Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 70 | 117 | 129 | 152 | 112 | 116 | 83 |
N.S. |
1 | 1.00 | 0.74 | 1.24 | 1.37 | 1.62 | 1.19 | 1.23 | 0.88 |
time (sec) |
N/A | 0.291 | 0.114 | 13.598 | 0.227 | 0.249 | 0.420 | 0.273 | 0.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 36 | 27 | 26 | 78 | 64 | 44 | 82 | 26 |
N.S. |
1 | 1.16 | 0.87 | 0.84 | 2.52 | 2.06 | 1.42 | 2.65 | 0.84 |
time (sec) |
N/A | 0.229 | 0.048 | 8.601 | 0.201 | 0.254 | 0.213 | 0.272 | 2.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 61 | 71 | 64 | 103 | 0 | 64 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.97 | 0.88 | 1.41 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.370 | 0.060 | 8.326 | 0.308 | 0.253 | 0.000 | 0.271 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 104 | 151 | 76 | 214 | 0 | 144 | 0 |
N.S. |
1 | 1.00 | 0.84 | 1.22 | 0.61 | 1.73 | 0.00 | 1.16 | 0.00 |
time (sec) |
N/A | 0.474 | 0.212 | 9.303 | 0.321 | 0.291 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 184 | 184 | 162 | 250 | 88 | 338 | 0 | 243 | 0 |
N.S. |
1 | 1.00 | 0.88 | 1.36 | 0.48 | 1.84 | 0.00 | 1.32 | 0.00 |
time (sec) |
N/A | 0.555 | 0.304 | 14.241 | 0.303 | 0.254 | 0.000 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 238 | 238 | 212 | 349 | 88 | 397 | 0 | 342 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.47 | 0.37 | 1.67 | 0.00 | 1.44 | 0.00 |
time (sec) |
N/A | 0.656 | 0.287 | 21.045 | 0.311 | 0.263 | 0.000 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 141 | 141 | 112 | 0 | 117 | 172 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.79 | 0.00 | 0.83 | 1.22 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.423 | 0.078 | 0.000 | 0.121 | 0.087 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 207 | 95 | 146 | 171 | 191 | 226 | 145 | 126 |
N.S. |
1 | 1.34 | 0.61 | 0.94 | 1.10 | 1.23 | 1.46 | 0.94 | 0.81 |
time (sec) |
N/A | 0.742 | 0.422 | 13.011 | 0.223 | 0.249 | 0.540 | 0.261 | 2.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 111 | 72 | 114 | 127 | 154 | 150 | 113 | 89 |
N.S. |
1 | 1.10 | 0.71 | 1.13 | 1.26 | 1.52 | 1.49 | 1.12 | 0.88 |
time (sec) |
N/A | 0.383 | 0.140 | 10.400 | 0.238 | 0.261 | 0.410 | 0.266 | 0.220 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 75 | 50 | 69 | 91 | 108 | 110 | 81 | 55 |
N.S. |
1 | 1.15 | 0.77 | 1.06 | 1.40 | 1.66 | 1.69 | 1.25 | 0.85 |
time (sec) |
N/A | 0.324 | 0.087 | 7.361 | 0.225 | 0.244 | 0.310 | 0.264 | 0.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 54 | 20 | 57 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 3.60 | 1.33 | 3.80 | 0.87 |
time (sec) |
N/A | 0.181 | 0.002 | 4.709 | 0.224 | 0.250 | 0.136 | 0.262 | 0.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 47 | 50 | 45 | 73 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.94 | 0.85 | 1.38 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.303 | 0.038 | 4.558 | 0.299 | 0.239 | 0.000 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 78 | 105 | 53 | 139 | 0 | 100 | 0 |
N.S. |
1 | 1.00 | 0.88 | 1.18 | 0.60 | 1.56 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.356 | 0.155 | 5.328 | 0.305 | 0.247 | 0.000 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 113 | 173 | 60 | 229 | 0 | 168 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.38 | 0.48 | 1.83 | 0.00 | 1.34 | 0.00 |
time (sec) |
N/A | 0.423 | 0.319 | 5.542 | 0.329 | 0.253 | 0.000 | 0.260 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 169 | 169 | 150 | 241 | 61 | 264 | 0 | 236 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.43 | 0.36 | 1.56 | 0.00 | 1.40 | 0.00 |
time (sec) |
N/A | 0.478 | 0.319 | 8.566 | 0.286 | 0.247 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 209 | 209 | 174 | 0 | 171 | 248 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.00 | 0.82 | 1.19 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.504 | 0.218 | 0.000 | 0.147 | 0.083 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 202 | 202 | 136 | 213 | 245 | 274 | 253 | 212 | 173 |
N.S. |
1 | 1.00 | 0.67 | 1.05 | 1.21 | 1.36 | 1.25 | 1.05 | 0.86 |
time (sec) |
N/A | 0.473 | 0.315 | 39.141 | 0.221 | 0.257 | 0.770 | 0.265 | 0.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 148 | 148 | 98 | 165 | 187 | 214 | 182 | 164 | 112 |
N.S. |
1 | 1.00 | 0.66 | 1.11 | 1.26 | 1.45 | 1.23 | 1.11 | 0.76 |
time (sec) |
N/A | 0.394 | 0.277 | 26.872 | 0.240 | 0.272 | 0.542 | 0.278 | 0.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 70 | 116 | 129 | 153 | 112 | 116 | 71 |
N.S. |
1 | 1.00 | 0.74 | 1.23 | 1.37 | 1.63 | 1.19 | 1.23 | 0.76 |
time (sec) |
N/A | 0.290 | 0.116 | 19.315 | 0.221 | 0.259 | 0.401 | 0.266 | 0.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 30 | 27 | 26 | 78 | 79 | 44 | 82 | 26 |
N.S. |
1 | 0.97 | 0.87 | 0.84 | 2.52 | 2.55 | 1.42 | 2.65 | 0.84 |
time (sec) |
N/A | 0.215 | 0.049 | 12.892 | 0.206 | 0.251 | 0.209 | 0.278 | 2.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 63 | 71 | 64 | 103 | 0 | 64 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.97 | 0.88 | 1.41 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.362 | 0.054 | 11.172 | 0.307 | 0.251 | 0.000 | 0.315 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 106 | 147 | 76 | 203 | 0 | 140 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.19 | 0.61 | 1.64 | 0.00 | 1.13 | 0.00 |
time (sec) |
N/A | 0.450 | 0.162 | 12.740 | 0.321 | 0.247 | 0.000 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 184 | 184 | 164 | 246 | 88 | 336 | 0 | 239 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.34 | 0.48 | 1.83 | 0.00 | 1.30 | 0.00 |
time (sec) |
N/A | 0.530 | 0.241 | 13.449 | 0.309 | 0.258 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 238 | 238 | 212 | 349 | 88 | 392 | 0 | 342 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.47 | 0.37 | 1.65 | 0.00 | 1.44 | 0.00 |
time (sec) |
N/A | 0.629 | 0.287 | 21.615 | 0.333 | 0.245 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 155 | 155 | 119 | 0 | 117 | 172 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.75 | 1.11 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.457 | 0.130 | 0.000 | 0.131 | 0.085 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 143 | 143 | 90 | 146 | 171 | 248 | 314 | 145 | 126 |
N.S. |
1 | 1.00 | 0.63 | 1.02 | 1.20 | 1.73 | 2.20 | 1.01 | 0.88 |
time (sec) |
N/A | 0.402 | 0.587 | 88.148 | 0.226 | 0.262 | 1.017 | 0.266 | 2.465 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 72 | 114 | 127 | 202 | 212 | 113 | 89 |
N.S. |
1 | 1.00 | 0.69 | 1.09 | 1.21 | 1.92 | 2.02 | 1.08 | 0.85 |
time (sec) |
N/A | 0.339 | 0.151 | 63.257 | 0.219 | 0.279 | 0.771 | 0.261 | 0.347 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 50 | 82 | 91 | 148 | 148 | 81 | 55 |
N.S. |
1 | 1.00 | 0.75 | 1.22 | 1.36 | 2.21 | 2.21 | 1.21 | 0.82 |
time (sec) |
N/A | 0.261 | 0.163 | 44.818 | 0.216 | 0.255 | 0.545 | 0.269 | 0.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 29 | 35 | 34 | 56 | 72 | 42 | 57 | 26 |
N.S. |
1 | 0.94 | 1.13 | 1.10 | 1.81 | 2.32 | 1.35 | 1.84 | 0.84 |
time (sec) |
N/A | 0.220 | 0.050 | 31.923 | 0.206 | 0.243 | 0.309 | 0.269 | 0.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 47 | 50 | 45 | 73 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.94 | 0.85 | 1.38 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.319 | 0.526 | 28.397 | 0.286 | 0.254 | 0.000 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 78 | 105 | 53 | 159 | 0 | 100 | 0 |
N.S. |
1 | 1.00 | 0.88 | 1.18 | 0.60 | 1.79 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.385 | 0.143 | 30.955 | 0.288 | 0.245 | 0.000 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 131 | 131 | 118 | 173 | 61 | 274 | 0 | 168 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.32 | 0.47 | 2.09 | 0.00 | 1.28 | 0.00 |
time (sec) |
N/A | 0.447 | 0.156 | 32.460 | 0.298 | 0.262 | 0.000 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 169 | 169 | 150 | 241 | 61 | 315 | 0 | 236 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.43 | 0.36 | 1.86 | 0.00 | 1.40 | 0.00 |
time (sec) |
N/A | 0.506 | 0.212 | 49.265 | 0.278 | 0.250 | 0.000 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 16 | 100 | 18 | 17 | 18 | 20 |
N.S. |
1 | 1.00 | 1.20 | 1.60 | 10.00 | 1.80 | 1.70 | 1.80 | 2.00 |
time (sec) |
N/A | 0.192 | 0.336 | 0.132 | 0.489 | 0.257 | 10.115 | 0.272 | 2.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 118 | 88 | 116 | 84 | 257 | 0 | 0 | 0 |
N.S. |
1 | 1.30 | 0.97 | 1.27 | 0.92 | 2.82 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.603 | 0.178 | 0.468 | 0.262 | 0.273 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 88 | 66 | 94 | 63 | 207 | 0 | 0 | 0 |
N.S. |
1 | 1.35 | 1.02 | 1.45 | 0.97 | 3.18 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.470 | 0.116 | 0.504 | 0.259 | 0.258 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 59 | 44 | 70 | 40 | 141 | 0 | 0 | 0 |
N.S. |
1 | 1.31 | 0.98 | 1.56 | 0.89 | 3.13 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.329 | 0.088 | 0.470 | 0.263 | 0.257 | 0.000 | 0.000 | 0.000 |
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 | 11 | 11 | 11 | 13 | 21 | 37 | 0 | 24 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.18 | 1.91 | 3.36 | 0.00 | 2.18 | 1.00 |
time (sec) |
N/A | 0.170 | 0.001 | 0.164 | 0.213 | 0.245 | 0.000 | 0.258 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 16 | 22 | 18 | 15 | 18 | 20 |
N.S. |
1 | 1.00 | 1.20 | 1.60 | 2.20 | 1.80 | 1.50 | 1.80 | 2.00 |
time (sec) |
N/A | 0.184 | 9.075 | 0.225 | 0.267 | 0.248 | 1.006 | 0.250 | 2.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 16 | 29 | 18 | 17 | 18 | 20 |
N.S. |
1 | 1.00 | 1.20 | 1.60 | 2.90 | 1.80 | 1.70 | 1.80 | 2.00 |
time (sec) |
N/A | 0.188 | 16.638 | 0.212 | 0.266 | 0.255 | 0.847 | 0.251 | 2.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 18 | 20 | 20 | 19 | 20 | 20 |
N.S. |
1 | 1.00 | 1.12 | 1.12 | 1.25 | 1.25 | 1.19 | 1.25 | 1.25 |
time (sec) |
N/A | 0.464 | 48.176 | 0.123 | 0.361 | 0.252 | 35.580 | 0.277 | 2.214 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 113 | 125 | 130 | 0 | 0 | 672 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 1.15 | 0.00 | 0.00 | 5.95 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.544 | 0.217 | 0.000 | 0.000 | 0.267 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 75 | 85 | 154 | 0 | 468 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.23 | 2.23 | 0.00 | 6.78 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.354 | 0.223 | 0.751 | 0.000 | 0.255 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 32 | 59 | 37 | 116 | 0 | 70 | 49 |
N.S. |
1 | 1.00 | 1.33 | 2.46 | 1.54 | 4.83 | 0.00 | 2.92 | 2.04 |
time (sec) |
N/A | 0.234 | 0.036 | 0.482 | 0.362 | 0.258 | 0.000 | 0.263 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 12 | 23 | 54 | 0 | 23 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 2.09 | 4.91 | 0.00 | 2.09 | 1.18 |
time (sec) |
N/A | 0.180 | 0.003 | 0.245 | 0.200 | 0.241 | 0.000 | 0.272 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 18 | 60 | 20 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.12 | 1.12 | 3.75 | 1.25 | 1.06 | 1.25 | 1.25 |
time (sec) |
N/A | 0.323 | 6.146 | 0.209 | 0.325 | 0.245 | 1.448 | 0.414 | 2.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 18 | 64 | 20 | 19 | 20 | 20 |
N.S. |
1 | 1.00 | 1.12 | 1.12 | 4.00 | 1.25 | 1.19 | 1.25 | 1.25 |
time (sec) |
N/A | 0.344 | 6.594 | 0.212 | 0.331 | 0.256 | 1.520 | 0.684 | 2.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 20 | 19 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 1.06 | 1.11 | 1.11 |
time (sec) |
N/A | 0.560 | 39.727 | 0.120 | 0.358 | 0.252 | 110.413 | 0.290 | 2.259 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 102 | 86 | 121 | 110 | 1113 | 0 | 0 | 0 |
N.S. |
1 | 1.23 | 1.04 | 1.46 | 1.33 | 13.41 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.559 | 0.978 | 2.531 | 0.284 | 0.269 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 47 | 55 | 73 | 94 | 378 | 0 | 142 | 102 |
N.S. |
1 | 1.12 | 1.31 | 1.74 | 2.24 | 9.00 | 0.00 | 3.38 | 2.43 |
time (sec) |
N/A | 0.344 | 0.091 | 1.640 | 0.282 | 0.260 | 0.000 | 0.297 | 2.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 43 | 131 | 105 | 0 | 184 | 36 |
N.S. |
1 | 1.00 | 1.00 | 1.43 | 4.37 | 3.50 | 0.00 | 6.13 | 1.20 |
time (sec) |
N/A | 0.251 | 0.181 | 1.152 | 0.216 | 0.247 | 0.000 | 0.278 | 2.203 |
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 | 15 | 15 | 15 | 14 | 23 | 84 | 0 | 27 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 1.53 | 5.60 | 0.00 | 1.80 | 0.87 |
time (sec) |
N/A | 0.186 | 0.001 | 0.610 | 0.208 | 0.241 | 0.000 | 0.256 | 2.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 101 | 20 | 17 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 5.61 | 1.11 | 0.94 | 1.11 | 1.11 |
time (sec) |
N/A | 0.345 | 22.239 | 0.230 | 0.305 | 0.245 | 3.862 | 0.273 | 2.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 100 | 20 | 19 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 5.56 | 1.11 | 1.06 | 1.11 | 1.11 |
time (sec) |
N/A | 0.387 | 18.928 | 0.272 | 0.306 | 0.253 | 4.616 | 0.268 | 2.219 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 18 | 20 | 20 | 19 | 20 | 22 |
N.S. |
1 | 1.00 | 1.12 | 1.12 | 1.25 | 1.25 | 1.19 | 1.25 | 1.38 |
time (sec) |
N/A | 0.414 | 14.706 | 0.200 | 0.375 | 0.246 | 38.334 | 0.263 | 2.203 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 195 | 226 | 211 | 0 | 0 | 609 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 1.08 | 0.00 | 0.00 | 3.12 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.109 | 0.196 | 0.000 | 0.000 | 0.267 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 135 | 153 | 153 | 0 | 0 | 477 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 1.13 | 0.00 | 0.00 | 3.53 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.767 | 0.144 | 0.000 | 0.000 | 0.267 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 93 | 162 | 0 | 328 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.21 | 2.10 | 0.00 | 4.26 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.439 | 0.085 | 0.664 | 0.000 | 0.260 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 21 | 23 | 21 | 41 | 86 | 0 | 32 | 49 |
N.S. |
1 | 0.91 | 1.00 | 0.91 | 1.78 | 3.74 | 0.00 | 1.39 | 2.13 |
time (sec) |
N/A | 0.190 | 0.003 | 0.322 | 0.321 | 0.252 | 0.000 | 0.266 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 18 | 20 | 20 | 17 | 20 | 22 |
N.S. |
1 | 1.00 | 1.12 | 1.12 | 1.25 | 1.25 | 1.06 | 1.25 | 1.38 |
time (sec) |
N/A | 0.445 | 5.168 | 0.411 | 0.430 | 0.250 | 1.346 | 0.319 | 2.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 18 | 20 | 20 | 19 | 20 | 22 |
N.S. |
1 | 1.00 | 1.12 | 1.12 | 1.25 | 1.25 | 1.19 | 1.25 | 1.38 |
time (sec) |
N/A | 0.559 | 4.607 | 0.335 | 0.400 | 0.266 | 1.407 | 0.348 | 2.199 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 20 | 144 | 22 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.17 | 1.67 | 12.00 | 1.83 | 1.67 | 1.83 | 1.83 |
time (sec) |
N/A | 0.199 | 0.408 | 0.233 | 0.703 | 0.247 | 120.276 | 0.286 | 2.224 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 113 | 99 | 125 | 108 | 721 | 0 | 0 | 0 |
N.S. |
1 | 1.27 | 1.11 | 1.40 | 1.21 | 8.10 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.609 | 1.069 | 1.003 | 0.284 | 0.262 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 84 | 77 | 99 | 84 | 515 | 0 | 0 | 0 |
N.S. |
1 | 1.29 | 1.18 | 1.52 | 1.29 | 7.92 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.435 | 0.673 | 0.893 | 0.268 | 0.266 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 46 | 41 | 95 | 185 | 0 | 95 | 45 |
N.S. |
1 | 1.00 | 1.48 | 1.32 | 3.06 | 5.97 | 0.00 | 3.06 | 1.45 |
time (sec) |
N/A | 0.254 | 0.115 | 0.954 | 0.238 | 0.257 | 0.000 | 0.285 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 23 | 17 | 25 | 33 | 0 | 24 | 20 |
N.S. |
1 | 1.00 | 1.77 | 1.31 | 1.92 | 2.54 | 0.00 | 1.85 | 1.54 |
time (sec) |
N/A | 0.175 | 0.001 | 0.266 | 0.217 | 0.263 | 0.000 | 0.289 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 20 | 49 | 22 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.17 | 1.67 | 4.08 | 1.83 | 1.58 | 1.83 | 1.83 |
time (sec) |
N/A | 0.198 | 17.056 | 0.380 | 0.297 | 0.246 | 3.313 | 0.284 | 2.211 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 20 | 68 | 22 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.17 | 1.67 | 5.67 | 1.83 | 1.67 | 1.83 | 1.83 |
time (sec) |
N/A | 0.198 | 10.978 | 0.376 | 0.299 | 0.242 | 3.960 | 0.285 | 2.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 20 | 22 | 22 | 0 | 22 | 22 |
N.S. |
1 | 1.00 | 1.11 | 1.11 | 1.22 | 1.22 | 0.00 | 1.22 | 1.22 |
time (sec) |
N/A | 0.291 | 52.673 | 0.213 | 0.392 | 0.253 | 0.000 | 0.293 | 2.282 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 240 | 420 | 245 | 0 | 0 | 2163 | 0 | 0 | 0 |
N.S. |
1 | 1.75 | 1.02 | 0.00 | 0.00 | 9.01 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.685 | 2.006 | 0.000 | 0.000 | 0.293 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 143 | 259 | 180 | 0 | 0 | 1577 | 0 | 0 | 0 |
N.S. |
1 | 1.81 | 1.26 | 0.00 | 0.00 | 11.03 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.246 | 0.588 | 0.000 | 0.000 | 0.287 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 147 | 116 | 178 | 0 | 1064 | 0 | 0 | 0 |
N.S. |
1 | 1.62 | 1.27 | 1.96 | 0.00 | 11.69 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.673 | 0.638 | 1.395 | 0.000 | 0.287 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 34 | 43 | 66 | 269 | 0 | 76 | 82 |
N.S. |
1 | 1.00 | 1.00 | 1.26 | 1.94 | 7.91 | 0.00 | 2.24 | 2.41 |
time (sec) |
N/A | 0.258 | 0.003 | 1.033 | 0.292 | 0.265 | 0.000 | 0.266 | 2.219 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 20 | 131 | 22 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.11 | 1.11 | 7.28 | 1.22 | 1.06 | 1.22 | 1.22 |
time (sec) |
N/A | 0.288 | 15.276 | 0.351 | 0.357 | 0.257 | 8.664 | 1.766 | 2.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 20 | 133 | 22 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.11 | 1.11 | 7.39 | 1.22 | 1.11 | 1.22 | 1.22 |
time (sec) |
N/A | 0.287 | 11.082 | 0.407 | 0.361 | 0.247 | 10.785 | 1.633 | 2.304 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 20 | 19 | 20 | 22 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 1.06 | 1.11 | 1.22 |
time (sec) |
N/A | 0.508 | 17.722 | 0.273 | 0.442 | 0.251 | 113.002 | 0.279 | 2.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 222 | 159 | 189 | 181 | 966 | 0 | 0 | 0 |
N.S. |
1 | 1.20 | 0.86 | 1.02 | 0.98 | 5.22 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.204 | 0.286 | 2.301 | 0.267 | 0.282 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 154 | 122 | 152 | 138 | 789 | 0 | 0 | 0 |
N.S. |
1 | 1.18 | 0.94 | 1.17 | 1.06 | 6.07 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.887 | 0.251 | 1.651 | 0.277 | 0.277 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 108 | 72 | 110 | 95 | 558 | 0 | 0 | 0 |
N.S. |
1 | 1.21 | 0.81 | 1.24 | 1.07 | 6.27 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.595 | 0.299 | 1.242 | 0.266 | 0.252 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 25 | 25 | 25 | 56 | 197 | 0 | 60 | 48 |
N.S. |
1 | 0.89 | 0.89 | 0.89 | 2.00 | 7.04 | 0.00 | 2.14 | 1.71 |
time (sec) |
N/A | 0.207 | 0.012 | 0.731 | 0.307 | 0.261 | 0.000 | 0.269 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 46 | 20 | 17 | 20 | 22 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 2.56 | 1.11 | 0.94 | 1.11 | 1.22 |
time (sec) |
N/A | 0.539 | 12.197 | 0.419 | 0.357 | 0.242 | 2.823 | 0.268 | 2.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 53 | 20 | 19 | 20 | 22 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 2.94 | 1.11 | 1.06 | 1.11 | 1.22 |
time (sec) |
N/A | 0.633 | 10.521 | 0.379 | 0.331 | 0.238 | 3.444 | 0.261 | 2.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 20 | 22 | 22 | 0 | 22 | 22 |
N.S. |
1 | 1.00 | 1.11 | 1.11 | 1.22 | 1.22 | 0.00 | 1.22 | 1.22 |
time (sec) |
N/A | 0.558 | 45.958 | 0.277 | 0.440 | 0.248 | 0.000 | 0.281 | 2.305 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 162 | 201 | 196 | 0 | 0 | 1225 | 0 | 0 | 0 |
N.S. |
1 | 1.24 | 1.21 | 0.00 | 0.00 | 7.56 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.125 | 0.878 | 0.000 | 0.000 | 0.281 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 125 | 132 | 205 | 0 | 879 | 0 | 0 | 0 |
N.S. |
1 | 1.20 | 1.27 | 1.97 | 0.00 | 8.45 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.769 | 0.812 | 0.893 | 0.000 | 0.268 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | C | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 56 | 50 | 94 | 81 | 283 | 0 | 102 | 90 |
N.S. |
1 | 1.22 | 1.09 | 2.04 | 1.76 | 6.15 | 0.00 | 2.22 | 1.96 |
time (sec) |
N/A | 0.456 | 0.223 | 0.717 | 0.355 | 0.257 | 0.000 | 0.301 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 22 | 21 | 33 | 54 | 31 | 0 | 41 | 22 |
N.S. |
1 | 1.05 | 1.00 | 1.57 | 2.57 | 1.48 | 0.00 | 1.95 | 1.05 |
time (sec) |
N/A | 0.212 | 0.005 | 0.373 | 0.208 | 0.251 | 0.000 | 0.271 | 0.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 20 | 79 | 22 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.11 | 1.11 | 4.39 | 1.22 | 1.06 | 1.22 | 1.22 |
time (sec) |
N/A | 0.561 | 8.597 | 0.350 | 0.352 | 0.248 | 8.511 | 0.876 | 2.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 20 | 87 | 22 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.11 | 1.11 | 4.83 | 1.22 | 1.11 | 1.22 | 1.22 |
time (sec) |
N/A | 0.698 | 6.401 | 0.348 | 0.350 | 0.266 | 10.905 | 1.227 | 2.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 20 | 171 | 22 | 0 | 22 | 22 |
N.S. |
1 | 1.00 | 1.17 | 1.67 | 14.25 | 1.83 | 0.00 | 1.83 | 1.83 |
time (sec) |
N/A | 0.211 | 0.687 | 0.250 | 0.735 | 0.253 | 0.000 | 0.312 | 2.328 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 183 | 230 | 249 | 234 | 236 | 2207 | 0 | 0 | 0 |
N.S. |
1 | 1.26 | 1.36 | 1.28 | 1.29 | 12.06 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.361 | 1.539 | 0.669 | 0.254 | 0.276 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 146 | 196 | 164 | 183 | 1649 | 0 | 0 | 0 |
N.S. |
1 | 1.26 | 1.69 | 1.41 | 1.58 | 14.22 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.856 | 1.354 | 0.661 | 0.265 | 0.278 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 100 | 69 | 111 | 131 | 1106 | 0 | 0 | 0 |
N.S. |
1 | 1.22 | 0.84 | 1.35 | 1.60 | 13.49 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.495 | 0.596 | 0.575 | 0.266 | 0.270 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 36 | 27 | 23 | 61 | 339 | 0 | 65 | 25 |
N.S. |
1 | 1.33 | 1.00 | 0.85 | 2.26 | 12.56 | 0.00 | 2.41 | 0.93 |
time (sec) |
N/A | 0.241 | 0.001 | 0.372 | 0.297 | 0.273 | 0.000 | 0.277 | 2.219 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 20 | 111 | 22 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.17 | 1.67 | 9.25 | 1.83 | 1.58 | 1.83 | 1.83 |
time (sec) |
N/A | 0.200 | 13.219 | 0.405 | 0.286 | 0.249 | 19.856 | 0.280 | 2.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 20 | 143 | 22 | 20 | 22 | 22 |
N.S. |
1 | 1.00 | 1.17 | 1.67 | 11.92 | 1.83 | 1.67 | 1.83 | 1.83 |
time (sec) |
N/A | 0.207 | 8.077 | 0.394 | 0.292 | 0.242 | 27.048 | 0.273 | 2.370 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 16 | 102 | 18 | 17 | 18 | 20 |
N.S. |
1 | 1.00 | 1.20 | 1.60 | 10.20 | 1.80 | 1.70 | 1.80 | 2.00 |
time (sec) |
N/A | 0.202 | 5.997 | 0.120 | 0.502 | 0.255 | 108.551 | 0.263 | 2.203 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 142 | 91 | 200 | 130 | 216 | 0 | 0 | 0 |
N.S. |
1 | 1.63 | 1.05 | 2.30 | 1.49 | 2.48 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.649 | 0.003 | 0.323 | 0.256 | 0.262 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 106 | 66 | 166 | 96 | 168 | 0 | 0 | 0 |
N.S. |
1 | 1.68 | 1.05 | 2.63 | 1.52 | 2.67 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.492 | 0.003 | 0.313 | 0.251 | 0.268 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 71 | 47 | 122 | 58 | 112 | 0 | 0 | 0 |
N.S. |
1 | 1.58 | 1.04 | 2.71 | 1.29 | 2.49 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.342 | 0.003 | 0.318 | 0.240 | 0.258 | 0.000 | 0.000 | 0.000 |