |
time (sec) |
N/A | 0.538 | 1.846 | 1.714 | 0.000 | 0.213 | 0.000 | 0.541 | 10.434 | 9.740 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 428 | 430 | 439 | 532 | 0 | 20436 | 0 | 2866 | 21472 | 45676 |
N.S. |
1 | 1.00 | 1.03 | 1.24 | 0.00 | 47.75 | 0.00 | 6.70 | 50.17 | 106.72 |
time (sec) |
N/A | 0.825 | 3.218 | 1.769 | 0.000 | 3.534 | 0.000 | 0.624 | 22.068 | 9.915 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 604 | 577 | 601 | 653 | 0 | 40675 | 0 | 5642 | 22 | 126405 |
N.S. |
1 | 0.96 | 1.00 | 1.08 | 0.00 | 67.34 | 0.00 | 9.34 | 0.04 | 209.28 |
time (sec) |
N/A | 1.368 | 8.069 | 1.924 | 0.000 | 29.359 | 0.000 | 1.364 | 200.040 | 16.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 683 | 674 | 720 | 785 | 0 | 8780 | 0 | 3037 | 22 | 20000 |
N.S. |
1 | 0.99 | 1.05 | 1.15 | 0.00 | 12.86 | 0.00 | 4.45 | 0.03 | 29.28 |
time (sec) |
N/A | 1.426 | 15.050 | 5.862 | 0.000 | 1.798 | 0.000 | 1.702 | 200.034 | 21.171 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 548 | 517 | 506 | 639 | 0 | 5124 | 0 | 2512 | 22 | 13637 |
N.S. |
1 | 0.94 | 0.92 | 1.17 | 0.00 | 9.35 | 0.00 | 4.58 | 0.04 | 24.89 |
time (sec) |
N/A | 1.069 | 13.519 | 2.261 | 0.000 | 0.316 | 0.000 | 0.969 | 200.036 | 16.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 441 | 469 | 4707 | 530 | 0 | 11128 | 0 | 2116 | 22 | 13764 |
N.S. |
1 | 1.06 | 10.67 | 1.20 | 0.00 | 25.23 | 0.00 | 4.80 | 0.05 | 31.21 |
time (sec) |
N/A | 0.969 | 16.351 | 1.769 | 0.000 | 0.475 | 0.000 | 1.023 | 200.037 | 18.769 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 634 | 601 | 580 | 778 | 0 | 30962 | 0 | 5171 | 22 | 23750 |
N.S. |
1 | 0.95 | 0.91 | 1.23 | 0.00 | 48.84 | 0.00 | 8.16 | 0.03 | 37.46 |
time (sec) |
N/A | 1.324 | 12.528 | 3.416 | 0.000 | 19.324 | 0.000 | 1.441 | 200.033 | 51.385 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 834 | 807 | 799 | 1027 | 0 | 55168 | 0 | 9101 | 22 | 132771 |
N.S. |
1 | 0.97 | 0.96 | 1.23 | 0.00 | 66.15 | 0.00 | 10.91 | 0.03 | 159.20 |
time (sec) |
N/A | 2.321 | 13.735 | 54.806 | 0.000 | 104.586 | 0.000 | 2.339 | 200.066 | 15.395 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 479 | 733 | 232 | 662 | 0 | 753 | 0 | 0 | 24 | 711 |
N.S. |
1 | 1.53 | 0.48 | 1.38 | 0.00 | 1.57 | 0.00 | 0.00 | 0.05 | 1.48 |
time (sec) |
N/A | 1.292 | 0.704 | 16.026 | 0.000 | 0.094 | 0.000 | 0.000 | 200.033 | 6.454 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 535 | 802 | 188 | 678 | 0 | 2759 | 0 | 0 | 43 | 4530 |
N.S. |
1 | 1.50 | 0.35 | 1.27 | 0.00 | 5.16 | 0.00 | 0.00 | 0.08 | 8.47 |
time (sec) |
N/A | 1.179 | 0.783 | 4.017 | 0.000 | 0.129 | 0.000 | 0.000 | 0.431 | 6.686 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 330 | 124 | 251 | 0 | 244 | 0 | 614 | 331 | 200 |
N.S. |
1 | 1.51 | 0.57 | 1.15 | 0.00 | 1.11 | 0.00 | 2.80 | 1.51 | 0.91 |
time (sec) |
N/A | 0.669 | 0.708 | 4.816 | 0.000 | 0.084 | 0.000 | 0.910 | 0.190 | 5.762 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 310 | 119 | 247 | 0 | 222 | 0 | 605 | 320 | 191 |
N.S. |
1 | 1.50 | 0.58 | 1.20 | 0.00 | 1.08 | 0.00 | 2.94 | 1.55 | 0.93 |
time (sec) |
N/A | 0.630 | 0.473 | 2.429 | 0.000 | 0.083 | 0.000 | 0.886 | 0.181 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 292 | 114 | 243 | 0 | 234 | 0 | 594 | 311 | 182 |
N.S. |
1 | 1.51 | 0.59 | 1.26 | 0.00 | 1.21 | 0.00 | 3.08 | 1.61 | 0.94 |
time (sec) |
N/A | 0.585 | 0.422 | 2.346 | 0.000 | 0.091 | 0.000 | 0.923 | 0.199 | 0.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 260 | 100 | 212 | 0 | 188 | 0 | 461 | 307 | 116 |
N.S. |
1 | 1.50 | 0.58 | 1.23 | 0.00 | 1.09 | 0.00 | 2.66 | 1.77 | 0.67 |
time (sec) |
N/A | 0.531 | 0.317 | 2.254 | 0.000 | 0.085 | 0.000 | 0.712 | 0.184 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 254 | 100 | 219 | 0 | 199 | 0 | 279 | 307 | 167 |
N.S. |
1 | 1.48 | 0.58 | 1.27 | 0.00 | 1.16 | 0.00 | 1.62 | 1.78 | 0.97 |
time (sec) |
N/A | 0.474 | 0.225 | 2.108 | 0.000 | 0.087 | 0.000 | 0.567 | 0.220 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 294 | 114 | 253 | 0 | 262 | 0 | 594 | 362 | 182 |
N.S. |
1 | 1.52 | 0.59 | 1.31 | 0.00 | 1.36 | 0.00 | 3.08 | 1.88 | 0.94 |
time (sec) |
N/A | 0.512 | 0.625 | 2.516 | 0.000 | 0.087 | 0.000 | 0.548 | 0.225 | 5.591 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 316 | 119 | 256 | 0 | 276 | 0 | 599 | 730 | 187 |
N.S. |
1 | 1.53 | 0.58 | 1.24 | 0.00 | 1.34 | 0.00 | 2.91 | 3.54 | 0.91 |
time (sec) |
N/A | 0.606 | 0.746 | 2.378 | 0.000 | 0.090 | 0.000 | 0.597 | 0.229 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 345 | 136 | 274 | 0 | 297 | 0 | 633 | 980 | 216 |
N.S. |
1 | 1.46 | 0.58 | 1.16 | 0.00 | 1.26 | 0.00 | 2.68 | 4.15 | 0.92 |
time (sec) |
N/A | 0.678 | 1.279 | 2.378 | 0.000 | 0.090 | 0.000 | 0.784 | 0.226 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 327 | 129 | 270 | 0 | 274 | 0 | 624 | 969 | 208 |
N.S. |
1 | 1.47 | 0.58 | 1.21 | 0.00 | 1.23 | 0.00 | 2.80 | 4.35 | 0.93 |
time (sec) |
N/A | 0.640 | 1.199 | 2.461 | 0.000 | 0.087 | 0.000 | 0.845 | 0.235 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 309 | 129 | 270 | 0 | 274 | 0 | 622 | 969 | 208 |
N.S. |
1 | 1.47 | 0.61 | 1.29 | 0.00 | 1.30 | 0.00 | 2.96 | 4.61 | 0.99 |
time (sec) |
N/A | 0.597 | 1.007 | 2.191 | 0.000 | 0.092 | 0.000 | 0.804 | 0.227 | 5.620 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 307 | 129 | 244 | 0 | 275 | 0 | 622 | 969 | 208 |
N.S. |
1 | 1.46 | 0.61 | 1.16 | 0.00 | 1.31 | 0.00 | 2.96 | 4.61 | 0.99 |
time (sec) |
N/A | 0.574 | 0.684 | 3.738 | 0.000 | 0.089 | 0.000 | 0.738 | 0.232 | 5.653 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 315 | 129 | 249 | 0 | 274 | 0 | 622 | 969 | 207 |
N.S. |
1 | 1.50 | 0.61 | 1.19 | 0.00 | 1.30 | 0.00 | 2.96 | 4.61 | 0.99 |
time (sec) |
N/A | 0.540 | 0.784 | 2.558 | 0.000 | 0.087 | 0.000 | 0.548 | 0.215 | 5.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 333 | 138 | 283 | 0 | 321 | 0 | 633 | 1114 | 217 |
N.S. |
1 | 1.49 | 0.62 | 1.27 | 0.00 | 1.44 | 0.00 | 2.84 | 5.00 | 0.97 |
time (sec) |
N/A | 0.615 | 1.333 | 2.259 | 0.000 | 0.096 | 0.000 | 0.612 | 0.224 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 351 | 143 | 293 | 0 | 366 | 0 | 638 | 1498 | 226 |
N.S. |
1 | 1.49 | 0.61 | 1.24 | 0.00 | 1.55 | 0.00 | 2.70 | 6.35 | 0.96 |
time (sec) |
N/A | 0.652 | 1.551 | 2.272 | 0.000 | 0.090 | 0.000 | 0.581 | 0.200 | 0.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 362 | 143 | 283 | 0 | 365 | 0 | 642 | 1653 | 245 |
N.S. |
1 | 1.43 | 0.57 | 1.12 | 0.00 | 1.44 | 0.00 | 2.54 | 6.53 | 0.97 |
time (sec) |
N/A | 0.682 | 2.055 | 2.383 | 0.000 | 0.093 | 0.000 | 0.818 | 0.215 | 5.713 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 344 | 141 | 282 | 0 | 330 | 0 | 642 | 1653 | 245 |
N.S. |
1 | 1.43 | 0.59 | 1.18 | 0.00 | 1.38 | 0.00 | 2.68 | 6.89 | 1.02 |
time (sec) |
N/A | 0.653 | 1.803 | 2.336 | 0.000 | 0.093 | 0.000 | 0.753 | 0.212 | 5.619 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 344 | 143 | 283 | 0 | 362 | 0 | 642 | 1653 | 245 |
N.S. |
1 | 1.43 | 0.60 | 1.18 | 0.00 | 1.51 | 0.00 | 2.68 | 6.89 | 1.02 |
time (sec) |
N/A | 0.636 | 1.825 | 2.245 | 0.000 | 0.089 | 0.000 | 0.768 | 0.209 | 5.650 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 350 | 143 | 282 | 0 | 365 | 0 | 640 | 1653 | 245 |
N.S. |
1 | 1.46 | 0.60 | 1.18 | 0.00 | 1.52 | 0.00 | 2.67 | 6.89 | 1.02 |
time (sec) |
N/A | 0.653 | 1.702 | 2.387 | 0.000 | 0.085 | 0.000 | 0.807 | 0.203 | 5.824 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 350 | 141 | 324 | 0 | 335 | 0 | 642 | 1653 | 245 |
N.S. |
1 | 1.46 | 0.59 | 1.35 | 0.00 | 1.40 | 0.00 | 2.68 | 6.89 | 1.02 |
time (sec) |
N/A | 0.650 | 0.786 | 3.602 | 0.000 | 0.088 | 0.000 | 0.797 | 0.205 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 350 | 143 | 324 | 0 | 365 | 0 | 642 | 1653 | 246 |
N.S. |
1 | 1.46 | 0.60 | 1.35 | 0.00 | 1.52 | 0.00 | 2.68 | 6.89 | 1.02 |
time (sec) |
N/A | 0.650 | 0.844 | 3.805 | 0.000 | 0.088 | 0.000 | 0.589 | 0.204 | 5.625 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 368 | 148 | 295 | 0 | 407 | 0 | 651 | 1882 | 252 |
N.S. |
1 | 1.45 | 0.58 | 1.17 | 0.00 | 1.61 | 0.00 | 2.57 | 7.44 | 1.00 |
time (sec) |
N/A | 0.666 | 2.117 | 2.366 | 0.000 | 0.091 | 0.000 | 0.610 | 0.201 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 225 | 295 | 391 | 0 | 787 | 887 | 393 | 22 | 632 |
N.S. |
1 | 0.91 | 1.19 | 1.58 | 0.00 | 3.17 | 3.58 | 1.58 | 0.09 | 2.55 |
time (sec) |
N/A | 0.408 | 2.308 | 1.060 | 0.000 | 0.135 | 1.099 | 0.362 | 200.032 | 6.280 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 178 | 195 | 229 | 0 | 505 | 473 | 236 | 589 | 332 |
N.S. |
1 | 1.08 | 1.18 | 1.39 | 0.00 | 3.06 | 2.87 | 1.43 | 3.57 | 2.01 |
time (sec) |
N/A | 0.343 | 1.622 | 0.971 | 0.000 | 0.103 | 0.952 | 0.324 | 1.597 | 6.452 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 114 | 115 | 115 | 0 | 297 | 224 | 121 | 295 | 145 |
N.S. |
1 | 0.99 | 1.00 | 1.00 | 0.00 | 2.58 | 1.95 | 1.05 | 2.57 | 1.26 |
time (sec) |
N/A | 0.237 | 0.669 | 0.899 | 0.000 | 0.098 | 0.726 | 0.304 | 0.209 | 6.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 75 | 65 | 0 | 177 | 119 | 66 | 123 | 63 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.00 | 2.36 | 1.59 | 0.88 | 1.64 | 0.84 |
time (sec) |
N/A | 0.192 | 0.312 | 0.881 | 0.000 | 0.099 | 0.372 | 0.325 | 0.194 | 6.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 158 | 175 | 236 | 0 | 992 | 0 | 0 | 3976 | 0 |
N.S. |
1 | 1.04 | 1.15 | 1.55 | 0.00 | 6.53 | 0.00 | 0.00 | 26.16 | 0.00 |
time (sec) |
N/A | 0.365 | 0.940 | 1.118 | 0.000 | 0.704 | 0.000 | 0.000 | 0.354 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 167 | 151 | 675 | 0 | 1456 | 0 | 0 | 702 | 0 |
N.S. |
1 | 1.04 | 0.94 | 4.22 | 0.00 | 9.10 | 0.00 | 0.00 | 4.39 | 0.00 |
time (sec) |
N/A | 0.330 | 1.339 | 1.089 | 0.000 | 1.080 | 0.000 | 0.000 | 0.386 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 149 | 1138 | 0 | 918 | 0 | 693 | 1033 | 0 |
N.S. |
1 | 1.00 | 0.97 | 7.44 | 0.00 | 6.00 | 0.00 | 4.53 | 6.75 | 0.00 |
time (sec) |
N/A | 0.287 | 10.130 | 1.178 | 0.000 | 0.469 | 0.000 | 0.378 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 229 | 206 | 1253 | 0 | 1950 | 0 | 1992 | 2879 | 0 |
N.S. |
1 | 1.07 | 0.96 | 5.83 | 0.00 | 9.07 | 0.00 | 9.27 | 13.39 | 0.00 |
time (sec) |
N/A | 0.354 | 10.357 | 1.339 | 0.000 | 2.306 | 0.000 | 0.449 | 1.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 325 | 276 | 2525 | 0 | 3780 | 0 | 0 | 6410 | 0 |
N.S. |
1 | 1.06 | 0.90 | 8.20 | 0.00 | 12.27 | 0.00 | 0.00 | 20.81 | 0.00 |
time (sec) |
N/A | 0.511 | 10.528 | 1.362 | 0.000 | 10.977 | 0.000 | 0.000 | 11.385 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 321 | 267 | 509 | 754 | 0 | 1359 | 3259 | 737 | 22 | 0 |
N.S. |
1 | 0.83 | 1.59 | 2.35 | 0.00 | 4.23 | 10.15 | 2.30 | 0.07 | 0.00 |
time (sec) |
N/A | 0.440 | 5.599 | 1.005 | 0.000 | 0.166 | 1.046 | 0.326 | 200.028 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 221 | 337 | 460 | 0 | 899 | 1656 | 465 | 22 | 0 |
N.S. |
1 | 0.97 | 1.47 | 2.01 | 0.00 | 3.93 | 7.23 | 2.03 | 0.10 | 0.00 |
time (sec) |
N/A | 0.383 | 3.133 | 1.116 | 0.000 | 0.141 | 0.998 | 0.308 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 157 | 192 | 233 | 0 | 529 | 711 | 250 | 589 | 305 |
N.S. |
1 | 0.98 | 1.19 | 1.45 | 0.00 | 3.29 | 4.42 | 1.55 | 3.66 | 1.89 |
time (sec) |
N/A | 0.261 | 1.628 | 1.034 | 0.000 | 0.104 | 0.762 | 0.273 | 0.404 | 5.751 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 118 | 104 | 104 | 0 | 277 | 539 | 121 | 252 | 103 |
N.S. |
1 | 1.05 | 0.93 | 0.93 | 0.00 | 2.47 | 4.81 | 1.08 | 2.25 | 0.92 |
time (sec) |
N/A | 0.225 | 0.681 | 0.839 | 0.000 | 0.092 | 1.102 | 0.272 | 0.192 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 271 | 247 | 383 | 0 | 1523 | 0 | 0 | 9833 | 0 |
N.S. |
1 | 1.08 | 0.98 | 1.52 | 0.00 | 6.04 | 0.00 | 0.00 | 39.02 | 0.00 |
time (sec) |
N/A | 0.600 | 1.728 | 1.076 | 0.000 | 112.406 | 0.000 | 0.000 | 0.945 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 239 | 214 | 619 | 0 | 1583 | 0 | 0 | 828 | 0 |
N.S. |
1 | 1.05 | 0.94 | 2.73 | 0.00 | 6.97 | 0.00 | 0.00 | 3.65 | 0.00 |
time (sec) |
N/A | 0.513 | 10.357 | 1.087 | 0.000 | 7.277 | 0.000 | 0.000 | 0.383 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 236 | 245 | 311 | 1174 | 0 | 2711 | 0 | 794 | 2243 | 0 |
N.S. |
1 | 1.04 | 1.32 | 4.97 | 0.00 | 11.49 | 0.00 | 3.36 | 9.50 | 0.00 |
time (sec) |
N/A | 0.464 | 10.689 | 1.176 | 0.000 | 11.050 | 0.000 | 0.413 | 0.347 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 355 | 421 | 3085 | 0 | 4911 | 0 | 2059 | 4565 | 0 |
N.S. |
1 | 1.21 | 1.44 | 10.53 | 0.00 | 16.76 | 0.00 | 7.03 | 15.58 | 0.00 |
time (sec) |
N/A | 0.638 | 11.131 | 1.174 | 0.000 | 155.044 | 0.000 | 3.865 | 1.142 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 246 | 222 | 5074 | 0 | 2570 | 0 | 0 | 3483 | 0 |
N.S. |
1 | 1.09 | 0.99 | 22.55 | 0.00 | 11.42 | 0.00 | 0.00 | 15.48 | 0.00 |
time (sec) |
N/A | 0.374 | 10.557 | 1.316 | 0.000 | 9.587 | 0.000 | 0.000 | 11.340 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 296 | 322 | 275 | 5189 | 0 | 4830 | 0 | 8409 | 7679 | 0 |
N.S. |
1 | 1.09 | 0.93 | 17.53 | 0.00 | 16.32 | 0.00 | 28.41 | 25.94 | 0.00 |
time (sec) |
N/A | 0.450 | 11.058 | 1.747 | 0.000 | 41.088 | 0.000 | 1.067 | 68.128 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 409 | 418 | 349 | 10397 | 0 | 8058 | 0 | 14486 | 22 | 0 |
N.S. |
1 | 1.02 | 0.85 | 25.42 | 0.00 | 19.70 | 0.00 | 35.42 | 0.05 | 0.00 |
time (sec) |
N/A | 0.604 | 11.643 | 2.068 | 0.000 | 108.810 | 0.000 | 10.498 | 200.044 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 400 | 311 | 280 | 1207 | 0 | 2119 | 11123 | 1193 | 22 | 0 |
N.S. |
1 | 0.78 | 0.70 | 3.02 | 0.00 | 5.30 | 27.81 | 2.98 | 0.06 | 0.00 |
time (sec) |
N/A | 0.492 | 10.571 | 1.063 | 0.000 | 0.299 | 1.288 | 0.461 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 264 | 541 | 661 | 0 | 1425 | 5671 | 770 | 22 | 0 |
N.S. |
1 | 0.90 | 1.85 | 2.26 | 0.00 | 4.86 | 19.35 | 2.63 | 0.08 | 0.00 |
time (sec) |
N/A | 0.417 | 7.215 | 1.151 | 0.000 | 0.213 | 1.093 | 0.415 | 200.052 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 200 | 311 | 314 | 0 | 857 | 2428 | 423 | 987 | 0 |
N.S. |
1 | 0.97 | 1.50 | 1.52 | 0.00 | 4.14 | 11.73 | 2.04 | 4.77 | 0.00 |
time (sec) |
N/A | 0.309 | 3.197 | 0.943 | 0.000 | 0.133 | 0.864 | 0.340 | 2.428 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 161 | 150 | 143 | 0 | 425 | 1732 | 206 | 431 | 143 |
N.S. |
1 | 1.08 | 1.01 | 0.96 | 0.00 | 2.85 | 11.62 | 1.38 | 2.89 | 0.96 |
time (sec) |
N/A | 0.264 | 1.539 | 0.886 | 0.000 | 0.102 | 1.851 | 0.220 | 0.381 | 5.434 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 459 | 490 | 443 | 715 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.07 | 0.97 | 1.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 1.043 | 3.686 | 1.144 | 0.000 | 0.000 | 0.000 | 0.000 | 200.079 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | F(-1) | F | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 388 | 411 | 370 | 916 | 0 | 0 | 0 | 0 | 2264 | 0 |
N.S. |
1 | 1.06 | 0.95 | 2.36 | 0.00 | 0.00 | 0.00 | 0.00 | 5.84 | 0.00 |
time (sec) |
N/A | 0.952 | 10.789 | 1.247 | 0.000 | 0.000 | 0.000 | 0.000 | 1.004 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 349 | 445 | 1431 | 0 | 3019 | 0 | 1500 | 2452 | 0 |
N.S. |
1 | 1.05 | 1.34 | 4.32 | 0.00 | 9.12 | 0.00 | 4.53 | 7.41 | 0.00 |
time (sec) |
N/A | 0.733 | 11.249 | 1.415 | 0.000 | 65.414 | 0.000 | 0.358 | 2.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 337 | 353 | 559 | 2385 | 0 | 5131 | 0 | 2152 | 4902 | 0 |
N.S. |
1 | 1.05 | 1.66 | 7.08 | 0.00 | 15.23 | 0.00 | 6.39 | 14.55 | 0.00 |
time (sec) |
N/A | 0.718 | 12.116 | 1.432 | 0.000 | 101.437 | 0.000 | 3.938 | 2.529 | 0.000 |