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 | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 102 | 78 | 118 | 268 | 549 | 857 | 284 | 87 |
N.S. |
1 | 1.00 | 1.02 | 0.78 | 1.18 | 2.68 | 5.49 | 8.57 | 2.84 | 0.87 |
time (sec) |
N/A | 0.221 | 0.075 | 0.294 | 0.292 | 0.223 | 0.464 | 0.321 | 0.001 | 0.082 |
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 | 71 | 71 | 61 | 54 | 68 | 174 | 355 | 558 | 180 | 68 |
N.S. |
1 | 1.00 | 0.86 | 0.76 | 0.96 | 2.45 | 5.00 | 7.86 | 2.54 | 0.96 |
time (sec) |
N/A | 0.197 | 0.046 | 0.270 | 0.287 | 0.224 | 0.373 | 0.302 | 0.001 | 0.113 |
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 | 42 | 42 | 30 | 27 | 33 | 93 | 194 | 306 | 92 | 29 |
N.S. |
1 | 1.00 | 0.71 | 0.64 | 0.79 | 2.21 | 4.62 | 7.29 | 2.19 | 0.69 |
time (sec) |
N/A | 0.170 | 0.027 | 0.257 | 0.237 | 0.221 | 0.392 | 0.320 | 0.000 | 0.047 |
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 | 16 | 16 | 16 | 13 | 12 | 39 | 12 | 95 | 38 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 2.44 | 0.75 | 5.94 | 2.38 | 0.75 |
time (sec) |
N/A | 0.133 | 0.003 | 0.227 | 0.187 | 0.214 | 0.018 | 0.323 | 0.000 | 0.025 |
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 | 120 | 108 | 115 | 0 | 290 | 146 | 171 | 223 | 130 |
N.S. |
1 | 1.07 | 0.96 | 1.03 | 0.00 | 2.59 | 1.30 | 1.53 | 1.99 | 1.16 |
time (sec) |
N/A | 0.224 | 0.122 | 0.753 | 0.000 | 0.231 | 1.498 | 0.325 | 0.001 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 121 | 116 | 120 | 0 | 330 | 0 | 181 | 273 | 161 |
N.S. |
1 | 1.10 | 1.05 | 1.09 | 0.00 | 3.00 | 0.00 | 1.65 | 2.48 | 1.46 |
time (sec) |
N/A | 0.222 | 0.281 | 0.806 | 0.000 | 0.247 | 0.000 | 0.313 | 0.002 | 0.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 124 | 119 | 117 | 0 | 344 | 0 | 171 | 246 | 199 |
N.S. |
1 | 1.04 | 1.00 | 0.98 | 0.00 | 2.89 | 0.00 | 1.44 | 2.07 | 1.67 |
time (sec) |
N/A | 0.220 | 0.404 | 0.387 | 0.000 | 0.229 | 0.000 | 0.333 | 0.002 | 0.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 134 | 119 | 122 | 0 | 563 | 0 | 161 | 410 | 222 |
N.S. |
1 | 1.06 | 0.94 | 0.97 | 0.00 | 4.47 | 0.00 | 1.28 | 3.25 | 1.76 |
time (sec) |
N/A | 0.214 | 0.496 | 0.583 | 0.000 | 0.242 | 0.000 | 0.302 | 0.002 | 0.386 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 172 | 172 | 159 | 0 | 894 | 0 | 259 | 661 | 309 |
N.S. |
1 | 1.06 | 1.06 | 0.98 | 0.00 | 5.52 | 0.00 | 1.60 | 4.08 | 1.91 |
time (sec) |
N/A | 0.236 | 0.848 | 0.439 | 0.000 | 0.258 | 0.000 | 0.315 | 0.004 | 0.420 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 218 | 222 | 205 | 0 | 1337 | 0 | 380 | 973 | 411 |
N.S. |
1 | 1.10 | 1.12 | 1.04 | 0.00 | 6.75 | 0.00 | 1.92 | 4.91 | 2.08 |
time (sec) |
N/A | 0.267 | 1.159 | 0.560 | 0.000 | 0.270 | 0.000 | 0.328 | 0.006 | 0.509 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 35 | 30 | 29 | 33 | 105 | 29 | 42 | 29 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.83 | 0.94 | 3.00 | 0.83 | 1.20 | 0.83 |
time (sec) |
N/A | 0.152 | 0.040 | 0.258 | 0.282 | 0.228 | 1.193 | 0.318 | 0.000 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 61 | 43 | 38 | 43 | 46 | 168 | 37 | 71 | 45 |
N.S. |
1 | 1.09 | 0.77 | 0.68 | 0.77 | 0.82 | 3.00 | 0.66 | 1.27 | 0.80 |
time (sec) |
N/A | 0.161 | 0.051 | 0.234 | 0.279 | 0.221 | 2.324 | 0.297 | 0.001 | 0.039 |
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 | 154 | 154 | 216 | 121 | 283 | 261 | 333 | 283 | 271 | 137 |
N.S. |
1 | 1.00 | 1.40 | 0.79 | 1.84 | 1.69 | 2.16 | 1.84 | 1.76 | 0.89 |
time (sec) |
N/A | 0.261 | 0.104 | 0.754 | 0.212 | 0.237 | 1.016 | 0.325 | 0.001 | 0.065 |
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 | 127 | 127 | 153 | 99 | 204 | 182 | 241 | 204 | 184 | 112 |
N.S. |
1 | 1.00 | 1.20 | 0.78 | 1.61 | 1.43 | 1.90 | 1.61 | 1.45 | 0.88 |
time (sec) |
N/A | 0.245 | 0.080 | 0.277 | 0.213 | 0.220 | 1.023 | 0.309 | 0.000 | 0.248 |
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 | 96 | 96 | 101 | 76 | 137 | 115 | 165 | 137 | 114 | 87 |
N.S. |
1 | 1.00 | 1.05 | 0.79 | 1.43 | 1.20 | 1.72 | 1.43 | 1.19 | 0.91 |
time (sec) |
N/A | 0.216 | 0.055 | 0.268 | 0.206 | 0.219 | 0.852 | 0.315 | 0.001 | 0.068 |
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 | 69 | 69 | 60 | 54 | 82 | 64 | 104 | 82 | 61 | 68 |
N.S. |
1 | 1.00 | 0.87 | 0.78 | 1.19 | 0.93 | 1.51 | 1.19 | 0.88 | 0.99 |
time (sec) |
N/A | 0.196 | 0.035 | 0.249 | 0.204 | 0.223 | 0.832 | 0.308 | 0.000 | 0.062 |
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 | 40 | 40 | 29 | 26 | 39 | 25 | 53 | 39 | 24 | 28 |
N.S. |
1 | 1.00 | 0.72 | 0.65 | 0.98 | 0.62 | 1.32 | 0.98 | 0.60 | 0.70 |
time (sec) |
N/A | 0.170 | 0.023 | 0.234 | 0.205 | 0.215 | 0.494 | 0.309 | 0.001 | 0.043 |
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 | 14 | 14 | 13 | 12 | 12 | 10 | 12 | 11 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 0.86 | 0.71 | 0.86 | 0.79 | 0.86 |
time (sec) |
N/A | 0.132 | 0.001 | 0.224 | 0.202 | 0.225 | 0.018 | 0.322 | 0.000 | 0.018 |
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 | 47 | 47 | 47 | 37 | 0 | 119 | 53 | 38 | 50 | 38 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.00 | 2.53 | 1.13 | 0.81 | 1.06 | 0.81 |
time (sec) |
N/A | 0.164 | 0.047 | 0.482 | 0.000 | 0.235 | 1.989 | 0.318 | 0.000 | 0.259 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 75 | 64 | 0 | 280 | 0 | 87 | 156 | 74 |
N.S. |
1 | 1.00 | 0.99 | 0.84 | 0.00 | 3.68 | 0.00 | 1.14 | 2.05 | 0.97 |
time (sec) |
N/A | 0.185 | 0.169 | 0.504 | 0.000 | 0.230 | 0.000 | 0.316 | 0.001 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 122 | 96 | 102 | 0 | 549 | 0 | 148 | 352 | 142 |
N.S. |
1 | 1.07 | 0.84 | 0.89 | 0.00 | 4.82 | 0.00 | 1.30 | 3.09 | 1.25 |
time (sec) |
N/A | 0.206 | 0.249 | 0.516 | 0.000 | 0.244 | 0.000 | 0.306 | 0.002 | 0.427 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 168 | 128 | 130 | 0 | 884 | 0 | 231 | 597 | 218 |
N.S. |
1 | 1.14 | 0.87 | 0.88 | 0.00 | 6.01 | 0.00 | 1.57 | 4.06 | 1.48 |
time (sec) |
N/A | 0.235 | 0.292 | 0.789 | 0.000 | 0.245 | 0.000 | 0.313 | 0.003 | 0.420 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 214 | 166 | 169 | 0 | 1325 | 0 | 331 | 903 | 307 |
N.S. |
1 | 1.19 | 0.92 | 0.94 | 0.00 | 7.36 | 0.00 | 1.84 | 5.02 | 1.71 |
time (sec) |
N/A | 0.265 | 0.492 | 0.789 | 0.000 | 0.254 | 0.000 | 0.303 | 0.004 | 0.459 |
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 | 152 | 152 | 214 | 206 | 267 | 271 | 272 | 350 | 273 | 192 |
N.S. |
1 | 1.00 | 1.41 | 1.36 | 1.76 | 1.78 | 1.79 | 2.30 | 1.80 | 1.26 |
time (sec) |
N/A | 0.257 | 0.112 | 0.323 | 0.222 | 0.227 | 7.539 | 0.318 | 0.000 | 0.081 |
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 | 123 | 123 | 151 | 145 | 189 | 192 | 196 | 240 | 186 | 153 |
N.S. |
1 | 1.00 | 1.23 | 1.18 | 1.54 | 1.56 | 1.59 | 1.95 | 1.51 | 1.24 |
time (sec) |
N/A | 0.233 | 0.076 | 0.303 | 0.210 | 0.223 | 4.075 | 0.313 | 0.000 | 0.054 |
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 | 94 | 94 | 99 | 94 | 125 | 124 | 134 | 152 | 115 | 114 |
N.S. |
1 | 1.00 | 1.05 | 1.00 | 1.33 | 1.32 | 1.43 | 1.62 | 1.22 | 1.21 |
time (sec) |
N/A | 0.214 | 0.058 | 0.277 | 0.239 | 0.223 | 2.411 | 0.302 | 0.000 | 0.085 |
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 | 67 | 67 | 59 | 55 | 75 | 73 | 88 | 84 | 62 | 67 |
N.S. |
1 | 1.00 | 0.88 | 0.82 | 1.12 | 1.09 | 1.31 | 1.25 | 0.93 | 1.00 |
time (sec) |
N/A | 0.195 | 0.040 | 0.272 | 0.198 | 0.220 | 1.482 | 0.298 | 0.001 | 0.283 |
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 | 38 | 38 | 27 | 26 | 37 | 35 | 60 | 34 | 26 | 25 |
N.S. |
1 | 1.00 | 0.71 | 0.68 | 0.97 | 0.92 | 1.58 | 0.89 | 0.68 | 0.66 |
time (sec) |
N/A | 0.166 | 0.025 | 0.240 | 0.203 | 0.217 | 0.238 | 0.338 | 0.000 | 0.049 |
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 | 14 | 14 | 13 | 12 | 20 | 12 | 12 | 13 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 1.43 | 0.86 | 0.86 | 0.93 | 0.86 |
time (sec) |
N/A | 0.128 | 0.001 | 0.703 | 0.208 | 0.223 | 0.023 | 0.310 | 0.000 | 0.022 |
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 | 69 | 69 | 69 | 68 | 0 | 214 | 82 | 69 | 84 | 57 |
N.S. |
1 | 1.00 | 1.00 | 0.99 | 0.00 | 3.10 | 1.19 | 1.00 | 1.22 | 0.83 |
time (sec) |
N/A | 0.178 | 0.099 | 0.265 | 0.000 | 0.235 | 2.877 | 0.324 | 0.001 | 0.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 113 | 90 | 78 | 0 | 423 | 0 | 143 | 220 | 123 |
N.S. |
1 | 1.14 | 0.91 | 0.79 | 0.00 | 4.27 | 0.00 | 1.44 | 2.22 | 1.24 |
time (sec) |
N/A | 0.200 | 0.275 | 0.759 | 0.000 | 0.249 | 0.000 | 0.322 | 0.002 | 0.181 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 159 | 126 | 122 | 0 | 782 | 0 | 234 | 437 | 205 |
N.S. |
1 | 1.14 | 0.90 | 0.87 | 0.00 | 5.59 | 0.00 | 1.67 | 3.12 | 1.46 |
time (sec) |
N/A | 0.226 | 0.483 | 0.569 | 0.000 | 0.251 | 0.000 | 0.337 | 0.003 | 0.425 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 205 | 170 | 156 | 0 | 1204 | 0 | 326 | 702 | 294 |
N.S. |
1 | 1.18 | 0.98 | 0.90 | 0.00 | 6.96 | 0.00 | 1.88 | 4.06 | 1.70 |
time (sec) |
N/A | 0.257 | 0.643 | 0.339 | 0.000 | 0.274 | 0.000 | 0.336 | 0.005 | 0.589 |
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 | 152 | 152 | 217 | 194 | 265 | 283 | 223 | 335 | 280 | 229 |
N.S. |
1 | 1.00 | 1.43 | 1.28 | 1.74 | 1.86 | 1.47 | 2.20 | 1.84 | 1.51 |
time (sec) |
N/A | 0.257 | 0.107 | 0.331 | 0.239 | 0.226 | 7.771 | 0.340 | 0.001 | 0.161 |
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 | 125 | 125 | 153 | 128 | 187 | 203 | 162 | 229 | 193 | 175 |
N.S. |
1 | 1.00 | 1.22 | 1.02 | 1.50 | 1.62 | 1.30 | 1.83 | 1.54 | 1.40 |
time (sec) |
N/A | 0.229 | 0.095 | 0.305 | 0.229 | 0.221 | 4.566 | 0.328 | 0.001 | 0.298 |
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 | 96 | 96 | 101 | 66 | 122 | 136 | 461 | 141 | 122 | 128 |
N.S. |
1 | 1.00 | 1.05 | 0.69 | 1.27 | 1.42 | 4.80 | 1.47 | 1.27 | 1.33 |
time (sec) |
N/A | 0.209 | 0.068 | 0.295 | 0.243 | 0.238 | 0.421 | 0.334 | 0.000 | 0.081 |
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 | 67 | 67 | 62 | 50 | 72 | 85 | 265 | 72 | 70 | 68 |
N.S. |
1 | 1.00 | 0.93 | 0.75 | 1.07 | 1.27 | 3.96 | 1.07 | 1.04 | 1.01 |
time (sec) |
N/A | 0.182 | 0.048 | 0.272 | 0.215 | 0.231 | 0.458 | 0.314 | 0.000 | 0.065 |
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 | 40 | 40 | 29 | 26 | 28 | 46 | 124 | 28 | 34 | 29 |
N.S. |
1 | 1.00 | 0.72 | 0.65 | 0.70 | 1.15 | 3.10 | 0.70 | 0.85 | 0.72 |
time (sec) |
N/A | 0.164 | 0.026 | 0.245 | 0.224 | 0.223 | 0.423 | 0.344 | 0.000 | 0.262 |
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 | 16 | 16 | 16 | 13 | 12 | 31 | 14 | 12 | 20 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 1.94 | 0.88 | 0.75 | 1.25 | 0.75 |
time (sec) |
N/A | 0.126 | 0.002 | 0.235 | 0.215 | 0.218 | 0.038 | 0.322 | 0.000 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 105 | 85 | 90 | 0 | 398 | 107 | 113 | 223 | 100 |
N.S. |
1 | 1.13 | 0.91 | 0.97 | 0.00 | 4.28 | 1.15 | 1.22 | 2.40 | 1.08 |
time (sec) |
N/A | 0.198 | 0.179 | 0.523 | 0.000 | 0.234 | 3.054 | 0.344 | 0.001 | 0.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 149 | 125 | 121 | 0 | 782 | 0 | 216 | 493 | 161 |
N.S. |
1 | 1.20 | 1.01 | 0.98 | 0.00 | 6.31 | 0.00 | 1.74 | 3.98 | 1.30 |
time (sec) |
N/A | 0.226 | 0.295 | 0.605 | 0.000 | 0.242 | 0.000 | 0.327 | 0.002 | 0.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 195 | 168 | 143 | 0 | 1226 | 0 | 298 | 804 | 243 |
N.S. |
1 | 1.17 | 1.01 | 0.86 | 0.00 | 7.34 | 0.00 | 1.78 | 4.81 | 1.46 |
time (sec) |
N/A | 0.248 | 0.577 | 0.336 | 0.000 | 0.269 | 0.000 | 0.343 | 0.004 | 0.250 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 241 | 220 | 177 | 0 | 1840 | 0 | 432 | 1220 | 334 |
N.S. |
1 | 1.20 | 1.10 | 0.88 | 0.00 | 9.20 | 0.00 | 2.16 | 6.10 | 1.67 |
time (sec) |
N/A | 0.281 | 0.863 | 0.363 | 0.000 | 0.351 | 0.000 | 0.328 | 0.007 | 0.736 |
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 | 22 | 22 | 25 | 19 | 18 | 95 | 66 | 637 | 85 | 17 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.82 | 4.32 | 3.00 | 28.95 | 3.86 | 0.77 |
time (sec) |
N/A | 0.136 | 0.012 | 0.262 | 0.213 | 0.226 | 0.792 | 0.343 | 0.001 | 0.059 |
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 | 22 | 22 | 25 | 19 | 18 | 75 | 66 | 495 | 73 | 17 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.82 | 3.41 | 3.00 | 22.50 | 3.32 | 0.77 |
time (sec) |
N/A | 0.136 | 0.006 | 0.737 | 0.211 | 0.213 | 0.655 | 0.323 | 0.000 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 25 | 19 | 374 | 67 | 88 | 374 | 65 | 17 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 17.00 | 3.05 | 4.00 | 17.00 | 2.95 | 0.77 |
time (sec) |
N/A | 0.137 | 0.008 | 0.251 | 0.226 | 0.228 | 0.615 | 0.330 | 0.001 | 0.029 |
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 | 22 | 22 | 25 | 19 | 18 | 56 | 88 | 266 | 54 | 17 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.82 | 2.55 | 4.00 | 12.09 | 2.45 | 0.77 |
time (sec) |
N/A | 0.136 | 0.008 | 0.250 | 0.217 | 0.226 | 0.771 | 0.333 | 0.000 | 0.029 |
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 | 22 | 22 | 25 | 19 | 18 | 45 | 88 | 178 | 43 | 17 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.82 | 2.05 | 4.00 | 8.09 | 1.95 | 0.77 |
time (sec) |
N/A | 0.136 | 0.008 | 0.251 | 0.222 | 0.220 | 0.641 | 0.318 | 0.001 | 0.028 |
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 | 22 | 22 | 25 | 19 | 18 | 34 | 80 | 106 | 32 | 17 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 0.82 | 1.55 | 3.64 | 4.82 | 1.45 | 0.77 |
time (sec) |
N/A | 0.136 | 0.007 | 0.740 | 0.227 | 0.231 | 0.642 | 0.318 | 0.000 | 0.029 |
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 | 22 | 22 | 26 | 19 | 18 | 23 | 53 | 54 | 21 | 17 |
N.S. |
1 | 1.00 | 1.18 | 0.86 | 0.82 | 1.05 | 2.41 | 2.45 | 0.95 | 0.77 |
time (sec) |
N/A | 0.136 | 0.008 | 0.252 | 0.215 | 0.218 | 0.983 | 0.335 | 0.000 | 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 | 20 | 20 | 24 | 18 | 18 | 18 | 29 | 18 | 16 | 17 |
N.S. |
1 | 1.00 | 1.20 | 0.90 | 0.90 | 0.90 | 1.45 | 0.90 | 0.80 | 0.85 |
time (sec) |
N/A | 0.135 | 0.004 | 0.253 | 0.216 | 0.216 | 1.258 | 0.330 | 0.001 | 0.028 |
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 | 20 | 20 | 24 | 18 | 18 | 29 | 41 | 18 | 18 | 17 |
N.S. |
1 | 1.00 | 1.20 | 0.90 | 0.90 | 1.45 | 2.05 | 0.90 | 0.90 | 0.85 |
time (sec) |
N/A | 0.136 | 0.005 | 0.258 | 0.226 | 0.224 | 2.126 | 0.339 | 0.001 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 21 | 21 | 21 | 26 | 22 | 19 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 1.50 | 1.50 | 1.86 | 1.57 | 1.36 | 0.71 |
time (sec) |
N/A | 0.134 | 0.013 | 0.484 | 0.220 | 0.220 | 0.439 | 0.312 | 0.001 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 19 | 18 | 18 | 61 | 18 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.72 | 0.72 | 2.44 | 0.72 | 0.68 | 0.60 |
time (sec) |
N/A | 0.142 | 0.033 | 0.558 | 0.310 | 0.222 | 0.586 | 0.315 | 0.000 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 91 | 112 | 84 | 86 | 86 | 170 | 87 | 155 | 104 |
N.S. |
1 | 1.08 | 1.33 | 1.00 | 1.02 | 1.02 | 2.02 | 1.04 | 1.85 | 1.24 |
time (sec) |
N/A | 0.204 | 0.102 | 2.232 | 0.306 | 0.221 | 1.803 | 0.343 | 0.007 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 18 | 15 | 19 | 19 | 112 | 26 | 19 | 14 |
N.S. |
1 | 1.00 | 0.67 | 0.56 | 0.70 | 0.70 | 4.15 | 0.96 | 0.70 | 0.52 |
time (sec) |
N/A | 0.152 | 0.013 | 0.294 | 0.188 | 0.215 | 0.701 | 0.320 | 0.001 | 0.247 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 23 | 20 | 28 | 24 | 144 | 38 | 24 | 21 |
N.S. |
1 | 1.00 | 0.61 | 0.53 | 0.74 | 0.63 | 3.79 | 1.00 | 0.63 | 0.55 |
time (sec) |
N/A | 0.157 | 0.015 | 0.287 | 0.215 | 0.218 | 1.105 | 0.324 | 0.001 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 154 | 143 | 0 | 570 | 0 | 196 | 230 | 204 |
N.S. |
1 | 1.00 | 1.11 | 1.03 | 0.00 | 4.10 | 0.00 | 1.41 | 1.65 | 1.47 |
time (sec) |
N/A | 0.260 | 0.179 | 0.672 | 0.000 | 0.241 | 0.000 | 0.339 | 0.018 | 0.183 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 154 | 145 | 0 | 900 | 0 | 207 | 234 | 206 |
N.S. |
1 | 1.00 | 1.10 | 1.04 | 0.00 | 6.43 | 0.00 | 1.48 | 1.67 | 1.47 |
time (sec) |
N/A | 0.248 | 0.148 | 0.307 | 0.000 | 0.255 | 0.000 | 0.333 | 0.013 | 0.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 230 | 237 | 221 | 239 | 0 | 702 | 0 | 1107 | 651 | 0 |
N.S. |
1 | 1.03 | 0.96 | 1.04 | 0.00 | 3.05 | 0.00 | 4.81 | 2.83 | 0.00 |
time (sec) |
N/A | 0.288 | 0.467 | 0.261 | 0.000 | 0.276 | 0.000 | 0.470 | 0.043 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 196 | 167 | 206 | 0 | 540 | 0 | 726 | 471 | 0 |
N.S. |
1 | 1.02 | 0.87 | 1.07 | 0.00 | 2.81 | 0.00 | 3.78 | 2.45 | 0.00 |
time (sec) |
N/A | 0.254 | 0.335 | 0.259 | 0.000 | 0.251 | 0.000 | 0.433 | 0.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 155 | 128 | 173 | 0 | 410 | 0 | 438 | 320 | 0 |
N.S. |
1 | 1.01 | 0.83 | 1.12 | 0.00 | 2.66 | 0.00 | 2.84 | 2.08 | 0.00 |
time (sec) |
N/A | 0.224 | 0.242 | 0.269 | 0.000 | 0.254 | 0.000 | 0.402 | 0.011 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 114 | 95 | 140 | 0 | 300 | 0 | 232 | 196 | 88 |
N.S. |
1 | 0.98 | 0.82 | 1.21 | 0.00 | 2.59 | 0.00 | 2.00 | 1.69 | 0.76 |
time (sec) |
N/A | 0.196 | 0.022 | 0.751 | 0.000 | 0.245 | 0.000 | 0.357 | 0.004 | 0.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 72 | 107 | 0 | 236 | 0 | 93 | 102 | 260 |
N.S. |
1 | 1.00 | 1.00 | 1.49 | 0.00 | 3.28 | 0.00 | 1.29 | 1.42 | 3.61 |
time (sec) |
N/A | 0.171 | 0.119 | 0.259 | 0.000 | 0.240 | 0.000 | 0.332 | 0.003 | 3.950 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 66 | 0 | 0 | 241 | 0 | 131 | 78 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 3.65 | 0.00 | 1.98 | 1.18 | 0.00 |
time (sec) |
N/A | 0.164 | 0.074 | 0.000 | 0.000 | 0.261 | 0.000 | 0.349 | 0.003 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 27 | 0 | 65 | 0 | 152 | 89 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.00 | 2.03 | 0.00 | 4.75 | 2.78 | 0.84 |
time (sec) |
N/A | 0.135 | 0.024 | 0.258 | 0.000 | 0.261 | 0.000 | 0.359 | 0.005 | 0.723 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 46 | 54 | 0 | 175 | 0 | 447 | 239 | 127 |
N.S. |
1 | 1.00 | 0.70 | 0.82 | 0.00 | 2.65 | 0.00 | 6.77 | 3.62 | 1.92 |
time (sec) |
N/A | 0.159 | 0.074 | 0.259 | 0.000 | 0.379 | 0.000 | 0.399 | 0.006 | 0.960 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 114 | 77 | 105 | 0 | 337 | 0 | 689 | 446 | 203 |
N.S. |
1 | 1.13 | 0.76 | 1.04 | 0.00 | 3.34 | 0.00 | 6.82 | 4.42 | 2.01 |
time (sec) |
N/A | 0.182 | 0.127 | 0.749 | 0.000 | 0.656 | 0.000 | 0.415 | 0.012 | 0.960 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 162 | 118 | 171 | 0 | 532 | 0 | 989 | 706 | 292 |
N.S. |
1 | 1.19 | 0.87 | 1.26 | 0.00 | 3.91 | 0.00 | 7.27 | 5.19 | 2.15 |
time (sec) |
N/A | 0.209 | 0.226 | 0.256 | 0.000 | 2.178 | 0.000 | 0.448 | 0.027 | 1.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 210 | 170 | 248 | 0 | 781 | 0 | 1345 | 1027 | 397 |
N.S. |
1 | 1.23 | 0.99 | 1.45 | 0.00 | 4.57 | 0.00 | 7.87 | 6.01 | 2.32 |
time (sec) |
N/A | 0.232 | 0.333 | 0.258 | 0.000 | 4.730 | 0.000 | 0.463 | 0.044 | 1.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 237 | 220 | 239 | 0 | 702 | 0 | 1740 | 651 | 0 |
N.S. |
1 | 1.04 | 0.97 | 1.05 | 0.00 | 3.09 | 0.00 | 7.67 | 2.87 | 0.00 |
time (sec) |
N/A | 0.264 | 0.408 | 0.262 | 0.000 | 0.274 | 0.000 | 0.552 | 0.045 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 189 | 196 | 167 | 206 | 0 | 534 | 0 | 1071 | 471 | 0 |
N.S. |
1 | 1.04 | 0.88 | 1.09 | 0.00 | 2.83 | 0.00 | 5.67 | 2.49 | 0.00 |
time (sec) |
N/A | 0.236 | 0.298 | 0.258 | 0.000 | 0.255 | 0.000 | 0.449 | 0.016 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 155 | 127 | 173 | 0 | 410 | 0 | 576 | 320 | 0 |
N.S. |
1 | 1.03 | 0.84 | 1.15 | 0.00 | 2.72 | 0.00 | 3.81 | 2.12 | 0.00 |
time (sec) |
N/A | 0.211 | 0.217 | 0.756 | 0.000 | 0.252 | 0.000 | 0.399 | 0.010 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 113 | 94 | 140 | 0 | 306 | 0 | 233 | 198 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.24 | 0.00 | 2.71 | 0.00 | 2.06 | 1.75 | 0.00 |
time (sec) |
N/A | 0.189 | 0.147 | 0.256 | 0.000 | 0.242 | 0.000 | 0.358 | 0.004 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 102 | 86 | 0 | 0 | 311 | 0 | 204 | 170 | 0 |
N.S. |
1 | 1.04 | 0.88 | 0.00 | 0.00 | 3.17 | 0.00 | 2.08 | 1.73 | 0.00 |
time (sec) |
N/A | 0.183 | 0.160 | 0.000 | 0.000 | 0.279 | 0.000 | 0.389 | 0.005 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 97 | 81 | 0 | 0 | 325 | 0 | 455 | 150 | 0 |
N.S. |
1 | 1.05 | 0.88 | 0.00 | 0.00 | 3.53 | 0.00 | 4.95 | 1.63 | 0.00 |
time (sec) |
N/A | 0.183 | 0.126 | 0.000 | 0.000 | 0.305 | 0.000 | 0.432 | 0.004 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 27 | 0 | 104 | 0 | 374 | 161 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.00 | 3.25 | 0.00 | 11.69 | 5.03 | 0.84 |
time (sec) |
N/A | 0.143 | 0.028 | 0.258 | 0.000 | 0.384 | 0.000 | 0.435 | 0.008 | 0.754 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 46 | 54 | 0 | 235 | 0 | 1024 | 345 | 178 |
N.S. |
1 | 1.00 | 0.70 | 0.82 | 0.00 | 3.56 | 0.00 | 15.52 | 5.23 | 2.70 |
time (sec) |
N/A | 0.160 | 0.091 | 0.260 | 0.000 | 0.719 | 0.000 | 0.487 | 0.012 | 0.864 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 114 | 77 | 105 | 0 | 426 | 0 | 1394 | 592 | 268 |
N.S. |
1 | 1.13 | 0.76 | 1.04 | 0.00 | 4.22 | 0.00 | 13.80 | 5.86 | 2.65 |
time (sec) |
N/A | 0.192 | 0.166 | 0.767 | 0.000 | 2.304 | 0.000 | 0.542 | 0.028 | 1.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 162 | 118 | 171 | 0 | 649 | 0 | 1823 | 892 | 376 |
N.S. |
1 | 1.19 | 0.87 | 1.26 | 0.00 | 4.77 | 0.00 | 13.40 | 6.56 | 2.76 |
time (sec) |
N/A | 0.215 | 0.302 | 0.266 | 0.000 | 4.971 | 0.000 | 0.596 | 0.048 | 1.299 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 262 | 278 | 283 | 272 | 0 | 882 | 0 | 3120 | 860 | 0 |
N.S. |
1 | 1.06 | 1.08 | 1.04 | 0.00 | 3.37 | 0.00 | 11.91 | 3.28 | 0.00 |
time (sec) |
N/A | 0.297 | 0.492 | 0.263 | 0.000 | 0.272 | 0.000 | 0.694 | 0.074 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 237 | 220 | 239 | 0 | 702 | 0 | 1962 | 651 | 0 |
N.S. |
1 | 1.06 | 0.98 | 1.07 | 0.00 | 3.13 | 0.00 | 8.76 | 2.91 | 0.00 |
time (sec) |
N/A | 0.269 | 0.359 | 0.259 | 0.000 | 0.277 | 0.000 | 0.590 | 0.041 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 196 | 168 | 206 | 0 | 540 | 0 | 1083 | 471 | 0 |
N.S. |
1 | 1.05 | 0.90 | 1.11 | 0.00 | 2.90 | 0.00 | 5.82 | 2.53 | 0.00 |
time (sec) |
N/A | 0.248 | 0.274 | 0.258 | 0.000 | 0.256 | 0.000 | 0.478 | 0.019 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 154 | 124 | 173 | 0 | 412 | 0 | 446 | 320 | 0 |
N.S. |
1 | 1.04 | 0.84 | 1.17 | 0.00 | 2.78 | 0.00 | 3.01 | 2.16 | 0.00 |
time (sec) |
N/A | 0.219 | 0.195 | 0.761 | 0.000 | 0.248 | 0.000 | 0.365 | 0.010 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 143 | 124 | 0 | 0 | 439 | 0 | 287 | 304 | 0 |
N.S. |
1 | 1.04 | 0.90 | 0.00 | 0.00 | 3.18 | 0.00 | 2.08 | 2.20 | 0.00 |
time (sec) |
N/A | 0.216 | 0.238 | 0.000 | 0.000 | 0.296 | 0.000 | 0.608 | 0.012 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 136 | 119 | 0 | 0 | 475 | 0 | 650 | 379 | 0 |
N.S. |
1 | 1.06 | 0.93 | 0.00 | 0.00 | 3.71 | 0.00 | 5.08 | 2.96 | 0.00 |
time (sec) |
N/A | 0.210 | 0.187 | 0.000 | 0.000 | 0.358 | 0.000 | 0.818 | 0.017 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 128 | 111 | 0 | 0 | 463 | 0 | 1025 | 332 | 0 |
N.S. |
1 | 1.07 | 0.92 | 0.00 | 0.00 | 3.86 | 0.00 | 8.54 | 2.77 | 0.00 |
time (sec) |
N/A | 0.205 | 0.145 | 0.000 | 0.000 | 0.495 | 0.000 | 0.568 | 0.009 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 27 | 0 | 138 | 0 | 706 | 229 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.00 | 4.31 | 0.00 | 22.06 | 7.16 | 0.84 |
time (sec) |
N/A | 0.142 | 0.030 | 0.264 | 0.000 | 0.687 | 0.000 | 0.545 | 0.021 | 1.252 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 46 | 54 | 0 | 295 | 0 | 1826 | 451 | 229 |
N.S. |
1 | 1.00 | 0.70 | 0.82 | 0.00 | 4.47 | 0.00 | 27.67 | 6.83 | 3.47 |
time (sec) |
N/A | 0.158 | 0.123 | 0.259 | 0.000 | 2.442 | 0.000 | 0.656 | 0.027 | 1.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 114 | 77 | 105 | 0 | 513 | 0 | 2316 | 738 | 333 |
N.S. |
1 | 1.13 | 0.76 | 1.04 | 0.00 | 5.08 | 0.00 | 22.93 | 7.31 | 3.30 |
time (sec) |
N/A | 0.184 | 0.221 | 0.262 | 0.000 | 5.479 | 0.000 | 0.805 | 0.052 | 1.295 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 162 | 118 | 171 | 0 | 765 | 0 | 2868 | 1078 | 459 |
N.S. |
1 | 1.19 | 0.87 | 1.26 | 0.00 | 5.62 | 0.00 | 21.09 | 7.93 | 3.38 |
time (sec) |
N/A | 0.219 | 0.417 | 0.265 | 0.000 | 11.229 | 0.000 | 0.938 | 0.093 | 1.471 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 196 | 164 | 206 | 0 | 542 | 0 | 268 | 471 | 0 |
N.S. |
1 | 1.07 | 0.90 | 1.13 | 0.00 | 2.96 | 0.00 | 1.46 | 2.57 | 0.00 |
time (sec) |
N/A | 0.246 | 0.367 | 0.782 | 0.000 | 0.282 | 0.000 | 0.333 | 0.020 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 155 | 125 | 173 | 0 | 412 | 0 | 198 | 320 | 0 |
N.S. |
1 | 1.05 | 0.84 | 1.17 | 0.00 | 2.78 | 0.00 | 1.34 | 2.16 | 0.00 |
time (sec) |
N/A | 0.222 | 0.283 | 0.258 | 0.000 | 0.245 | 0.000 | 0.313 | 0.011 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 114 | 94 | 140 | 0 | 306 | 0 | 139 | 198 | 0 |
N.S. |
1 | 1.01 | 0.83 | 1.24 | 0.00 | 2.71 | 0.00 | 1.23 | 1.75 | 0.00 |
time (sec) |
N/A | 0.191 | 0.179 | 0.259 | 0.000 | 0.254 | 0.000 | 0.338 | 0.005 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 72 | 107 | 0 | 235 | 0 | 97 | 102 | 261 |
N.S. |
1 | 1.00 | 0.99 | 1.47 | 0.00 | 3.22 | 0.00 | 1.33 | 1.40 | 3.58 |
time (sec) |
N/A | 0.166 | 0.122 | 0.259 | 0.000 | 0.237 | 0.000 | 0.325 | 0.002 | 3.762 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 42 | 76 | 0 | 178 | 0 | 50 | 44 | 45 |
N.S. |
1 | 1.00 | 1.00 | 1.81 | 0.00 | 4.24 | 0.00 | 1.19 | 1.05 | 1.07 |
time (sec) |
N/A | 0.149 | 0.047 | 0.680 | 0.000 | 0.243 | 0.000 | 0.342 | 0.001 | 0.301 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 27 | 0 | 42 | 0 | 66 | 43 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.00 | 1.40 | 0.00 | 2.20 | 1.43 | 0.87 |
time (sec) |
N/A | 0.136 | 0.022 | 0.262 | 0.000 | 0.231 | 0.000 | 0.320 | 0.002 | 0.971 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 45 | 54 | 0 | 118 | 0 | 121 | 131 | 71 |
N.S. |
1 | 1.00 | 0.68 | 0.82 | 0.00 | 1.79 | 0.00 | 1.83 | 1.98 | 1.08 |
time (sec) |
N/A | 0.154 | 0.064 | 0.264 | 0.000 | 0.262 | 0.000 | 0.325 | 0.003 | 0.851 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 114 | 75 | 95 | 0 | 251 | 0 | 227 | 302 | 133 |
N.S. |
1 | 1.13 | 0.74 | 0.94 | 0.00 | 2.49 | 0.00 | 2.25 | 2.99 | 1.32 |
time (sec) |
N/A | 0.178 | 0.107 | 0.520 | 0.000 | 0.375 | 0.000 | 0.323 | 0.007 | 0.997 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 162 | 116 | 135 | 0 | 419 | 0 | 386 | 522 | 209 |
N.S. |
1 | 1.19 | 0.85 | 0.99 | 0.00 | 3.08 | 0.00 | 2.84 | 3.84 | 1.54 |
time (sec) |
N/A | 0.201 | 0.174 | 0.519 | 0.000 | 0.633 | 0.000 | 0.353 | 0.012 | 1.263 |