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 | 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 | 15 | 15 | 17 | 15 | 17 | 17 | 14 | 17 | 17 |
N.S. |
1 | 1.00 | 1.13 | 1.00 | 1.13 | 1.13 | 0.93 | 1.13 | 1.13 |
time (sec) |
N/A | 0.282 | 6.785 | 0.117 | 1.032 | 0.266 | 161.550 | 0.546 | 0.788 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 142 | 167 | 134 | 1405 | 129 | 293 | 0 | 0 | 0 |
N.S. |
1 | 1.18 | 0.94 | 9.89 | 0.91 | 2.06 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.791 | 0.163 | 1.720 | 1.243 | 0.269 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 113 | 133 | 103 | 1369 | 106 | 247 | 0 | 0 | 0 |
N.S. |
1 | 1.18 | 0.91 | 12.12 | 0.94 | 2.19 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.615 | 0.075 | 1.013 | 1.260 | 0.278 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 92 | 71 | 545 | 80 | 187 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 0.90 | 6.90 | 1.01 | 2.37 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.422 | 1.476 | 1.153 | 1.252 | 0.286 | 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 | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 21 | 17 | 77 | 37 | 0 | 19 | 20 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 4.05 | 1.95 | 0.00 | 1.00 | 1.05 |
time (sec) |
N/A | 0.286 | 3.430 | 0.190 | 0.597 | 0.267 | 0.000 | 0.366 | 1.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 145 | 170 | 134 | 1410 | 129 | 293 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 0.92 | 9.72 | 0.89 | 2.02 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.790 | 0.163 | 1.826 | 1.246 | 0.288 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 116 | 135 | 103 | 1374 | 107 | 247 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 0.89 | 11.84 | 0.92 | 2.13 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.633 | 0.100 | 1.035 | 1.236 | 0.275 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 96 | 71 | 516 | 80 | 187 | 0 | 0 | 0 |
N.S. |
1 | 1.17 | 0.87 | 6.29 | 0.98 | 2.28 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.437 | 1.430 | 1.144 | 1.259 | 0.292 | 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 | F(-1) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 24 | 20 | 72 | 37 | 0 | 19 | 20 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 3.27 | 1.68 | 0.00 | 0.86 | 0.91 |
time (sec) |
N/A | 0.289 | 3.445 | 0.167 | 0.641 | 0.257 | 0.000 | 0.358 | 1.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 59 | 53 | 34 | 40 | 0 | 0 | 21 |
N.S. |
1 | 1.00 | 1.90 | 1.71 | 1.10 | 1.29 | 0.00 | 0.00 | 0.68 |
time (sec) |
N/A | 0.230 | 0.018 | 0.307 | 0.303 | 0.277 | 0.000 | 0.000 | 0.803 |
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 | 63 | 57 | 50 | 44 | 0 | 65 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 0.79 | 0.70 | 0.00 | 1.03 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.333 | 0.012 | 0.431 | 0.000 | 0.272 | 0.000 | 0.000 | 0.000 |
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 | 91 | 93 | 80 | 70 | 0 | 87 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.88 | 0.77 | 0.00 | 0.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.467 | 0.013 | 0.644 | 0.000 | 0.279 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 43 | 83 | 95 | 63 | 103 | 0 | 0 | 37 |
N.S. |
1 | 0.96 | 1.84 | 2.11 | 1.40 | 2.29 | 0.00 | 0.00 | 0.82 |
time (sec) |
N/A | 0.237 | 0.167 | 0.245 | 0.294 | 0.275 | 0.000 | 0.000 | 0.850 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 87 | 71 | 349 | 0 | 151 | 0 | 0 | 0 |
N.S. |
1 | 0.96 | 0.78 | 3.84 | 0.00 | 1.66 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.384 | 0.013 | 0.378 | 0.000 | 0.284 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 141 | 115 | 407 | 0 | 187 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.86 | 3.06 | 0.00 | 1.41 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.550 | 0.020 | 0.417 | 0.000 | 0.279 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 196 | 177 | 167 | 162 | 189 | 212 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 0.85 | 0.83 | 0.96 | 1.08 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.536 | 0.310 | 0.740 | 0.313 | 0.284 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 232 | 238 | 236 | 672 | 0 | 304 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.02 | 2.90 | 0.00 | 1.31 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.695 | 0.063 | 0.880 | 0.000 | 0.288 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 302 | 321 | 299 | 758 | 0 | 378 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.99 | 2.51 | 0.00 | 1.25 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.969 | 0.033 | 1.247 | 0.000 | 0.282 | 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 | 25 | 33 | 25 | 23 | 19 | 28 | 19 | 20 | 20 |
N.S. |
1 | 1.32 | 1.00 | 0.92 | 0.76 | 1.12 | 0.76 | 0.80 | 0.80 |
time (sec) |
N/A | 0.221 | 0.013 | 0.085 | 0.176 | 0.271 | 1.417 | 0.272 | 0.094 |
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 | 45 | 53 | 35 | 32 | 31 | 50 | 153 | 32 | 31 |
N.S. |
1 | 1.18 | 0.78 | 0.71 | 0.69 | 1.11 | 3.40 | 0.71 | 0.69 |
time (sec) |
N/A | 0.236 | 0.025 | 0.267 | 0.274 | 0.263 | 0.220 | 0.271 | 0.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 64 | 74 | 81 | 54 | 54 | 77 | 223 | 0 | 46 |
N.S. |
1 | 1.16 | 1.27 | 0.84 | 0.84 | 1.20 | 3.48 | 0.00 | 0.72 |
time (sec) |
N/A | 0.320 | 0.036 | 0.296 | 0.289 | 0.269 | 0.254 | 0.000 | 0.868 |
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 | 30 | 30 | 22 | 25 | 24 | 18 | 26 | 24 | 24 |
N.S. |
1 | 1.00 | 0.73 | 0.83 | 0.80 | 0.60 | 0.87 | 0.80 | 0.80 |
time (sec) |
N/A | 0.194 | 0.019 | 0.023 | 0.282 | 0.274 | 0.089 | 0.267 | 0.087 |
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 | 5 | 5 | 5 | 6 | 5 | 5 | 5 | 5 | 5 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.187 | 0.046 | 0.246 | 0.203 | 0.258 | 0.110 | 0.271 | 0.245 |
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 | 17 | 17 | 17 | 14 | 16 | 15 | 14 | 16 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.94 | 0.88 | 0.82 | 0.94 | 0.88 |
time (sec) |
N/A | 0.210 | 0.073 | 0.247 | 0.199 | 0.267 | 0.194 | 0.274 | 0.143 |
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 | 18 | 18 | 18 | 17 | 16 | 26 | 53 | 104 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.89 | 1.44 | 2.94 | 5.78 | 0.89 |
time (sec) |
N/A | 0.344 | 0.024 | 0.322 | 0.354 | 0.255 | 0.257 | 0.290 | 0.139 |
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 | 68 | 74 | 58 | 45 | 44 | 40 | 0 | 44 | 72 |
N.S. |
1 | 1.09 | 0.85 | 0.66 | 0.65 | 0.59 | 0.00 | 0.65 | 1.06 |
time (sec) |
N/A | 0.263 | 0.042 | 0.032 | 0.305 | 0.306 | 0.000 | 0.287 | 1.915 |
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 | 65 | 53 | 40 | 39 | 35 | 46 | 39 | 65 |
N.S. |
1 | 1.10 | 0.90 | 0.68 | 0.66 | 0.59 | 0.78 | 0.66 | 1.10 |
time (sec) |
N/A | 0.250 | 0.023 | 0.034 | 0.313 | 0.268 | 175.227 | 0.291 | 1.110 |
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 | 50 | 56 | 48 | 35 | 34 | 28 | 39 | 34 | 58 |
N.S. |
1 | 1.12 | 0.96 | 0.70 | 0.68 | 0.56 | 0.78 | 0.68 | 1.16 |
time (sec) |
N/A | 0.237 | 0.022 | 0.034 | 0.308 | 0.285 | 34.992 | 0.288 | 1.030 |
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 | 37 | 41 | 31 | 28 | 26 | 22 | 29 | 27 | 40 |
N.S. |
1 | 1.11 | 0.84 | 0.76 | 0.70 | 0.59 | 0.78 | 0.73 | 1.08 |
time (sec) |
N/A | 0.215 | 0.073 | 0.030 | 0.297 | 0.267 | 8.412 | 0.273 | 1.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 84 | 374 | 43 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.00 | 8.90 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.295 | 0.140 | 0.765 | 0.271 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 44 | 40 | 57 | 29 | 28 | 537 | 28 | 44 |
N.S. |
1 | 1.07 | 0.98 | 1.39 | 0.71 | 0.68 | 13.10 | 0.68 | 1.07 |
time (sec) |
N/A | 0.234 | 0.022 | 0.033 | 0.302 | 0.284 | 88.100 | 0.281 | 1.582 |
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 | 50 | 56 | 48 | 35 | 34 | 35 | 0 | 34 | 49 |
N.S. |
1 | 1.12 | 0.96 | 0.70 | 0.68 | 0.70 | 0.00 | 0.68 | 0.98 |
time (sec) |
N/A | 0.236 | 0.023 | 0.045 | 0.295 | 0.273 | 0.000 | 0.288 | 1.435 |
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 | 59 | 65 | 51 | 40 | 39 | 40 | 0 | 39 | 56 |
N.S. |
1 | 1.10 | 0.86 | 0.68 | 0.66 | 0.68 | 0.00 | 0.66 | 0.95 |
time (sec) |
N/A | 0.251 | 0.029 | 0.052 | 0.296 | 0.282 | 0.000 | 0.299 | 1.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 63 | 59 | 0 | 126 | 0 | 0 | 57 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.00 | 2.00 | 0.00 | 0.00 | 0.90 |
time (sec) |
N/A | 0.372 | 0.044 | 0.758 | 0.000 | 0.302 | 0.000 | 0.000 | 0.842 |
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 | 59 | 59 | 59 | 57 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.364 | 0.022 | 0.372 | 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(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 59 | 57 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.322 | 0.016 | 0.382 | 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 | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 55 | 55 | 0 | 83 | 0 | 0 | 49 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 1.51 | 0.00 | 0.00 | 0.89 |
time (sec) |
N/A | 0.351 | 0.121 | 1.294 | 0.000 | 0.296 | 0.000 | 0.000 | 0.724 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 57 | 57 | 29 | 82 | 0 | 0 | 51 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.51 | 1.44 | 0.00 | 0.00 | 0.89 |
time (sec) |
N/A | 0.342 | 0.019 | 0.356 | 0.335 | 0.259 | 0.000 | 0.000 | 0.689 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 59 | 57 | 29 | 82 | 0 | 0 | 51 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 0.49 | 1.39 | 0.00 | 0.00 | 0.86 |
time (sec) |
N/A | 0.342 | 0.018 | 0.352 | 0.366 | 0.263 | 0.000 | 0.000 | 0.873 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 66 | 0 | 0 | 132 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 1.83 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.378 | 0.106 | 0.000 | 0.000 | 0.292 | 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 | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 62 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.365 | 0.058 | 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 | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 62 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.325 | 0.029 | 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) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 58 | 0 | 0 | 83 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 1.30 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.364 | 0.051 | 0.000 | 0.000 | 0.276 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 60 | 0 | 0 | 82 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 1.24 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.354 | 0.050 | 0.000 | 0.000 | 0.269 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 62 | 0 | 0 | 83 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 1.22 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.353 | 0.044 | 0.000 | 0.000 | 0.266 | 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 | 101 | 89 | 79 | 1087 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.88 | 0.78 | 10.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.608 | 0.105 | 6.954 | 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 | A | F | A | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 48 | 46 | 61 | 1299 | 48 | 75 | 0 | 65 | 66 |
N.S. |
1 | 0.96 | 1.27 | 27.06 | 1.00 | 1.56 | 0.00 | 1.35 | 1.38 |
time (sec) |
N/A | 0.314 | 0.057 | 1.111 | 0.284 | 0.298 | 0.000 | 0.293 | 0.852 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | A | B | F | A | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 103 | 104 | 146 | 1371 | 131 | 221 | 0 | 154 | 133 |
N.S. |
1 | 1.01 | 1.42 | 13.31 | 1.27 | 2.15 | 0.00 | 1.50 | 1.29 |
time (sec) |
N/A | 0.489 | 0.083 | 5.592 | 0.279 | 0.274 | 0.000 | 0.297 | 0.341 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | A | C | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 180 | 175 | 89 | 1355 | 167 | 258 | 0 | 0 | 164 |
N.S. |
1 | 0.97 | 0.49 | 7.53 | 0.93 | 1.43 | 0.00 | 0.00 | 0.91 |
time (sec) |
N/A | 0.507 | 0.066 | 1.384 | 0.270 | 0.282 | 0.000 | 0.000 | 1.591 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | A | C | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 180 | 175 | 89 | 1355 | 167 | 258 | 0 | 0 | 164 |
N.S. |
1 | 0.97 | 0.49 | 7.53 | 0.93 | 1.43 | 0.00 | 0.00 | 0.91 |
time (sec) |
N/A | 0.505 | 0.064 | 1.226 | 0.280 | 0.288 | 0.000 | 0.000 | 1.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | A | B | F | A | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 103 | 104 | 145 | 838 | 169 | 276 | 0 | 154 | 135 |
N.S. |
1 | 1.01 | 1.41 | 8.14 | 1.64 | 2.68 | 0.00 | 1.50 | 1.31 |
time (sec) |
N/A | 0.458 | 0.079 | 4.969 | 0.310 | 0.287 | 0.000 | 0.288 | 0.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | F | A | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 47 | 44 | 57 | 885 | 47 | 131 | 0 | 66 | 67 |
N.S. |
1 | 0.94 | 1.21 | 18.83 | 1.00 | 2.79 | 0.00 | 1.40 | 1.43 |
time (sec) |
N/A | 0.330 | 0.051 | 1.017 | 0.276 | 0.272 | 0.000 | 0.281 | 0.833 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 163 | 163 | 116 | 547 | 0 | 250 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.71 | 3.36 | 0.00 | 1.53 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.798 | 0.202 | 212.623 | 0.000 | 0.289 | 0.000 | 0.000 | 0.000 |