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 | B | F | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 175 | 247 | 314 | 0 | 7993 | 0 | 0 | 9430 | 0 |
N.S. |
1 | 1.14 | 1.61 | 2.05 | 0.00 | 52.24 | 0.00 | 0.00 | 61.63 | 0.00 |
time (sec) |
N/A | 0.377 | 3.166 | 2.931 | 0.000 | 0.449 | 0.000 | 0.000 | 0.437 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 57 | 62 | 92 | 327 | 0 | 108 | 407 | 433 |
N.S. |
1 | 1.00 | 1.19 | 1.29 | 1.92 | 6.81 | 0.00 | 2.25 | 8.48 | 9.02 |
time (sec) |
N/A | 0.287 | 0.015 | 4.015 | 0.044 | 0.192 | 0.000 | 0.153 | 0.194 | 2.319 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 46 | 43 | 49 | 78 | 1072 | 80 | 119 | 281 | 173 |
N.S. |
1 | 0.94 | 0.88 | 1.00 | 1.59 | 21.88 | 1.63 | 2.43 | 5.73 | 3.53 |
time (sec) |
N/A | 0.258 | 0.063 | 2.439 | 0.130 | 0.231 | 0.296 | 0.149 | 0.213 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 38 | 41 | 52 | 42 | 155 | 0 | 72 | 186 | 163 |
N.S. |
1 | 1.19 | 1.28 | 1.62 | 1.31 | 4.84 | 0.00 | 2.25 | 5.81 | 5.09 |
time (sec) |
N/A | 0.281 | 0.009 | 1.648 | 0.040 | 0.177 | 0.000 | 0.135 | 0.220 | 2.256 |
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 | 29 | 27 | 29 | 28 | 27 | 359 | 42 | 83 | 38 | 72 |
N.S. |
1 | 0.93 | 1.00 | 0.97 | 0.93 | 12.38 | 1.45 | 2.86 | 1.31 | 2.48 |
time (sec) |
N/A | 0.226 | 0.011 | 0.929 | 0.035 | 0.291 | 0.139 | 0.119 | 0.212 | 2.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 16 | 23 | 36 | 0 | 23 | 50 | 23 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.53 | 2.40 | 0.00 | 1.53 | 3.33 | 1.53 |
time (sec) |
N/A | 0.160 | 0.001 | 0.227 | 0.036 | 0.253 | 0.000 | 0.112 | 0.211 | 2.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 37 | 36 | 24 | 65 | 69 | 0 | 55 | 74 | 167 |
N.S. |
1 | 1.32 | 1.29 | 0.86 | 2.32 | 2.46 | 0.00 | 1.96 | 2.64 | 5.96 |
time (sec) |
N/A | 0.258 | 0.025 | 0.659 | 0.116 | 0.291 | 0.000 | 0.126 | 0.201 | 0.153 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 26 | 41 | 30 | 47 | 39 | 0 | 30 | 64 | 25 |
N.S. |
1 | 1.44 | 2.28 | 1.67 | 2.61 | 2.17 | 0.00 | 1.67 | 3.56 | 1.39 |
time (sec) |
N/A | 0.271 | 0.011 | 1.135 | 0.040 | 0.284 | 0.000 | 0.134 | 0.218 | 2.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 41 | 43 | 37 | 108 | 378 | 0 | 84 | 212 | 76 |
N.S. |
1 | 1.32 | 1.39 | 1.19 | 3.48 | 12.19 | 0.00 | 2.71 | 6.84 | 2.45 |
time (sec) |
N/A | 0.260 | 0.043 | 1.723 | 0.044 | 0.229 | 0.000 | 0.170 | 0.221 | 2.230 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 38 | 49 | 64 | 170 | 140 | 0 | 70 | 136 | 161 |
N.S. |
1 | 1.12 | 1.44 | 1.88 | 5.00 | 4.12 | 0.00 | 2.06 | 4.00 | 4.74 |
time (sec) |
N/A | 0.273 | 0.011 | 2.914 | 0.046 | 0.200 | 0.000 | 0.152 | 0.201 | 2.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 66 | 53 | 67 | 251 | 1099 | 0 | 120 | 389 | 179 |
N.S. |
1 | 1.29 | 1.04 | 1.31 | 4.92 | 21.55 | 0.00 | 2.35 | 7.63 | 3.51 |
time (sec) |
N/A | 0.285 | 0.225 | 4.649 | 0.047 | 0.227 | 0.000 | 0.185 | 0.221 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 75 | 395 | 93 | 649 | 721 | 0 | 278 | 718 | 1022 |
N.S. |
1 | 0.97 | 5.13 | 1.21 | 8.43 | 9.36 | 0.00 | 3.61 | 9.32 | 13.27 |
time (sec) |
N/A | 0.342 | 1.517 | 29.623 | 0.057 | 0.216 | 0.000 | 0.167 | 0.206 | 0.166 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 71 | 107 | 81 | 333 | 2591 | 129 | 244 | 445 | 349 |
N.S. |
1 | 0.92 | 1.39 | 1.05 | 4.32 | 33.65 | 1.68 | 3.17 | 5.78 | 4.53 |
time (sec) |
N/A | 0.314 | 0.207 | 20.750 | 0.127 | 0.257 | 0.662 | 0.169 | 0.231 | 2.349 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 61 | 281 | 83 | 325 | 435 | 0 | 196 | 372 | 513 |
N.S. |
1 | 1.03 | 4.76 | 1.41 | 5.51 | 7.37 | 0.00 | 3.32 | 6.31 | 8.69 |
time (sec) |
N/A | 0.315 | 1.107 | 14.467 | 0.053 | 0.208 | 0.000 | 0.149 | 0.251 | 0.113 |
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 | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 46 | 82 | 42 | 55 | 1180 | 63 | 162 | 56 | 182 |
N.S. |
1 | 0.96 | 1.71 | 0.88 | 1.15 | 24.58 | 1.31 | 3.38 | 1.17 | 3.79 |
time (sec) |
N/A | 0.251 | 0.089 | 9.645 | 0.033 | 0.283 | 0.303 | 0.135 | 0.219 | 2.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 44 | 50 | 45 | 120 | 176 | 0 | 79 | 154 | 163 |
N.S. |
1 | 1.10 | 1.25 | 1.12 | 3.00 | 4.40 | 0.00 | 1.98 | 3.85 | 4.08 |
time (sec) |
N/A | 0.231 | 0.273 | 0.466 | 0.041 | 0.317 | 0.000 | 0.117 | 0.213 | 2.255 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 55 | 84 | 50 | 161 | 665 | 0 | 150 | 613 | 308 |
N.S. |
1 | 1.04 | 1.58 | 0.94 | 3.04 | 12.55 | 0.00 | 2.83 | 11.57 | 5.81 |
time (sec) |
N/A | 0.287 | 0.157 | 6.618 | 0.142 | 0.358 | 0.000 | 0.145 | 0.216 | 0.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 40 | 82 | 64 | 71 | 106 | 0 | 68 | 115 | 60 |
N.S. |
1 | 1.11 | 2.28 | 1.78 | 1.97 | 2.94 | 0.00 | 1.89 | 3.19 | 1.67 |
time (sec) |
N/A | 0.325 | 2.048 | 6.932 | 0.048 | 0.298 | 0.000 | 0.146 | 0.209 | 2.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 64 | 82 | 64 | 206 | 637 | 0 | 148 | 458 | 240 |
N.S. |
1 | 1.16 | 1.49 | 1.16 | 3.75 | 11.58 | 0.00 | 2.69 | 8.33 | 4.36 |
time (sec) |
N/A | 0.298 | 0.146 | 10.510 | 0.129 | 0.271 | 0.000 | 0.181 | 0.200 | 0.200 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 50 | 160 | 94 | 268 | 201 | 0 | 100 | 170 | 183 |
N.S. |
1 | 1.09 | 3.48 | 2.04 | 5.83 | 4.37 | 0.00 | 2.17 | 3.70 | 3.98 |
time (sec) |
N/A | 0.324 | 0.911 | 16.008 | 0.052 | 0.191 | 0.000 | 0.167 | 0.205 | 2.247 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 69 | 77 | 84 | 282 | 1252 | 0 | 150 | 438 | 207 |
N.S. |
1 | 1.33 | 1.48 | 1.62 | 5.42 | 24.08 | 0.00 | 2.88 | 8.42 | 3.98 |
time (sec) |
N/A | 0.296 | 0.173 | 23.177 | 0.042 | 0.332 | 0.000 | 0.215 | 0.225 | 2.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 66 | 256 | 163 | 613 | 425 | 0 | 170 | 302 | 511 |
N.S. |
1 | 1.03 | 4.00 | 2.55 | 9.58 | 6.64 | 0.00 | 2.66 | 4.72 | 7.98 |
time (sec) |
N/A | 0.345 | 2.687 | 32.896 | 0.049 | 0.205 | 0.000 | 0.184 | 0.215 | 2.269 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 105 | 107 | 132 | 696 | 2548 | 0 | 219 | 675 | 377 |
N.S. |
1 | 1.22 | 1.24 | 1.53 | 8.09 | 29.63 | 0.00 | 2.55 | 7.85 | 4.38 |
time (sec) |
N/A | 0.316 | 0.351 | 44.931 | 0.053 | 0.238 | 0.000 | 0.236 | 0.216 | 2.391 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 105 | 301 | 135 | 1453 | 1323 | 0 | 475 | 1027 | 1834 |
N.S. |
1 | 0.95 | 2.74 | 1.23 | 13.21 | 12.03 | 0.00 | 4.32 | 9.34 | 16.67 |
time (sec) |
N/A | 0.369 | 5.104 | 138.757 | 0.053 | 0.335 | 0.000 | 0.188 | 0.229 | 2.475 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 94 | 128 | 113 | 652 | 4658 | 178 | 387 | 605 | 573 |
N.S. |
1 | 0.91 | 1.24 | 1.10 | 6.33 | 45.22 | 1.73 | 3.76 | 5.87 | 5.56 |
time (sec) |
N/A | 0.301 | 0.505 | 106.646 | 0.149 | 0.484 | 1.254 | 0.192 | 0.242 | 2.512 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 91 | 479 | 124 | 788 | 881 | 0 | 359 | 613 | 1133 |
N.S. |
1 | 0.99 | 5.21 | 1.35 | 8.57 | 9.58 | 0.00 | 3.90 | 6.66 | 12.32 |
time (sec) |
N/A | 0.405 | 2.413 | 78.327 | 0.051 | 0.211 | 0.000 | 0.177 | 0.213 | 0.186 |
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 | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 64 | 100 | 59 | 85 | 2519 | 87 | 271 | 72 | 347 |
N.S. |
1 | 0.90 | 1.41 | 0.83 | 1.20 | 35.48 | 1.23 | 3.82 | 1.01 | 4.89 |
time (sec) |
N/A | 0.304 | 0.843 | 58.924 | 0.037 | 0.367 | 0.605 | 0.152 | 0.203 | 0.185 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 74 | 102 | 83 | 332 | 470 | 0 | 182 | 319 | 502 |
N.S. |
1 | 1.01 | 1.40 | 1.14 | 4.55 | 6.44 | 0.00 | 2.49 | 4.37 | 6.88 |
time (sec) |
N/A | 0.259 | 0.703 | 0.856 | 0.050 | 0.315 | 0.000 | 0.122 | 0.248 | 2.442 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 83 | 114 | 86 | 300 | 2376 | 0 | 283 | 1544 | 360 |
N.S. |
1 | 0.99 | 1.36 | 1.02 | 3.57 | 28.29 | 0.00 | 3.37 | 18.38 | 4.29 |
time (sec) |
N/A | 0.312 | 0.447 | 44.254 | 0.133 | 0.281 | 0.000 | 0.151 | 0.239 | 2.612 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 62 | 162 | 111 | 172 | 359 | 0 | 135 | 264 | 234 |
N.S. |
1 | 1.02 | 2.66 | 1.82 | 2.82 | 5.89 | 0.00 | 2.21 | 4.33 | 3.84 |
time (sec) |
N/A | 0.377 | 4.330 | 44.640 | 0.047 | 0.202 | 0.000 | 0.164 | 0.259 | 0.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 83 | 110 | 110 | 314 | 1701 | 0 | 247 | 803 | 324 |
N.S. |
1 | 1.02 | 1.36 | 1.36 | 3.88 | 21.00 | 0.00 | 3.05 | 9.91 | 4.00 |
time (sec) |
N/A | 0.344 | 0.876 | 45.079 | 0.125 | 0.287 | 0.000 | 0.200 | 0.217 | 2.845 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 61 | 343 | 149 | 366 | 354 | 0 | 158 | 249 | 260 |
N.S. |
1 | 1.02 | 5.72 | 2.48 | 6.10 | 5.90 | 0.00 | 2.63 | 4.15 | 4.33 |
time (sec) |
N/A | 0.351 | 2.327 | 62.615 | 0.058 | 0.182 | 0.000 | 0.186 | 0.229 | 2.331 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 94 | 101 | 119 | 422 | 1830 | 0 | 227 | 842 | 384 |
N.S. |
1 | 1.16 | 1.25 | 1.47 | 5.21 | 22.59 | 0.00 | 2.80 | 10.40 | 4.74 |
time (sec) |
N/A | 0.328 | 0.479 | 87.280 | 0.131 | 0.295 | 0.000 | 0.222 | 0.219 | 2.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 71 | 303 | 199 | 826 | 521 | 0 | 213 | 347 | 547 |
N.S. |
1 | 1.03 | 4.39 | 2.88 | 11.97 | 7.55 | 0.00 | 3.09 | 5.03 | 7.93 |
time (sec) |
N/A | 0.350 | 1.878 | 116.032 | 0.048 | 0.231 | 0.000 | 0.203 | 0.228 | 2.498 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 94 | 98 | 149 | 727 | 2632 | 0 | 242 | 701 | 411 |
N.S. |
1 | 1.22 | 1.27 | 1.94 | 9.44 | 34.18 | 0.00 | 3.14 | 9.10 | 5.34 |
time (sec) |
N/A | 0.321 | 0.539 | 156.150 | 0.062 | 0.232 | 0.000 | 0.266 | 0.237 | 2.565 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 109 | 175 | 129 | 703 | 941 | 0 | 334 | 538 | 1083 |
N.S. |
1 | 0.98 | 1.58 | 1.16 | 6.33 | 8.48 | 0.00 | 3.01 | 4.85 | 9.76 |
time (sec) |
N/A | 0.293 | 3.255 | 1.234 | 0.047 | 0.261 | 0.000 | 0.130 | 0.203 | 0.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 158 | 269 | 185 | 1277 | 1652 | 0 | 537 | 811 | 1952 |
N.S. |
1 | 0.97 | 1.65 | 1.13 | 7.83 | 10.13 | 0.00 | 3.29 | 4.98 | 11.98 |
time (sec) |
N/A | 0.339 | 5.070 | 2.431 | 0.058 | 0.222 | 0.000 | 0.135 | 0.210 | 0.293 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F(-2) | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 63 | 98 | 183 | 131 | 736 | 0 | 0 | 1292 | 421 |
N.S. |
1 | 0.90 | 1.40 | 2.61 | 1.87 | 10.51 | 0.00 | 0.00 | 18.46 | 6.01 |
time (sec) |
N/A | 0.312 | 0.199 | 4.059 | 0.120 | 0.319 | 0.000 | 0.000 | 0.270 | 2.615 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 70 | 196 | 184 | 637 | 683 | 0 | 94 | 564 | 183 |
N.S. |
1 | 1.19 | 3.32 | 3.12 | 10.80 | 11.58 | 0.00 | 1.59 | 9.56 | 3.10 |
time (sec) |
N/A | 0.360 | 1.162 | 2.655 | 0.262 | 0.322 | 0.000 | 0.588 | 0.260 | 2.716 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 41 | 115 | 77 | 112 | 0 | 0 | 213 | 238 |
N.S. |
1 | 1.00 | 0.91 | 2.56 | 1.71 | 2.49 | 0.00 | 0.00 | 4.73 | 5.29 |
time (sec) |
N/A | 0.295 | 0.091 | 1.611 | 0.150 | 0.350 | 0.000 | 0.000 | 0.230 | 0.325 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 54 | 174 | 104 | 291 | 419 | 0 | 66 | 124 | 105 |
N.S. |
1 | 1.17 | 3.78 | 2.26 | 6.33 | 9.11 | 0.00 | 1.43 | 2.70 | 2.28 |
time (sec) |
N/A | 0.335 | 0.510 | 1.069 | 0.187 | 0.254 | 0.000 | 0.380 | 0.216 | 0.385 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 26 | 38 | 51 | 76 | 114 | 0 | 97 | 51 |
N.S. |
1 | 1.00 | 1.13 | 1.65 | 2.22 | 3.30 | 4.96 | 0.00 | 4.22 | 2.22 |
time (sec) |
N/A | 0.240 | 0.133 | 0.559 | 0.039 | 0.206 | 1.301 | 0.000 | 0.207 | 0.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 172 | 108 | 83 | 436 | 0 | 64 | 131 | 470 |
N.S. |
1 | 1.00 | 3.74 | 2.35 | 1.80 | 9.48 | 0.00 | 1.39 | 2.85 | 10.22 |
time (sec) |
N/A | 0.281 | 1.266 | 0.288 | 0.122 | 0.361 | 0.000 | 0.149 | 0.209 | 2.983 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 52 | 42 | 119 | 100 | 115 | 0 | 0 | 140 | 228 |
N.S. |
1 | 1.13 | 0.91 | 2.59 | 2.17 | 2.50 | 0.00 | 0.00 | 3.04 | 4.96 |
time (sec) |
N/A | 0.295 | 0.083 | 1.080 | 0.039 | 0.387 | 0.000 | 0.000 | 0.232 | 2.717 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 77 | 193 | 133 | 429 | 749 | 0 | 92 | 416 | 977 |
N.S. |
1 | 1.24 | 3.11 | 2.15 | 6.92 | 12.08 | 0.00 | 1.48 | 6.71 | 15.76 |
time (sec) |
N/A | 0.360 | 1.252 | 1.704 | 0.153 | 0.439 | 0.000 | 0.422 | 0.241 | 4.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 77 | 100 | 171 | 187 | 862 | 0 | 0 | 871 | 523 |
N.S. |
1 | 1.05 | 1.37 | 2.34 | 2.56 | 11.81 | 0.00 | 0.00 | 11.93 | 7.16 |
time (sec) |
N/A | 0.327 | 0.180 | 2.632 | 0.046 | 0.333 | 0.000 | 0.000 | 0.274 | 2.846 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | B | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 107 | 380 | 192 | 1435 | 2705 | 0 | 164 | 1112 | 779 |
N.S. |
1 | 1.23 | 4.37 | 2.21 | 16.49 | 31.09 | 0.00 | 1.89 | 12.78 | 8.95 |
time (sec) |
N/A | 0.448 | 2.686 | 4.300 | 0.269 | 0.418 | 0.000 | 0.532 | 0.300 | 4.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 70 | 109 | 184 | 154 | 853 | 0 | 0 | 2053 | 0 |
N.S. |
1 | 0.92 | 1.43 | 2.42 | 2.03 | 11.22 | 0.00 | 0.00 | 27.01 | 0.00 |
time (sec) |
N/A | 0.323 | 0.299 | 31.872 | 0.131 | 0.280 | 0.000 | 0.000 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 105 | 228 | 259 | 1053 | 1479 | 0 | 173 | 971 | 0 |
N.S. |
1 | 1.15 | 2.51 | 2.85 | 11.57 | 16.25 | 0.00 | 1.90 | 10.67 | 0.00 |
time (sec) |
N/A | 0.372 | 1.849 | 21.769 | 0.319 | 0.246 | 0.000 | 0.891 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 48 | 81 | 115 | 108 | 485 | 0 | 0 | 1053 | 0 |
N.S. |
1 | 0.94 | 1.59 | 2.25 | 2.12 | 9.51 | 0.00 | 0.00 | 20.65 | 0.00 |
time (sec) |
N/A | 0.285 | 0.661 | 9.662 | 0.061 | 0.214 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | A | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 97 | 326 | 236 | 597 | 1846 | 0 | 137 | 1199 | 0 |
N.S. |
1 | 1.14 | 3.84 | 2.78 | 7.02 | 21.72 | 0.00 | 1.61 | 14.11 | 0.00 |
time (sec) |
N/A | 0.389 | 2.883 | 6.671 | 0.195 | 0.354 | 0.000 | 0.577 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 44 | 79 | 60 | 106 | 476 | 0 | 0 | 1033 | 53 |
N.S. |
1 | 0.90 | 1.61 | 1.22 | 2.16 | 9.71 | 0.00 | 0.00 | 21.08 | 1.08 |
time (sec) |
N/A | 0.295 | 0.372 | 6.495 | 0.052 | 0.231 | 0.000 | 0.000 | 0.246 | 2.526 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | A | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 112 | 221 | 254 | 187 | 1690 | 0 | 163 | 1283 | 0 |
N.S. |
1 | 1.20 | 2.38 | 2.73 | 2.01 | 18.17 | 0.00 | 1.75 | 13.80 | 0.00 |
time (sec) |
N/A | 0.327 | 2.570 | 0.540 | 0.129 | 0.451 | 0.000 | 0.181 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 84 | 115 | 206 | 209 | 1031 | 0 | 0 | 1990 | 0 |
N.S. |
1 | 1.01 | 1.39 | 2.48 | 2.52 | 12.42 | 0.00 | 0.00 | 23.98 | 0.00 |
time (sec) |
N/A | 0.384 | 0.214 | 15.533 | 0.048 | 0.408 | 0.000 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 142 | 268 | 288 | 1070 | 3624 | 0 | 273 | 2905 | 0 |
N.S. |
1 | 1.17 | 2.21 | 2.38 | 8.84 | 29.95 | 0.00 | 2.26 | 24.01 | 0.00 |
time (sec) |
N/A | 0.521 | 2.372 | 23.539 | 0.242 | 0.370 | 0.000 | 0.635 | 0.349 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 108 | 130 | 260 | 384 | 3624 | 0 | 0 | 2792 | 0 |
N.S. |
1 | 0.98 | 1.18 | 2.36 | 3.49 | 32.95 | 0.00 | 0.00 | 25.38 | 0.00 |
time (sec) |
N/A | 0.403 | 0.860 | 34.790 | 0.095 | 0.679 | 0.000 | 0.000 | 0.385 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | A | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 182 | 350 | 362 | 2961 | 9849 | 0 | 293 | 4961 | 0 |
N.S. |
1 | 1.13 | 2.17 | 2.25 | 18.39 | 61.17 | 0.00 | 1.82 | 30.81 | 0.00 |
time (sec) |
N/A | 0.610 | 3.796 | 50.687 | 0.430 | 0.463 | 0.000 | 1.107 | 9.583 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 173 | 515 | 389 | 3239 | 5463 | 0 | 354 | 3970 | 0 |
N.S. |
1 | 1.17 | 3.48 | 2.63 | 21.89 | 36.91 | 0.00 | 2.39 | 26.82 | 0.00 |
time (sec) |
N/A | 0.557 | 4.553 | 185.052 | 0.870 | 0.349 | 0.000 | 1.303 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 73 | 136 | 184 | 206 | 1741 | 0 | 0 | 2301 | 0 |
N.S. |
1 | 0.95 | 1.77 | 2.39 | 2.68 | 22.61 | 0.00 | 0.00 | 29.88 | 0.00 |
time (sec) |
N/A | 0.307 | 1.846 | 136.526 | 0.058 | 0.249 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 155 | 1317 | 343 | 2201 | 6464 | 0 | 281 | 4136 | 0 |
N.S. |
1 | 1.12 | 9.47 | 2.47 | 15.83 | 46.50 | 0.00 | 2.02 | 29.76 | 0.00 |
time (sec) |
N/A | 0.430 | 9.076 | 89.635 | 0.584 | 0.525 | 0.000 | 1.187 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 75 | 131 | 187 | 209 | 1753 | 0 | 0 | 1451 | 0 |
N.S. |
1 | 0.93 | 1.62 | 2.31 | 2.58 | 21.64 | 0.00 | 0.00 | 17.91 | 0.00 |
time (sec) |
N/A | 0.309 | 0.896 | 63.845 | 0.052 | 0.219 | 0.000 | 0.000 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 164 | 1317 | 335 | 1255 | 7158 | 0 | 296 | 4600 | 0 |
N.S. |
1 | 1.18 | 9.47 | 2.41 | 9.03 | 51.50 | 0.00 | 2.13 | 33.09 | 0.00 |
time (sec) |
N/A | 0.422 | 6.358 | 63.609 | 0.283 | 0.599 | 0.000 | 0.680 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 69 | 129 | 82 | 193 | 1666 | 0 | 0 | 2266 | 94 |
N.S. |
1 | 0.95 | 1.77 | 1.12 | 2.64 | 22.82 | 0.00 | 0.00 | 31.04 | 1.29 |
time (sec) |
N/A | 0.278 | 1.148 | 63.737 | 0.052 | 0.237 | 0.000 | 0.000 | 0.233 | 2.397 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 177 | 301 | 352 | 402 | 6538 | 0 | 327 | 4752 | 0 |
N.S. |
1 | 1.21 | 2.06 | 2.41 | 2.75 | 44.78 | 0.00 | 2.24 | 32.55 | 0.00 |
time (sec) |
N/A | 0.374 | 5.404 | 1.249 | 0.151 | 0.402 | 0.000 | 0.225 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 128 | 155 | 292 | 419 | 4132 | 0 | 0 | 4935 | 0 |
N.S. |
1 | 0.98 | 1.19 | 2.25 | 3.22 | 31.78 | 0.00 | 0.00 | 37.96 | 0.00 |
time (sec) |
N/A | 0.378 | 0.683 | 95.091 | 0.067 | 0.874 | 0.000 | 0.000 | 0.337 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 213 | 2083 | 394 | 1971 | 11606 | 0 | 389 | 6415 | 0 |
N.S. |
1 | 1.17 | 11.45 | 2.16 | 10.83 | 63.77 | 0.00 | 2.14 | 35.25 | 0.00 |
time (sec) |
N/A | 0.578 | 7.734 | 142.136 | 0.376 | 0.543 | 0.000 | 0.858 | 0.625 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 151 | 172 | 354 | 692 | 10255 | 0 | 0 | 8376 | 0 |
N.S. |
1 | 0.99 | 1.13 | 2.33 | 4.55 | 67.47 | 0.00 | 0.00 | 55.11 | 0.00 |
time (sec) |
N/A | 0.414 | 1.216 | 190.932 | 0.101 | 1.547 | 0.000 | 0.000 | 0.699 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 263 | 3334 | 468 | 4920 | 24263 | 0 | 469 | 9527 | 0 |
N.S. |
1 | 1.13 | 14.37 | 2.02 | 21.21 | 104.58 | 0.00 | 2.02 | 41.06 | 0.00 |
time (sec) |
N/A | 0.642 | 8.322 | 255.435 | 0.917 | 0.855 | 0.000 | 1.215 | 25.078 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 248 | 1405 | 545 | 718 | 17283 | 0 | 594 | 8934 | 0 |
N.S. |
1 | 1.20 | 6.79 | 2.63 | 3.47 | 83.49 | 0.00 | 2.87 | 43.16 | 0.00 |
time (sec) |
N/A | 0.464 | 8.570 | 4.161 | 0.200 | 0.296 | 0.000 | 0.263 | 0.588 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | C | A | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 32 | 25 | 26 | 33 | 183 | 0 | 72 | 30 | 0 |
N.S. |
1 | 1.10 | 0.86 | 0.90 | 1.14 | 6.31 | 0.00 | 2.48 | 1.03 | 0.00 |
time (sec) |
N/A | 0.334 | 0.022 | 0.261 | 0.116 | 0.082 | 0.000 | 0.109 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 17 | 13 | 18 | 0 | 26 | 11 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.21 | 0.93 | 1.29 | 0.00 | 1.86 | 0.79 | 0.00 |
time (sec) |
N/A | 0.271 | 0.007 | 0.222 | 0.113 | 0.082 | 0.000 | 0.111 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 79 | 22 | 18 | 0 | 31 | 22 | 0 |
N.S. |
1 | 1.00 | 1.00 | 5.64 | 1.57 | 1.29 | 0.00 | 2.21 | 1.57 | 0.00 |
time (sec) |
N/A | 0.270 | 0.009 | 0.135 | 0.120 | 0.094 | 0.000 | 0.116 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | C | B | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 27 | 95 | 33 | 404 | 0 | 83 | 26 | 0 |
N.S. |
1 | 1.00 | 0.79 | 2.79 | 0.97 | 11.88 | 0.00 | 2.44 | 0.76 | 0.00 |
time (sec) |
N/A | 0.324 | 0.014 | 0.131 | 0.123 | 0.086 | 0.000 | 0.114 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | B | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 26 | 13 | 70 | 0 | 31 | 9 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.62 | 0.81 | 4.38 | 0.00 | 1.94 | 0.56 | 0.00 |
time (sec) |
N/A | 0.264 | 0.006 | 0.196 | 0.140 | 0.099 | 0.000 | 0.115 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | B | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 29 | 22 | 69 | 0 | 36 | 18 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.81 | 1.38 | 4.31 | 0.00 | 2.25 | 1.12 | 0.00 |
time (sec) |
N/A | 0.268 | 0.007 | 0.192 | 0.124 | 0.085 | 0.000 | 0.114 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 88 | 108 | 0 | 0 | 4594 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.06 | 1.30 | 0.00 | 0.00 | 55.35 | 0.00 | 0.00 | 1.53 | 0.00 |
time (sec) |
N/A | 0.317 | 0.729 | 0.000 | 0.000 | 0.338 | 0.000 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 137 | 192 | 0 | 0 | 8720 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.10 | 1.54 | 0.00 | 0.00 | 69.76 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.467 | 0.379 | 0.000 | 0.000 | 0.376 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 64 | 56 | 0 | 0 | 2394 | 0 | 0 | 83 | 0 |
N.S. |
1 | 1.08 | 0.95 | 0.00 | 0.00 | 40.58 | 0.00 | 0.00 | 1.41 | 0.00 |
time (sec) |
N/A | 0.268 | 0.232 | 0.000 | 0.000 | 0.182 | 0.000 | 0.000 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 91 | 150 | 0 | 0 | 4184 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.05 | 1.72 | 0.00 | 0.00 | 48.09 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.386 | 0.244 | 0.000 | 0.000 | 0.209 | 0.000 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 45 | 90 | 43 | 0 | 1608 | 0 | 0 | 38 | 32 |
N.S. |
1 | 1.12 | 2.25 | 1.08 | 0.00 | 40.20 | 0.00 | 0.00 | 0.95 | 0.80 |
time (sec) |
N/A | 0.237 | 0.183 | 0.120 | 0.000 | 0.123 | 0.000 | 0.000 | 0.223 | 2.714 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 134 | 0 | 0 | 2817 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 2.27 | 0.00 | 0.00 | 47.75 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.249 | 0.536 | 0.000 | 0.000 | 0.155 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 61 | 56 | 0 | 0 | 3479 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.09 | 1.00 | 0.00 | 0.00 | 62.12 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.302 | 0.109 | 0.000 | 0.000 | 0.199 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 75 | 0 | 0 | 1237 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 1.56 | 0.00 | 0.00 | 25.77 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.339 | 0.367 | 0.000 | 0.000 | 0.139 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 95 | 156 | 0 | 0 | 5129 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.14 | 1.88 | 0.00 | 0.00 | 61.80 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.320 | 0.545 | 0.000 | 0.000 | 0.235 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 88 | 149 | 0 | 0 | 2275 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.05 | 1.77 | 0.00 | 0.00 | 27.08 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.397 | 0.408 | 0.000 | 0.000 | 0.184 | 0.000 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 156 | 191 | 0 | 0 | 12430 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.25 | 1.53 | 0.00 | 0.00 | 99.44 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.396 | 0.856 | 0.000 | 0.000 | 0.453 | 0.000 | 0.000 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 84 | 80 | 0 | 0 | 4226 | 0 | 0 | 125 | 0 |
N.S. |
1 | 1.11 | 1.05 | 0.00 | 0.00 | 55.61 | 0.00 | 0.00 | 1.64 | 0.00 |
time (sec) |
N/A | 0.298 | 0.462 | 0.000 | 0.000 | 0.347 | 0.000 | 0.000 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 134 | 197 | 0 | 0 | 8582 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.07 | 1.58 | 0.00 | 0.00 | 68.66 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.551 | 0.534 | 0.000 | 0.000 | 0.358 | 0.000 | 0.000 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 65 | 65 | 56 | 0 | 2312 | 0 | 0 | 57 | 45 |
N.S. |
1 | 1.14 | 1.14 | 0.98 | 0.00 | 40.56 | 0.00 | 0.00 | 1.00 | 0.79 |
time (sec) |
N/A | 0.271 | 0.080 | 0.114 | 0.000 | 0.193 | 0.000 | 0.000 | 0.231 | 4.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 91 | 152 | 0 | 0 | 4140 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.03 | 1.73 | 0.00 | 0.00 | 47.05 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.328 | 0.183 | 0.000 | 0.000 | 0.230 | 0.000 | 0.000 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 76 | 159 | 0 | 0 | 4005 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.09 | 2.27 | 0.00 | 0.00 | 57.21 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.322 | 0.469 | 0.000 | 0.000 | 0.237 | 0.000 | 0.000 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 144 | 0 | 0 | 3349 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 1.78 | 0.00 | 0.00 | 41.35 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.408 | 0.289 | 0.000 | 0.000 | 0.203 | 0.000 | 0.000 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 170 | 280 | 0 | 0 | 12240 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.00 | 1.65 | 0.00 | 0.00 | 72.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.428 | 6.888 | 0.000 | 0.000 | 0.576 | 0.000 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 72 | 84 | 0 | 0 | 2678 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.09 | 1.27 | 0.00 | 0.00 | 40.58 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.358 | 0.371 | 0.000 | 0.000 | 0.211 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 97 | 169 | 0 | 0 | 4569 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.08 | 1.88 | 0.00 | 0.00 | 50.77 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.462 | 0.385 | 0.000 | 0.000 | 0.252 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 48 | 42 | 0 | 0 | 1650 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.14 | 1.00 | 0.00 | 0.00 | 39.29 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.302 | 0.191 | 0.000 | 0.000 | 0.164 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 107 | 0 | 0 | 2856 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 1.78 | 0.00 | 0.00 | 47.60 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.410 | 0.191 | 0.000 | 0.000 | 0.182 | 0.000 | 0.000 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 30 | 0 | 1430 | 0 | 0 | 24 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 0.00 | 57.20 | 0.00 | 0.00 | 0.96 | 0.76 |
time (sec) |
N/A | 0.292 | 0.067 | 0.186 | 0.000 | 0.121 | 0.000 | 0.000 | 0.224 | 2.573 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 62 | 0 | 0 | 1059 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 2.14 | 0.00 | 0.00 | 36.52 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.237 | 0.031 | 0.000 | 0.000 | 0.125 | 0.000 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 61 | 124 | 0 | 0 | 3545 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.09 | 2.21 | 0.00 | 0.00 | 63.30 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.333 | 0.296 | 0.000 | 0.000 | 0.204 | 0.000 | 0.000 | 0.197 | 0.000 |