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 | C | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 169 | 144 | 45 | 144 | 905 | 36 | 112 | 196 |
N.S. |
1 | 0.91 | 0.78 | 0.24 | 0.78 | 4.89 | 0.19 | 0.61 | 1.06 |
time (sec) |
N/A | 0.368 | 0.075 | 4.526 | 0.283 | 0.959 | 0.537 | 0.297 | 5.817 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 170 | 144 | 34 | 124 | 637 | 36 | 112 | 197 |
N.S. |
1 | 0.92 | 0.78 | 0.18 | 0.67 | 3.44 | 0.19 | 0.61 | 1.06 |
time (sec) |
N/A | 0.371 | 0.081 | 4.506 | 0.300 | 0.982 | 0.839 | 0.301 | 6.655 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 170 | 144 | 40 | 124 | 980 | 36 | 112 | 200 |
N.S. |
1 | 0.92 | 0.78 | 0.22 | 0.67 | 5.30 | 0.19 | 0.61 | 1.08 |
time (sec) |
N/A | 0.353 | 0.053 | 4.539 | 0.276 | 0.944 | 0.488 | 0.296 | 0.266 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 168 | 169 | 144 | 32 | 144 | 539 | 34 | 112 | 182 |
N.S. |
1 | 1.01 | 0.86 | 0.19 | 0.86 | 3.21 | 0.20 | 0.67 | 1.08 |
time (sec) |
N/A | 0.353 | 0.045 | 4.493 | 0.289 | 0.926 | 0.790 | 0.285 | 5.825 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 190 | 176 | 149 | 50 | 149 | 1073 | 39 | 132 | 203 |
N.S. |
1 | 0.93 | 0.78 | 0.26 | 0.78 | 5.65 | 0.21 | 0.69 | 1.07 |
time (sec) |
N/A | 0.369 | 0.098 | 4.436 | 0.317 | 1.235 | 0.897 | 0.281 | 5.743 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 192 | 177 | 149 | 43 | 129 | 692 | 42 | 132 | 200 |
N.S. |
1 | 0.92 | 0.78 | 0.22 | 0.67 | 3.60 | 0.22 | 0.69 | 1.04 |
time (sec) |
N/A | 0.356 | 0.139 | 4.535 | 0.315 | 0.958 | 0.499 | 0.291 | 6.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 192 | 177 | 150 | 39 | 129 | 1174 | 42 | 132 | 207 |
N.S. |
1 | 0.92 | 0.78 | 0.20 | 0.67 | 6.11 | 0.22 | 0.69 | 1.08 |
time (sec) |
N/A | 0.353 | 0.134 | 4.540 | 0.310 | 0.976 | 0.875 | 0.302 | 0.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | A | F(-1) | A | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 83 | 87 | 72 | 0 | 124 | 172 | 0 | 58 | 0 |
N.S. |
1 | 1.05 | 0.87 | 0.00 | 1.49 | 2.07 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.232 | 1.823 | 0.000 | 0.301 | 0.645 | 0.000 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | A | A | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 57 | 55 | 58 | 0 | 81 | 136 | 49 | 44 | 0 |
N.S. |
1 | 0.96 | 1.02 | 0.00 | 1.42 | 2.39 | 0.86 | 0.77 | 0.00 |
time (sec) |
N/A | 0.202 | 0.393 | 0.000 | 0.297 | 0.626 | 93.976 | 0.321 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | B | A | A | A | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 32 | 30 | 33 | 0 | 45 | 97 | 24 | 25 | 0 |
N.S. |
1 | 0.94 | 1.03 | 0.00 | 1.41 | 3.03 | 0.75 | 0.78 | 0.00 |
time (sec) |
N/A | 0.175 | 0.510 | 0.000 | 0.318 | 0.615 | 0.725 | 0.300 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 18 | 17 | 17 | 22 | 23 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.74 | 0.74 | 0.96 | 1.00 | 0.00 |
time (sec) |
N/A | 0.146 | 0.360 | 4.425 | 0.191 | 0.291 | 2.379 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 31 | 26 | 35 | 27 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 0.65 | 0.54 | 0.73 | 0.56 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.168 | 1.799 | 4.346 | 0.196 | 0.276 | 0.000 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 52 | 46 | 38 | 86 | 46 | 0 | 36 | 0 |
N.S. |
1 | 1.11 | 0.98 | 0.81 | 1.83 | 0.98 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.192 | 1.452 | 4.694 | 0.204 | 0.304 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 39 | 30 | 58 | 35 | 22 | 29 | 0 |
N.S. |
1 | 1.00 | 1.34 | 1.03 | 2.00 | 1.21 | 0.76 | 1.00 | 0.00 |
time (sec) |
N/A | 0.166 | 0.245 | 4.589 | 0.188 | 0.332 | 101.721 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 20 | 7 | 33 | 22 | 8 | 16 | 0 |
N.S. |
1 | 1.00 | 2.00 | 0.70 | 3.30 | 2.20 | 0.80 | 1.60 | 0.00 |
time (sec) |
N/A | 0.150 | 0.345 | 4.384 | 0.200 | 0.305 | 0.623 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 13 | 12 | 12 | 14 | 11 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.72 | 0.67 | 0.67 | 0.78 | 0.61 | 0.00 |
time (sec) |
N/A | 0.139 | 0.249 | 4.372 | 0.193 | 0.266 | 2.356 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 25 | 20 | 25 | 19 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.68 | 0.54 | 0.68 | 0.51 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.152 | 1.217 | 4.355 | 0.189 | 0.309 | 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 | 40 | 39 | 40 | 32 | 31 | 89 | 63 | 31 | 28 |
N.S. |
1 | 0.98 | 1.00 | 0.80 | 0.78 | 2.22 | 1.58 | 0.78 | 0.70 |
time (sec) |
N/A | 0.164 | 0.019 | 4.437 | 0.277 | 0.264 | 0.130 | 0.267 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 135 | 186 | 36 | 115 | 114 | 27 | 120 | 130 |
N.S. |
1 | 1.02 | 1.40 | 0.27 | 0.86 | 0.86 | 0.20 | 0.90 | 0.98 |
time (sec) |
N/A | 0.318 | 0.057 | 4.513 | 0.280 | 0.307 | 0.107 | 0.287 | 5.631 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 220 | 222 | 182 | 34 | 194 | 212 | 22 | 180 | 227 |
N.S. |
1 | 1.01 | 0.83 | 0.15 | 0.88 | 0.96 | 0.10 | 0.82 | 1.03 |
time (sec) |
N/A | 0.463 | 0.037 | 4.425 | 0.285 | 0.304 | 0.090 | 0.274 | 5.553 |
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 | 15 | 15 | 15 | 14 | 13 | 13 | 10 | 14 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 0.67 | 0.93 | 0.87 |
time (sec) |
N/A | 0.146 | 0.006 | 4.537 | 0.190 | 0.284 | 0.099 | 0.406 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 215 | 220 | 154 | 27 | 184 | 248 | 26 | 190 | 134 |
N.S. |
1 | 1.02 | 0.72 | 0.13 | 0.86 | 1.15 | 0.12 | 0.88 | 0.62 |
time (sec) |
N/A | 0.423 | 0.022 | 4.454 | 0.292 | 0.290 | 0.077 | 0.441 | 0.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 126 | 154 | 29 | 104 | 318 | 26 | 118 | 118 |
N.S. |
1 | 1.02 | 1.25 | 0.24 | 0.85 | 2.59 | 0.21 | 0.96 | 0.96 |
time (sec) |
N/A | 0.285 | 0.020 | 4.422 | 0.274 | 0.301 | 0.091 | 0.370 | 5.725 |
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 | 29 | 29 | 29 | 19 | 18 | 72 | 56 | 18 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.66 | 0.62 | 2.48 | 1.93 | 0.62 | 0.66 |
time (sec) |
N/A | 0.157 | 0.008 | 4.461 | 0.284 | 0.291 | 0.104 | 0.363 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 121 | 154 | 27 | 104 | 313 | 22 | 118 | 105 |
N.S. |
1 | 0.98 | 1.25 | 0.22 | 0.85 | 2.54 | 0.18 | 0.96 | 0.85 |
time (sec) |
N/A | 0.285 | 0.026 | 4.444 | 0.294 | 0.309 | 0.096 | 0.288 | 5.625 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 215 | 210 | 154 | 27 | 184 | 216 | 20 | 190 | 219 |
N.S. |
1 | 0.98 | 0.72 | 0.13 | 0.86 | 1.00 | 0.09 | 0.88 | 1.02 |
time (sec) |
N/A | 0.406 | 0.021 | 4.381 | 0.299 | 0.293 | 0.080 | 0.280 | 0.157 |
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 | 22 | 26 | 22 | 21 | 23 | 18 | 15 | 24 | 18 |
N.S. |
1 | 1.18 | 1.00 | 0.95 | 1.05 | 0.82 | 0.68 | 1.09 | 0.82 |
time (sec) |
N/A | 0.158 | 0.008 | 4.483 | 0.222 | 0.362 | 0.171 | 0.281 | 5.663 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 223 | 235 | 189 | 50 | 198 | 257 | 29 | 196 | 149 |
N.S. |
1 | 1.05 | 0.85 | 0.22 | 0.89 | 1.15 | 0.13 | 0.88 | 0.67 |
time (sec) |
N/A | 0.439 | 0.046 | 4.629 | 0.329 | 0.290 | 0.102 | 0.321 | 5.613 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 141 | 203 | 55 | 112 | 115 | 34 | 127 | 116 |
N.S. |
1 | 1.06 | 1.53 | 0.41 | 0.84 | 0.86 | 0.26 | 0.95 | 0.87 |
time (sec) |
N/A | 0.310 | 0.036 | 4.535 | 0.308 | 0.281 | 0.127 | 0.277 | 5.542 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 101 | 32 | 31 | 90 | 71 | 31 | 28 |
N.S. |
1 | 1.00 | 2.52 | 0.80 | 0.78 | 2.25 | 1.78 | 0.78 | 0.70 |
time (sec) |
N/A | 0.163 | 0.023 | 4.395 | 0.311 | 0.269 | 0.147 | 0.280 | 5.394 |
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 | 49 | 53 | 49 | 40 | 40 | 128 | 83 | 39 | 37 |
N.S. |
1 | 1.08 | 1.00 | 0.82 | 0.82 | 2.61 | 1.69 | 0.80 | 0.76 |
time (sec) |
N/A | 0.172 | 0.030 | 4.544 | 0.355 | 0.270 | 0.213 | 0.272 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 142 | 148 | 197 | 48 | 122 | 409 | 42 | 138 | 118 |
N.S. |
1 | 1.04 | 1.39 | 0.34 | 0.86 | 2.88 | 0.30 | 0.97 | 0.83 |
time (sec) |
N/A | 0.308 | 0.119 | 4.554 | 0.314 | 0.331 | 0.193 | 0.273 | 5.567 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 232 | 235 | 191 | 43 | 205 | 352 | 39 | 205 | 242 |
N.S. |
1 | 1.01 | 0.82 | 0.19 | 0.88 | 1.52 | 0.17 | 0.88 | 1.04 |
time (sec) |
N/A | 0.435 | 0.119 | 4.541 | 0.279 | 0.271 | 0.165 | 0.275 | 5.527 |
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 | 16 | 16 | 16 | 15 | 14 | 15 | 15 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.94 | 0.94 | 0.88 | 0.88 |
time (sec) |
N/A | 0.144 | 0.007 | 4.395 | 0.189 | 0.263 | 0.134 | 0.292 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 234 | 247 | 193 | 48 | 206 | 383 | 46 | 207 | 160 |
N.S. |
1 | 1.06 | 0.82 | 0.21 | 0.88 | 1.64 | 0.20 | 0.88 | 0.68 |
time (sec) |
N/A | 0.438 | 0.118 | 4.456 | 0.289 | 0.295 | 0.167 | 0.318 | 5.771 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 142 | 153 | 195 | 50 | 130 | 416 | 46 | 135 | 146 |
N.S. |
1 | 1.08 | 1.37 | 0.35 | 0.92 | 2.93 | 0.32 | 0.95 | 1.03 |
time (sec) |
N/A | 0.310 | 0.106 | 4.580 | 0.279 | 0.280 | 0.186 | 0.284 | 5.807 |
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 | 49 | 53 | 49 | 40 | 39 | 128 | 83 | 39 | 37 |
N.S. |
1 | 1.08 | 1.00 | 0.82 | 0.80 | 2.61 | 1.69 | 0.80 | 0.76 |
time (sec) |
N/A | 0.165 | 0.032 | 4.702 | 0.290 | 0.286 | 0.200 | 0.272 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 142 | 148 | 197 | 47 | 130 | 407 | 41 | 135 | 128 |
N.S. |
1 | 1.04 | 1.39 | 0.33 | 0.92 | 2.87 | 0.29 | 0.95 | 0.90 |
time (sec) |
N/A | 0.305 | 0.110 | 4.396 | 0.273 | 0.286 | 0.178 | 0.277 | 5.464 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 232 | 235 | 192 | 46 | 204 | 351 | 39 | 205 | 242 |
N.S. |
1 | 1.01 | 0.83 | 0.20 | 0.88 | 1.51 | 0.17 | 0.88 | 1.04 |
time (sec) |
N/A | 0.419 | 0.130 | 4.378 | 0.274 | 0.275 | 0.175 | 0.277 | 5.591 |
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 | 38 | 39 | 33 | 35 | 37 | 47 | 34 | 47 | 34 |
N.S. |
1 | 1.03 | 0.87 | 0.92 | 0.97 | 1.24 | 0.89 | 1.24 | 0.89 |
time (sec) |
N/A | 0.186 | 0.015 | 4.382 | 0.185 | 0.283 | 0.267 | 0.276 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 244 | 262 | 205 | 70 | 218 | 396 | 56 | 214 | 169 |
N.S. |
1 | 1.07 | 0.84 | 0.29 | 0.89 | 1.62 | 0.23 | 0.88 | 0.69 |
time (sec) |
N/A | 0.467 | 0.172 | 4.405 | 0.280 | 0.281 | 0.218 | 0.344 | 5.536 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 152 | 168 | 208 | 75 | 134 | 160 | 60 | 147 | 140 |
N.S. |
1 | 1.11 | 1.37 | 0.49 | 0.88 | 1.05 | 0.39 | 0.97 | 0.92 |
time (sec) |
N/A | 0.339 | 0.134 | 4.410 | 0.270 | 0.281 | 0.242 | 0.273 | 5.669 |
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 | 59 | 67 | 114 | 49 | 53 | 148 | 94 | 51 | 50 |
N.S. |
1 | 1.14 | 1.93 | 0.83 | 0.90 | 2.51 | 1.59 | 0.86 | 0.85 |
time (sec) |
N/A | 0.183 | 0.089 | 4.426 | 0.271 | 0.313 | 0.266 | 0.275 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 14 | 30 | 18 | 22 | 22 | 20 | 24 | 12 |
N.S. |
1 | 0.88 | 1.88 | 1.12 | 1.38 | 1.38 | 1.25 | 1.50 | 0.75 |
time (sec) |
N/A | 0.145 | 0.009 | 4.394 | 0.200 | 0.253 | 0.045 | 0.265 | 0.056 |
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 | 56 | 60 | 78 | 48 | 43 | 43 | 51 | 44 | 57 |
N.S. |
1 | 1.07 | 1.39 | 0.86 | 0.77 | 0.77 | 0.91 | 0.79 | 1.02 |
time (sec) |
N/A | 0.224 | 0.025 | 4.434 | 0.271 | 0.284 | 0.064 | 0.269 | 5.459 |
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 | 50 | 80 | 78 | 65 | 68 | 68 | 85 | 70 | 93 |
N.S. |
1 | 1.60 | 1.56 | 1.30 | 1.36 | 1.36 | 1.70 | 1.40 | 1.86 |
time (sec) |
N/A | 0.257 | 0.014 | 4.564 | 0.270 | 0.281 | 0.125 | 0.300 | 5.451 |
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 | 12 | 12 | 12 | 9 | 8 | 8 | 8 | 9 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.67 | 0.67 | 0.67 | 0.75 | 0.67 |
time (sec) |
N/A | 0.146 | 0.005 | 4.385 | 0.196 | 0.256 | 0.038 | 0.293 | 0.040 |
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 | 47 | 79 | 75 | 62 | 65 | 65 | 83 | 67 | 53 |
N.S. |
1 | 1.68 | 1.60 | 1.32 | 1.38 | 1.38 | 1.77 | 1.43 | 1.13 |
time (sec) |
N/A | 0.254 | 0.012 | 4.406 | 0.274 | 0.289 | 0.131 | 0.268 | 5.492 |
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 | 49 | 56 | 73 | 43 | 38 | 38 | 46 | 39 | 52 |
N.S. |
1 | 1.14 | 1.49 | 0.88 | 0.78 | 0.78 | 0.94 | 0.80 | 1.06 |
time (sec) |
N/A | 0.215 | 0.010 | 4.468 | 0.283 | 0.290 | 0.063 | 0.273 | 0.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 23 | 7 | 17 | 17 | 15 | 19 | 6 |
N.S. |
1 | 1.00 | 2.88 | 0.88 | 2.12 | 2.12 | 1.88 | 2.38 | 0.75 |
time (sec) |
N/A | 0.142 | 0.005 | 4.387 | 0.190 | 0.247 | 0.044 | 0.269 | 5.753 |
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 | 49 | 55 | 73 | 43 | 38 | 38 | 46 | 39 | 52 |
N.S. |
1 | 1.12 | 1.49 | 0.88 | 0.78 | 0.78 | 0.94 | 0.80 | 1.06 |
time (sec) |
N/A | 0.208 | 0.011 | 4.400 | 0.290 | 0.263 | 0.065 | 0.282 | 5.766 |
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 | 47 | 77 | 75 | 66 | 65 | 65 | 83 | 67 | 86 |
N.S. |
1 | 1.64 | 1.60 | 1.40 | 1.38 | 1.38 | 1.77 | 1.43 | 1.83 |
time (sec) |
N/A | 0.239 | 0.011 | 4.400 | 0.269 | 0.532 | 0.130 | 0.277 | 0.035 |
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 | 15 | 19 | 15 | 12 | 15 | 11 | 10 | 16 | 11 |
N.S. |
1 | 1.27 | 1.00 | 0.80 | 1.00 | 0.73 | 0.67 | 1.07 | 0.73 |
time (sec) |
N/A | 0.143 | 0.006 | 4.409 | 0.185 | 0.273 | 0.052 | 0.285 | 5.759 |
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 | 52 | 84 | 86 | 67 | 70 | 76 | 87 | 72 | 64 |
N.S. |
1 | 1.62 | 1.65 | 1.29 | 1.35 | 1.46 | 1.67 | 1.38 | 1.23 |
time (sec) |
N/A | 0.250 | 0.022 | 4.522 | 0.281 | 0.269 | 0.139 | 0.262 | 5.687 |
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 | 56 | 61 | 78 | 42 | 43 | 53 | 53 | 44 | 57 |
N.S. |
1 | 1.09 | 1.39 | 0.75 | 0.77 | 0.95 | 0.95 | 0.79 | 1.02 |
time (sec) |
N/A | 0.218 | 0.023 | 4.428 | 0.273 | 0.283 | 0.081 | 0.280 | 0.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 14 | 30 | 18 | 22 | 28 | 22 | 24 | 12 |
N.S. |
1 | 0.88 | 1.88 | 1.12 | 1.38 | 1.75 | 1.38 | 1.50 | 0.75 |
time (sec) |
N/A | 0.148 | 0.006 | 4.404 | 0.196 | 0.296 | 0.058 | 0.274 | 0.037 |
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 | 56 | 62 | 78 | 42 | 43 | 52 | 53 | 44 | 57 |
N.S. |
1 | 1.11 | 1.39 | 0.75 | 0.77 | 0.93 | 0.95 | 0.79 | 1.02 |
time (sec) |
N/A | 0.213 | 0.023 | 4.398 | 0.273 | 0.270 | 0.081 | 0.274 | 0.084 |
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 | 80 | 84 | 82 | 67 | 70 | 89 | 90 | 72 | 95 |
N.S. |
1 | 1.05 | 1.02 | 0.84 | 0.88 | 1.11 | 1.12 | 0.90 | 1.19 |
time (sec) |
N/A | 0.257 | 0.027 | 4.408 | 0.284 | 0.278 | 0.142 | 0.274 | 5.657 |
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 | 22 | 24 | 22 | 17 | 20 | 24 | 17 | 26 | 16 |
N.S. |
1 | 1.09 | 1.00 | 0.77 | 0.91 | 1.09 | 0.77 | 1.18 | 0.73 |
time (sec) |
N/A | 0.167 | 0.007 | 4.405 | 0.186 | 0.248 | 0.060 | 0.274 | 5.638 |
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 | 85 | 91 | 87 | 76 | 77 | 94 | 95 | 79 | 69 |
N.S. |
1 | 1.07 | 1.02 | 0.89 | 0.91 | 1.11 | 1.12 | 0.93 | 0.81 |
time (sec) |
N/A | 0.263 | 0.031 | 4.432 | 0.283 | 0.259 | 0.148 | 0.278 | 5.732 |
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 | 16 | 14 | 16 | 13 | 12 | 12 | 10 | 12 | 12 |
N.S. |
1 | 0.88 | 1.00 | 0.81 | 0.75 | 0.75 | 0.62 | 0.75 | 0.75 |
time (sec) |
N/A | 0.149 | 0.007 | 4.572 | 0.282 | 0.269 | 0.043 | 0.292 | 0.027 |
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 | 56 | 59 | 79 | 44 | 45 | 45 | 51 | 45 | 57 |
N.S. |
1 | 1.05 | 1.41 | 0.79 | 0.80 | 0.80 | 0.91 | 0.80 | 1.02 |
time (sec) |
N/A | 0.223 | 0.018 | 4.439 | 0.305 | 0.259 | 0.065 | 0.288 | 5.779 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 85 | 76 | 31 | 61 | 136 | 70 | 61 | 88 |
N.S. |
1 | 1.05 | 0.94 | 0.38 | 0.75 | 1.68 | 0.86 | 0.75 | 1.09 |
time (sec) |
N/A | 0.278 | 0.019 | 4.451 | 0.286 | 0.272 | 0.107 | 0.275 | 0.112 |
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 | 10 | 10 | 10 | 9 | 8 | 8 | 7 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.80 | 0.80 | 0.70 | 0.80 | 0.80 |
time (sec) |
N/A | 0.140 | 0.004 | 4.380 | 0.198 | 0.261 | 0.035 | 0.267 | 5.753 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 84 | 73 | 33 | 60 | 173 | 68 | 60 | 53 |
N.S. |
1 | 1.05 | 0.91 | 0.41 | 0.75 | 2.16 | 0.85 | 0.75 | 0.66 |
time (sec) |
N/A | 0.272 | 0.013 | 4.445 | 0.278 | 0.276 | 0.105 | 0.283 | 5.758 |
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 | 49 | 55 | 74 | 39 | 40 | 40 | 46 | 40 | 52 |
N.S. |
1 | 1.12 | 1.51 | 0.80 | 0.82 | 0.82 | 0.94 | 0.82 | 1.06 |
time (sec) |
N/A | 0.218 | 0.011 | 4.448 | 0.303 | 0.275 | 0.064 | 0.275 | 0.126 |
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 | 8 | 8 | 8 | 7 | 6 | 6 | 5 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.62 | 0.75 | 0.75 |
time (sec) |
N/A | 0.141 | 0.004 | 4.563 | 0.280 | 0.268 | 0.042 | 0.267 | 5.671 |
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 | 49 | 55 | 78 | 41 | 40 | 40 | 46 | 40 | 52 |
N.S. |
1 | 1.12 | 1.59 | 0.84 | 0.82 | 0.82 | 0.94 | 0.82 | 1.06 |
time (sec) |
N/A | 0.215 | 0.010 | 4.408 | 0.309 | 0.260 | 0.065 | 0.287 | 5.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 84 | 73 | 28 | 60 | 135 | 68 | 60 | 85 |
N.S. |
1 | 1.05 | 0.91 | 0.35 | 0.75 | 1.69 | 0.85 | 0.75 | 1.06 |
time (sec) |
N/A | 0.259 | 0.013 | 4.456 | 0.295 | 0.288 | 0.101 | 0.271 | 0.045 |
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 | 13 | 17 | 13 | 12 | 15 | 11 | 10 | 15 | 11 |
N.S. |
1 | 1.31 | 1.00 | 0.92 | 1.15 | 0.85 | 0.77 | 1.15 | 0.85 |
time (sec) |
N/A | 0.144 | 0.008 | 4.401 | 0.199 | 0.286 | 0.044 | 0.284 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 89 | 82 | 38 | 65 | 182 | 71 | 65 | 56 |
N.S. |
1 | 1.05 | 0.96 | 0.45 | 0.76 | 2.14 | 0.84 | 0.76 | 0.66 |
time (sec) |
N/A | 0.275 | 0.025 | 4.452 | 0.283 | 0.272 | 0.114 | 0.273 | 0.096 |
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 | 56 | 61 | 83 | 44 | 45 | 54 | 53 | 45 | 57 |
N.S. |
1 | 1.09 | 1.48 | 0.79 | 0.80 | 0.96 | 0.95 | 0.80 | 1.02 |
time (sec) |
N/A | 0.222 | 0.023 | 4.690 | 0.292 | 0.265 | 0.075 | 0.287 | 0.079 |
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 | 16 | 16 | 16 | 13 | 12 | 15 | 14 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.94 | 0.88 | 0.75 | 0.75 |
time (sec) |
N/A | 0.147 | 0.007 | 4.575 | 0.294 | 0.283 | 0.056 | 0.274 | 5.728 |
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 | 56 | 63 | 79 | 44 | 45 | 55 | 53 | 45 | 57 |
N.S. |
1 | 1.12 | 1.41 | 0.79 | 0.80 | 0.98 | 0.95 | 0.80 | 1.02 |
time (sec) |
N/A | 0.223 | 0.022 | 4.477 | 0.278 | 0.280 | 0.077 | 0.274 | 5.889 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 91 | 79 | 35 | 65 | 156 | 75 | 65 | 92 |
N.S. |
1 | 1.05 | 0.91 | 0.40 | 0.75 | 1.79 | 0.86 | 0.75 | 1.06 |
time (sec) |
N/A | 0.269 | 0.028 | 4.627 | 0.300 | 0.294 | 0.117 | 0.265 | 5.870 |
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 | 22 | 22 | 22 | 19 | 20 | 24 | 17 | 25 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.91 | 1.09 | 0.77 | 1.14 | 0.82 |
time (sec) |
N/A | 0.161 | 0.006 | 4.442 | 0.195 | 0.300 | 0.059 | 0.284 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 94 | 84 | 42 | 72 | 199 | 80 | 39 | 62 |
N.S. |
1 | 1.04 | 0.93 | 0.47 | 0.80 | 2.21 | 0.89 | 0.43 | 0.69 |
time (sec) |
N/A | 0.284 | 0.030 | 4.569 | 0.286 | 0.294 | 0.127 | 0.298 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 180 | 166 | 162 | 24 | 224 | 127 | 15 | 114 | 164 |
N.S. |
1 | 0.92 | 0.90 | 0.13 | 1.24 | 0.71 | 0.08 | 0.63 | 0.91 |
time (sec) |
N/A | 0.364 | 0.088 | 4.447 | 0.285 | 0.289 | 0.298 | 0.276 | 5.887 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F(-1) | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 244 | 289 | 219 | 162 | 0 | 368 | 0 | 217 | 186 |
N.S. |
1 | 1.18 | 0.90 | 0.66 | 0.00 | 1.51 | 0.00 | 0.89 | 0.76 |
time (sec) |
N/A | 0.524 | 0.183 | 5.905 | 0.000 | 0.531 | 0.000 | 0.895 | 5.764 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 67 | 48 | 41 | 97 | 41 | 119 | 57 | 0 |
N.S. |
1 | 1.16 | 0.83 | 0.71 | 1.67 | 0.71 | 2.05 | 0.98 | 0.00 |
time (sec) |
N/A | 0.170 | 0.296 | 4.841 | 0.186 | 0.283 | 1.906 | 0.306 | 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 | 17 | 17 | 17 | 14 | 13 | 13 | 29 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 1.71 | 0.76 | 0.76 |
time (sec) |
N/A | 0.130 | 0.020 | 4.817 | 0.181 | 0.264 | 0.097 | 0.272 | 5.962 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 37 | 35 | 28 | 58 | 29 | 88 | 30 | 0 |
N.S. |
1 | 1.06 | 1.00 | 0.80 | 1.66 | 0.83 | 2.51 | 0.86 | 0.00 |
time (sec) |
N/A | 0.147 | 0.130 | 4.756 | 0.193 | 0.302 | 0.917 | 0.271 | 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 | 53 | 53 | 30 | 26 | 37 | 26 | 54 | 37 | 25 |
N.S. |
1 | 1.00 | 0.57 | 0.49 | 0.70 | 0.49 | 1.02 | 0.70 | 0.47 |
time (sec) |
N/A | 0.161 | 0.031 | 4.467 | 0.192 | 0.257 | 0.914 | 0.259 | 5.523 |
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 | 40 | 42 | 25 | 21 | 28 | 21 | 39 | 28 | 20 |
N.S. |
1 | 1.05 | 0.62 | 0.52 | 0.70 | 0.52 | 0.98 | 0.70 | 0.50 |
time (sec) |
N/A | 0.154 | 0.024 | 4.538 | 0.192 | 0.358 | 0.445 | 0.280 | 5.548 |
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 | 27 | 29 | 18 | 15 | 19 | 14 | 24 | 19 | 14 |
N.S. |
1 | 1.07 | 0.67 | 0.56 | 0.70 | 0.52 | 0.89 | 0.70 | 0.52 |
time (sec) |
N/A | 0.148 | 0.019 | 4.575 | 0.195 | 0.274 | 0.209 | 0.264 | 5.572 |
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 | 13 | 13 | 13 | 10 | 9 | 9 | 8 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.69 | 0.69 | 0.62 | 0.69 | 0.69 |
time (sec) |
N/A | 0.124 | 0.013 | 4.588 | 0.190 | 0.266 | 0.089 | 0.305 | 5.626 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 18 | 34 | 27 | 17 | 37 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.72 | 1.36 | 1.08 | 0.68 | 1.48 | 0.72 |
time (sec) |
N/A | 0.144 | 0.051 | 4.651 | 0.271 | 0.276 | 0.503 | 0.282 | 0.077 |
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 | 42 | 46 | 42 | 35 | 47 | 44 | 31 | 47 | 31 |
N.S. |
1 | 1.10 | 1.00 | 0.83 | 1.12 | 1.05 | 0.74 | 1.12 | 0.74 |
time (sec) |
N/A | 0.153 | 0.087 | 4.540 | 0.301 | 0.293 | 1.107 | 0.285 | 5.729 |
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 | 58 | 67 | 49 | 48 | 74 | 52 | 66 | 59 | 57 |
N.S. |
1 | 1.16 | 0.84 | 0.83 | 1.28 | 0.90 | 1.14 | 1.02 | 0.98 |
time (sec) |
N/A | 0.158 | 0.116 | 4.631 | 0.272 | 0.286 | 2.382 | 0.260 | 5.689 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 54 | 40 | 30 | 86 | 35 | 53 | 51 | 0 |
N.S. |
1 | 1.15 | 0.85 | 0.64 | 1.83 | 0.74 | 1.13 | 1.09 | 0.00 |
time (sec) |
N/A | 0.156 | 0.186 | 4.711 | 0.196 | 0.284 | 2.415 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 33 | 35 | 25 | 58 | 29 | 39 | 46 | 0 |
N.S. |
1 | 1.06 | 1.13 | 0.81 | 1.87 | 0.94 | 1.26 | 1.48 | 0.00 |
time (sec) |
N/A | 0.145 | 0.159 | 4.518 | 0.194 | 0.276 | 1.069 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 18 | 12 | 33 | 16 | 12 | 29 | 0 |
N.S. |
1 | 1.00 | 1.29 | 0.86 | 2.36 | 1.14 | 0.86 | 2.07 | 0.00 |
time (sec) |
N/A | 0.131 | 0.238 | 4.440 | 0.195 | 0.285 | 0.502 | 0.282 | 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 | 16 | 16 | 16 | 13 | 12 | 16 | 12 | 20 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 1.00 | 0.75 | 1.25 | 0.75 |
time (sec) |
N/A | 0.130 | 0.157 | 4.529 | 0.177 | 0.271 | 0.360 | 0.286 | 5.933 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 21 | 18 | 25 | 22 | 26 | 0 | 17 |
N.S. |
1 | 1.00 | 0.64 | 0.55 | 0.76 | 0.67 | 0.79 | 0.00 | 0.52 |
time (sec) |
N/A | 0.143 | 0.188 | 4.479 | 0.190 | 0.352 | 0.547 | 0.000 | 5.836 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 54 | 28 | 25 | 37 | 31 | 41 | 0 | 24 |
N.S. |
1 | 1.10 | 0.57 | 0.51 | 0.76 | 0.63 | 0.84 | 0.00 | 0.49 |
time (sec) |
N/A | 0.162 | 0.203 | 4.622 | 0.209 | 0.264 | 0.965 | 0.000 | 6.011 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 186 | 190 | 41 | 20 | 0 | 21 | 36 | 0 | 0 |
N.S. |
1 | 1.02 | 0.22 | 0.11 | 0.00 | 0.11 | 0.19 | 0.00 | 0.00 |
time (sec) |
N/A | 0.239 | 10.016 | 6.381 | 0.000 | 0.078 | 0.447 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 166 | 166 | 29 | 20 | 0 | 6 | 36 | 0 | 0 |
N.S. |
1 | 1.00 | 0.17 | 0.12 | 0.00 | 0.04 | 0.22 | 0.00 | 0.00 |
time (sec) |
N/A | 0.226 | 10.009 | 5.034 | 0.000 | 0.101 | 0.368 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 186 | 190 | 29 | 20 | 0 | 23 | 39 | 0 | 0 |
N.S. |
1 | 1.02 | 0.16 | 0.11 | 0.00 | 0.12 | 0.21 | 0.00 | 0.00 |
time (sec) |
N/A | 0.237 | 10.009 | 5.379 | 0.000 | 0.079 | 0.486 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 179 | 39 | 20 | 0 | 0 | 36 | 0 | 0 |
N.S. |
1 | 1.00 | 0.22 | 0.11 | 0.00 | 0.00 | 0.20 | 0.00 | 0.00 |
time (sec) |
N/A | 0.239 | 10.014 | 5.500 | 0.000 | 0.000 | 0.413 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 164 | 164 | 24 | 18 | 0 | 0 | 34 | 0 | 16 |
N.S. |
1 | 1.00 | 0.15 | 0.11 | 0.00 | 0.00 | 0.21 | 0.00 | 0.10 |
time (sec) |
N/A | 0.216 | 10.005 | 4.978 | 0.000 | 0.000 | 0.360 | 0.000 | 0.081 |