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 | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 24 | 0 | 37 | 0 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 0.00 | 1.54 | 0.00 | 1.08 | 1.08 |
time (sec) |
N/A | 0.181 | 29.941 | 0.807 | 0.000 | 0.330 | 0.000 | 0.367 | 1.549 |
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 | 24 | 24 | 26 | 24 | 26 | 35 | 20 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.46 | 0.83 | 1.08 | 1.08 |
time (sec) |
N/A | 0.176 | 0.180 | 0.181 | 0.295 | 0.303 | 14.233 | 0.321 | 1.614 |
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 | 22 | 22 | 24 | 22 | 24 | 24 | 19 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.86 | 1.09 | 1.09 |
time (sec) |
N/A | 0.167 | 0.142 | 0.050 | 0.299 | 0.281 | 5.656 | 0.303 | 1.441 |
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 | 24 | 24 | 26 | 24 | 26 | 26 | 20 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.08 | 0.83 | 1.08 | 1.08 |
time (sec) |
N/A | 0.178 | 7.204 | 0.217 | 0.264 | 0.301 | 101.482 | 0.292 | 1.684 |
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 | 24 | 24 | 26 | 24 | 26 | 37 | 0 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.08 | 1.54 | 0.00 | 1.08 | 1.08 |
time (sec) |
N/A | 0.174 | 9.493 | 0.240 | 0.266 | 0.321 | 0.000 | 0.488 | 1.498 |
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 | 24 | 24 | 26 | 24 | 152 | 35 | 22 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 6.33 | 1.46 | 0.92 | 1.08 | 1.08 |
time (sec) |
N/A | 0.172 | 0.419 | 0.006 | 0.316 | 0.295 | 18.464 | 0.296 | 1.456 |
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 | 22 | 22 | 24 | 22 | 104 | 24 | 20 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 4.73 | 1.09 | 0.91 | 1.09 | 1.09 |
time (sec) |
N/A | 0.163 | 0.268 | 0.003 | 0.313 | 0.337 | 8.645 | 0.291 | 1.579 |
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 | 24 | 24 | 26 | 24 | 159 | 26 | 22 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 6.62 | 1.08 | 0.92 | 1.08 | 1.08 |
time (sec) |
N/A | 0.187 | 9.468 | 0.004 | 0.279 | 0.341 | 139.765 | 0.323 | 1.499 |
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 | 24 | 24 | 26 | 24 | 215 | 37 | 0 | 26 | 26 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 8.96 | 1.54 | 0.00 | 1.08 | 1.08 |
time (sec) |
N/A | 0.174 | 10.862 | 0.026 | 0.298 | 0.348 | 0.000 | 0.352 | 1.531 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 142 | 146 | 170 | 140 | 132 | 152 | 0 | 399 | 127 |
N.S. |
1 | 1.03 | 1.20 | 0.99 | 0.93 | 1.07 | 0.00 | 2.81 | 0.89 |
time (sec) |
N/A | 0.370 | 0.034 | 1.589 | 0.192 | 0.344 | 0.000 | 0.328 | 1.550 |
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 | 119 | 124 | 140 | 117 | 108 | 128 | 156 | 269 | 103 |
N.S. |
1 | 1.04 | 1.18 | 0.98 | 0.91 | 1.08 | 1.31 | 2.26 | 0.87 |
time (sec) |
N/A | 0.332 | 0.022 | 1.069 | 0.192 | 0.337 | 61.460 | 0.312 | 1.505 |
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 | 97 | 98 | 127 | 99 | 99 | 126 | 143 | 78 |
N.S. |
1 | 1.03 | 1.04 | 1.35 | 1.05 | 1.05 | 1.34 | 1.52 | 0.83 |
time (sec) |
N/A | 0.260 | 0.023 | 0.848 | 0.193 | 0.323 | 15.771 | 0.316 | 1.486 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 75 | 80 | 157 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 0.98 | 1.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.283 | 0.018 | 0.313 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 89 | 92 | 155 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.99 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.291 | 0.022 | 0.434 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 100 | 105 | 88 | 77 | 97 | 167 | 209 | 85 |
N.S. |
1 | 1.08 | 1.13 | 0.95 | 0.83 | 1.04 | 1.80 | 2.25 | 0.91 |
time (sec) |
N/A | 0.307 | 0.031 | 0.481 | 0.199 | 0.306 | 74.453 | 0.309 | 1.687 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 118 | 134 | 108 | 104 | 129 | 0 | 316 | 113 |
N.S. |
1 | 0.94 | 1.07 | 0.86 | 0.83 | 1.03 | 0.00 | 2.53 | 0.90 |
time (sec) |
N/A | 0.340 | 0.050 | 0.887 | 0.205 | 0.316 | 0.000 | 0.329 | 1.724 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 148 | 143 | 162 | 131 | 132 | 155 | 0 | 379 | 134 |
N.S. |
1 | 0.97 | 1.09 | 0.89 | 0.89 | 1.05 | 0.00 | 2.56 | 0.91 |
time (sec) |
N/A | 0.352 | 0.071 | 1.517 | 0.203 | 0.331 | 0.000 | 0.318 | 1.685 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 154 | 154 | 118 | 118 | 0 | 300 | 320 | 121 | 126 |
N.S. |
1 | 1.00 | 0.77 | 0.77 | 0.00 | 1.95 | 2.08 | 0.79 | 0.82 |
time (sec) |
N/A | 0.302 | 0.044 | 1.195 | 0.000 | 0.336 | 31.345 | 0.297 | 1.651 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 117 | 89 | 0 | 220 | 260 | 94 | 97 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.00 | 1.88 | 2.22 | 0.80 | 0.83 |
time (sec) |
N/A | 0.252 | 0.021 | 0.294 | 0.000 | 0.355 | 7.798 | 0.288 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 93 | 62 | 73 | 0 | 199 | 204 | 68 | 83 |
N.S. |
1 | 1.29 | 0.86 | 1.01 | 0.00 | 2.76 | 2.83 | 0.94 | 1.15 |
time (sec) |
N/A | 0.245 | 0.037 | 0.666 | 0.000 | 0.347 | 15.371 | 0.320 | 1.615 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 96 | 77 | 0 | 191 | 901 | 88 | 65 |
N.S. |
1 | 1.00 | 0.89 | 0.71 | 0.00 | 1.77 | 8.34 | 0.81 | 0.60 |
time (sec) |
N/A | 0.264 | 0.029 | 0.536 | 0.000 | 0.342 | 36.668 | 0.308 | 1.708 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 140 | 140 | 101 | 96 | 0 | 259 | 1134 | 117 | 88 |
N.S. |
1 | 1.00 | 0.72 | 0.69 | 0.00 | 1.85 | 8.10 | 0.84 | 0.63 |
time (sec) |
N/A | 0.286 | 0.008 | 1.145 | 0.000 | 0.330 | 155.655 | 0.306 | 1.630 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 251 | 250 | 205 | 253 | 223 | 262 | 0 | 753 | 224 |
N.S. |
1 | 1.00 | 0.82 | 1.01 | 0.89 | 1.04 | 0.00 | 3.00 | 0.89 |
time (sec) |
N/A | 0.527 | 0.125 | 3.722 | 0.191 | 0.308 | 0.000 | 0.332 | 1.615 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 210 | 209 | 257 | 211 | 185 | 224 | 0 | 544 | 184 |
N.S. |
1 | 1.00 | 1.22 | 1.00 | 0.88 | 1.07 | 0.00 | 2.59 | 0.88 |
time (sec) |
N/A | 0.458 | 0.058 | 2.470 | 0.189 | 0.301 | 0.000 | 0.319 | 1.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 123 | 135 | 206 | 152 | 180 | 235 | 340 | 142 |
N.S. |
1 | 0.99 | 1.09 | 1.66 | 1.23 | 1.45 | 1.90 | 2.74 | 1.15 |
time (sec) |
N/A | 0.297 | 0.075 | 1.809 | 0.188 | 0.322 | 60.076 | 0.304 | 1.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 153 | 152 | 121 | 209 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.79 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.365 | 0.059 | 1.148 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 134 | 133 | 211 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.99 | 1.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.364 | 0.052 | 1.719 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 172 | 174 | 152 | 208 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.88 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.394 | 0.076 | 1.774 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 134 | 141 | 159 | 137 | 183 | 0 | 464 | 151 |
N.S. |
1 | 1.03 | 1.08 | 1.22 | 1.05 | 1.41 | 0.00 | 3.57 | 1.16 |
time (sec) |
N/A | 0.374 | 0.081 | 1.425 | 0.194 | 0.322 | 0.000 | 0.316 | 1.657 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 216 | 208 | 184 | 193 | 183 | 230 | 0 | 604 | 190 |
N.S. |
1 | 0.96 | 0.85 | 0.89 | 0.85 | 1.06 | 0.00 | 2.80 | 0.88 |
time (sec) |
N/A | 0.466 | 0.106 | 2.033 | 0.187 | 0.341 | 0.000 | 0.316 | 1.688 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 253 | 244 | 215 | 230 | 223 | 268 | 0 | 699 | 225 |
N.S. |
1 | 0.96 | 0.85 | 0.91 | 0.88 | 1.06 | 0.00 | 2.76 | 0.89 |
time (sec) |
N/A | 0.512 | 0.134 | 3.249 | 0.192 | 0.344 | 0.000 | 0.341 | 1.789 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 278 | 278 | 188 | 211 | 0 | 492 | 559 | 215 | 235 |
N.S. |
1 | 1.00 | 0.68 | 0.76 | 0.00 | 1.77 | 2.01 | 0.77 | 0.85 |
time (sec) |
N/A | 0.435 | 0.096 | 3.053 | 0.000 | 0.336 | 117.508 | 0.293 | 1.549 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 221 | 221 | 151 | 167 | 0 | 404 | 478 | 174 | 193 |
N.S. |
1 | 1.00 | 0.68 | 0.76 | 0.00 | 1.83 | 2.16 | 0.79 | 0.87 |
time (sec) |
N/A | 0.353 | 0.044 | 1.486 | 0.000 | 0.322 | 31.580 | 0.312 | 0.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 178 | 178 | 112 | 127 | 0 | 366 | 400 | 136 | 180 |
N.S. |
1 | 1.00 | 0.63 | 0.71 | 0.00 | 2.06 | 2.25 | 0.76 | 1.01 |
time (sec) |
N/A | 0.344 | 0.096 | 1.803 | 0.000 | 0.341 | 60.654 | 0.321 | 1.673 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 169 | 169 | 113 | 125 | 0 | 350 | 381 | 135 | 108 |
N.S. |
1 | 1.00 | 0.67 | 0.74 | 0.00 | 2.07 | 2.25 | 0.80 | 0.64 |
time (sec) |
N/A | 0.331 | 0.090 | 2.151 | 0.000 | 0.326 | 72.934 | 0.318 | 1.594 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 156 | 134 | 0 | 351 | 1603 | 163 | 115 |
N.S. |
1 | 1.00 | 0.78 | 0.67 | 0.00 | 1.76 | 8.02 | 0.82 | 0.58 |
time (sec) |
N/A | 0.356 | 0.047 | 1.902 | 0.000 | 0.337 | 156.417 | 0.315 | 1.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 252 | 252 | 161 | 167 | 0 | 429 | 0 | 207 | 149 |
N.S. |
1 | 1.00 | 0.64 | 0.66 | 0.00 | 1.70 | 0.00 | 0.82 | 0.59 |
time (sec) |
N/A | 0.401 | 0.024 | 2.388 | 0.000 | 0.344 | 0.000 | 0.343 | 1.660 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 188 | 181 | 143 | 410 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.76 | 2.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.441 | 0.075 | 2.483 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 112 | 107 | 91 | 358 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.81 | 3.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.347 | 0.030 | 1.500 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 70 | 68 | 64 | 301 | 138 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.91 | 4.30 | 1.97 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.311 | 0.007 | 1.744 | 0.195 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 119 | 113 | 92 | 420 | 140 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.77 | 3.53 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.360 | 0.028 | 1.232 | 0.328 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 176 | 168 | 168 | 471 | 178 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.95 | 2.68 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.422 | 0.044 | 2.137 | 0.321 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 667 | 667 | 697 | 616 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.04 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.924 | 0.436 | 1.448 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 585 | 585 | 619 | 525 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.776 | 0.241 | 1.153 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 533 | 506 | 564 | 449 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 1.06 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.645 | 0.041 | 0.860 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 581 | 581 | 613 | 526 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.770 | 0.210 | 1.579 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 651 | 651 | 670 | 602 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.829 | 0.318 | 2.598 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 199 | 191 | 166 | 442 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.83 | 2.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.457 | 0.176 | 2.089 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 155 | 145 | 131 | 381 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.85 | 2.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.390 | 0.065 | 2.083 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 83 | 77 | 73 | 75 | 74 | 91 | 0 | 126 | 80 |
N.S. |
1 | 0.93 | 0.88 | 0.90 | 0.89 | 1.10 | 0.00 | 1.52 | 0.96 |
time (sec) |
N/A | 0.240 | 0.036 | 1.529 | 0.193 | 0.339 | 0.000 | 0.323 | 2.629 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 201 | 187 | 170 | 492 | 197 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.85 | 2.45 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.442 | 0.069 | 1.565 | 0.343 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 251 | 248 | 224 | 535 | 295 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.89 | 2.13 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.513 | 0.104 | 4.671 | 0.244 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 802 | 802 | 915 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.488 | 1.281 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 746 | 746 | 850 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.373 | 0.827 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 751 | 751 | 877 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.983 | 0.436 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 803 | 803 | 939 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.412 | 1.078 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 163 | 168 | 128 | 264 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.79 | 1.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.501 | 0.039 | 1.250 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 239 | 222 | 159 | 194 | 208 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.67 | 0.81 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.502 | 0.083 | 1.043 | 0.281 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 217 | 245 | 335 | 282 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 1.54 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.486 | 0.097 | 0.727 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 144 | 127 | 118 | 267 | 0 | 148 | 0 | 0 | 0 |
N.S. |
1 | 0.88 | 0.82 | 1.85 | 0.00 | 1.03 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.335 | 0.121 | 2.649 | 0.000 | 0.417 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 124 | 110 | 100 | 249 | 0 | 133 | 0 | 0 | 0 |
N.S. |
1 | 0.89 | 0.81 | 2.01 | 0.00 | 1.07 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.308 | 0.076 | 2.666 | 0.000 | 0.380 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 83 | 75 | 68 | 223 | 0 | 100 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 0.82 | 2.69 | 0.00 | 1.20 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.284 | 0.040 | 2.161 | 0.000 | 0.392 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 97 | 91 | 90 | 242 | 0 | 114 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.93 | 2.49 | 0.00 | 1.18 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.318 | 0.062 | 2.902 | 0.000 | 0.344 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 126 | 117 | 104 | 267 | 0 | 150 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.83 | 2.12 | 0.00 | 1.19 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.348 | 0.127 | 2.638 | 0.000 | 0.339 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 327 | 286 | 209 | 436 | 0 | 291 | 0 | 0 | 0 |
N.S. |
1 | 0.87 | 0.64 | 1.33 | 0.00 | 0.89 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.485 | 0.203 | 6.079 | 0.000 | 0.377 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 254 | 222 | 171 | 375 | 0 | 242 | 0 | 0 | 0 |
N.S. |
1 | 0.87 | 0.67 | 1.48 | 0.00 | 0.95 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.433 | 0.167 | 5.569 | 0.000 | 0.346 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 176 | 156 | 124 | 314 | 0 | 192 | 0 | 0 | 0 |
N.S. |
1 | 0.89 | 0.70 | 1.78 | 0.00 | 1.09 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.363 | 0.112 | 3.212 | 0.000 | 0.349 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 193 | 180 | 160 | 334 | 0 | 210 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.83 | 1.73 | 0.00 | 1.09 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.430 | 0.209 | 6.569 | 0.000 | 0.357 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 257 | 235 | 188 | 396 | 0 | 265 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 0.73 | 1.54 | 0.00 | 1.03 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.484 | 0.369 | 6.129 | 0.000 | 0.376 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | C | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 266 | 252 | 0 | 478 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.00 | 1.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.587 | 0.000 | 3.084 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 121 | 113 | 92 | 323 | 154 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.76 | 2.67 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.380 | 0.059 | 1.721 | 0.275 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 70 | 68 | 64 | 243 | 112 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.91 | 3.47 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.371 | 0.019 | 3.036 | 0.274 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | C | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 221 | 213 | 0 | 398 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.00 | 1.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.580 | 0.000 | 8.892 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | C | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 419 | 393 | 0 | 635 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.00 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.739 | 0.000 | 11.003 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 204 | 187 | 171 | 414 | 233 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.92 | 0.84 | 2.03 | 1.14 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.456 | 0.123 | 2.928 | 0.289 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD |
size | 156 | 145 | 433 | 356 | 209 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 2.78 | 2.28 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.435 | 1.054 | 7.877 | 0.288 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | C | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 377 | 357 | 0 | 561 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.00 | 1.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.762 | 0.000 | 59.384 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 26 | 26 | 23 | 106 | 25 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.04 | 0.92 | 4.24 | 1.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.311 | 0.057 | 1.874 | 0.282 | 0.315 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 26 | 26 | 23 | 109 | 25 | 0 | 0 | 21 |
N.S. |
1 | 1.04 | 1.04 | 0.92 | 4.36 | 1.00 | 0.00 | 0.00 | 0.84 |
time (sec) |
N/A | 0.307 | 0.002 | 2.688 | 0.203 | 0.304 | 0.000 | 0.000 | 1.881 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 27 | 34 | 24 | 0 | 30 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.31 | 0.92 | 0.00 | 1.15 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.310 | 0.063 | 3.506 | 0.000 | 0.316 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 0 | 42 | 0 | 31 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 0.00 | 1.45 | 0.00 | 1.07 | 1.07 |
time (sec) |
N/A | 0.230 | 0.250 | 0.283 | 0.000 | 0.305 | 0.000 | 3.770 | 1.514 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 27 | 0 | 40 | 0 | 29 | 29 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 0.00 | 1.48 | 0.00 | 1.07 | 1.07 |
time (sec) |
N/A | 0.225 | 0.185 | 0.256 | 0.000 | 0.307 | 0.000 | 2.751 | 1.515 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 0 | 47 | 0 | 31 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 0.00 | 1.62 | 0.00 | 1.07 | 1.07 |
time (sec) |
N/A | 0.263 | 0.296 | 0.275 | 0.000 | 0.333 | 0.000 | 2.496 | 1.469 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 31 | 0 | 49 | 0 | 33 | 33 |
N.S. |
1 | 1.00 | 1.07 | 1.07 | 0.00 | 1.69 | 0.00 | 1.14 | 1.14 |
time (sec) |
N/A | 0.264 | 0.261 | 0.280 | 0.000 | 0.334 | 0.000 | 2.495 | 1.506 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 0 | 31 | 0 | 31 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 0.00 | 1.07 | 0.00 | 1.07 | 1.07 |
time (sec) |
N/A | 0.237 | 0.973 | 0.396 | 0.000 | 0.329 | 0.000 | 2.988 | 1.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 27 | 0 | 29 | 22 | 29 | 29 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 0.00 | 1.07 | 0.81 | 1.07 | 1.07 |
time (sec) |
N/A | 0.230 | 0.816 | 0.412 | 0.000 | 0.340 | 9.211 | 2.467 | 1.525 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 0 | 32 | 0 | 31 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 0.00 | 1.10 | 0.00 | 1.07 | 1.07 |
time (sec) |
N/A | 0.295 | 0.949 | 0.592 | 0.000 | 0.337 | 0.000 | 2.522 | 1.590 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 31 | 0 | 36 | 0 | 33 | 33 |
N.S. |
1 | 1.00 | 1.07 | 1.07 | 0.00 | 1.24 | 0.00 | 1.14 | 1.14 |
time (sec) |
N/A | 0.441 | 0.210 | 0.638 | 0.000 | 0.343 | 0.000 | 3.047 | 1.628 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 88 | 75 | 66 | 0 | 76 | 0 | 0 | 0 |
N.S. |
1 | 1.28 | 1.09 | 0.96 | 0.00 | 1.10 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.418 | 0.044 | 1.030 | 0.000 | 0.333 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 12 | 34 | 9 | 59 | 11 | 0 | 68 | 8 |
N.S. |
1 | 1.50 | 4.25 | 1.12 | 7.38 | 1.38 | 0.00 | 8.50 | 1.00 |
time (sec) |
N/A | 0.161 | 0.004 | 0.418 | 0.193 | 0.300 | 0.000 | 0.304 | 1.446 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 76 | 69 | 15 | 0 | 0 | 10 |
N.S. |
1 | 1.00 | 1.00 | 6.33 | 5.75 | 1.25 | 0.00 | 0.00 | 0.83 |
time (sec) |
N/A | 0.171 | 0.005 | 0.200 | 0.194 | 0.307 | 0.000 | 0.000 | 1.504 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 15 | 0 | 61 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 0.00 | 4.36 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.174 | 0.005 | 2.164 | 0.000 | 0.297 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 36 | 34 | 67 | 0 | 0 | 204 | 37 |
N.S. |
1 | 1.00 | 1.03 | 0.97 | 1.91 | 0.00 | 0.00 | 5.83 | 1.06 |
time (sec) |
N/A | 0.252 | 0.005 | 0.780 | 0.186 | 0.000 | 0.000 | 0.400 | 1.525 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 40 | 108 | 77 | 0 | 0 | 0 | 33 |
N.S. |
1 | 1.00 | 1.03 | 2.77 | 1.97 | 0.00 | 0.00 | 0.00 | 0.85 |
time (sec) |
N/A | 0.235 | 0.005 | 0.222 | 0.190 | 0.000 | 0.000 | 0.000 | 1.628 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 43 | 44 | 44 | 0 | 67 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 0.94 | 0.94 | 0.00 | 1.43 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.243 | 0.014 | 2.785 | 0.000 | 0.307 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 111 | 115 | 114 | 124 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.10 | 1.09 | 1.18 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.398 | 0.031 | 3.770 | 0.194 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 227 | 240 | 228 | 230 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.596 | 0.081 | 1.690 | 0.000 | 0.000 | 0.000 | 0.000 | 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 | 22 | 22 | 24 | 22 | 24 | 24 | 14 | 24 | 24 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.09 | 1.09 | 0.64 | 1.09 | 1.09 |
time (sec) |
N/A | 0.186 | 0.367 | 0.286 | 0.263 | 0.297 | 23.042 | 0.337 | 1.433 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 82 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.229 | 0.037 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 166 | 156 | 157 | 0 | 128 | 148 | 155 | 348 | 137 |
N.S. |
1 | 0.94 | 0.95 | 0.00 | 0.77 | 0.89 | 0.93 | 2.10 | 0.83 |
time (sec) |
N/A | 0.320 | 0.087 | 0.000 | 0.187 | 0.319 | 8.467 | 0.318 | 1.803 |