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 | F | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 172 | 172 | 174 | 73 | 0 | 327 | 63 | 152 | 250 |
N.S. |
1 | 1.00 | 1.01 | 0.42 | 0.00 | 1.90 | 0.37 | 0.88 | 1.45 |
time (sec) |
N/A | 0.065 | 0.241 | 0.100 | 0.000 | 0.280 | 0.751 | 0.356 | 8.311 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 182 | 182 | 166 | 73 | 0 | 347 | 63 | 152 | 268 |
N.S. |
1 | 1.00 | 0.91 | 0.40 | 0.00 | 1.91 | 0.35 | 0.84 | 1.47 |
time (sec) |
N/A | 0.086 | 0.211 | 0.104 | 0.000 | 0.280 | 0.753 | 0.358 | 8.533 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 173 | 173 | 189 | 79 | 0 | 324 | 73 | 159 | 257 |
N.S. |
1 | 1.00 | 1.09 | 0.46 | 0.00 | 1.87 | 0.42 | 0.92 | 1.49 |
time (sec) |
N/A | 0.095 | 0.226 | 0.108 | 0.000 | 0.264 | 0.775 | 0.393 | 8.328 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 189 | 189 | 189 | 79 | 0 | 352 | 70 | 159 | 291 |
N.S. |
1 | 1.00 | 1.00 | 0.42 | 0.00 | 1.86 | 0.37 | 0.84 | 1.54 |
time (sec) |
N/A | 0.115 | 0.242 | 0.117 | 0.000 | 0.282 | 0.803 | 0.348 | 8.385 |
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 | 21 | 21 | 21 | 18 | 17 | 17 | 15 | 17 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.81 | 0.81 | 0.71 | 0.81 | 0.76 |
time (sec) |
N/A | 0.008 | 0.009 | 0.048 | 0.180 | 0.245 | 0.047 | 0.296 | 0.041 |
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 | 26 | 26 | 26 | 23 | 22 | 22 | 19 | 22 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.85 | 0.85 | 0.73 | 0.85 | 0.85 |
time (sec) |
N/A | 0.013 | 0.010 | 0.042 | 0.179 | 0.248 | 0.061 | 0.306 | 8.318 |
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 | 37 | 37 | 31 | 30 | 30 | 37 | 30 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.81 | 0.81 | 1.00 | 0.81 | 0.86 |
time (sec) |
N/A | 0.025 | 0.023 | 0.055 | 0.263 | 0.260 | 0.067 | 1.101 | 8.396 |
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 | 23 | 23 | 23 | 19 | 18 | 18 | 27 | 18 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 0.78 | 1.17 | 0.78 | 0.87 |
time (sec) |
N/A | 0.015 | 0.012 | 0.036 | 0.271 | 0.271 | 0.056 | 1.101 | 8.422 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 197 | 31 | 36 | 32 | 41 | 33 | 34 |
N.S. |
1 | 1.00 | 5.05 | 0.79 | 0.92 | 0.82 | 1.05 | 0.85 | 0.87 |
time (sec) |
N/A | 0.024 | 0.048 | 0.098 | 0.262 | 0.264 | 0.078 | 0.300 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 208 | 38 | 41 | 49 | 48 | 45 | 41 |
N.S. |
1 | 1.00 | 4.33 | 0.79 | 0.85 | 1.02 | 1.00 | 0.94 | 0.85 |
time (sec) |
N/A | 0.033 | 0.047 | 0.089 | 0.267 | 0.287 | 0.091 | 0.288 | 8.305 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 197 | 31 | 0 | 32 | 41 | 33 | 34 |
N.S. |
1 | 1.00 | 5.05 | 0.79 | 0.00 | 0.82 | 1.05 | 0.85 | 0.87 |
time (sec) |
N/A | 0.023 | 0.021 | 0.063 | 0.000 | 0.278 | 0.080 | 0.285 | 0.019 |
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 | 147 | 147 | 140 | 164 | 0 | 466 | 605 | 145 | 183 |
N.S. |
1 | 1.00 | 0.95 | 1.12 | 0.00 | 3.17 | 4.12 | 0.99 | 1.24 |
time (sec) |
N/A | 0.090 | 0.122 | 0.155 | 0.000 | 0.290 | 0.735 | 0.277 | 0.095 |
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 | 118 | 118 | 112 | 128 | 0 | 383 | 498 | 113 | 151 |
N.S. |
1 | 1.00 | 0.95 | 1.08 | 0.00 | 3.25 | 4.22 | 0.96 | 1.28 |
time (sec) |
N/A | 0.071 | 0.066 | 0.123 | 0.000 | 0.312 | 0.602 | 0.283 | 8.289 |
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 | 89 | 89 | 84 | 98 | 0 | 297 | 381 | 86 | 112 |
N.S. |
1 | 1.00 | 0.94 | 1.10 | 0.00 | 3.34 | 4.28 | 0.97 | 1.26 |
time (sec) |
N/A | 0.058 | 0.073 | 0.077 | 0.000 | 0.285 | 0.467 | 0.307 | 8.318 |
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 | 70 | 70 | 73 | 75 | 0 | 235 | 306 | 67 | 172 |
N.S. |
1 | 1.00 | 1.04 | 1.07 | 0.00 | 3.36 | 4.37 | 0.96 | 2.46 |
time (sec) |
N/A | 0.034 | 0.046 | 0.044 | 0.000 | 0.294 | 0.336 | 0.294 | 0.082 |
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 | 56 | 56 | 57 | 56 | 0 | 185 | 216 | 55 | 112 |
N.S. |
1 | 1.00 | 1.02 | 1.00 | 0.00 | 3.30 | 3.86 | 0.98 | 2.00 |
time (sec) |
N/A | 0.023 | 0.023 | 0.037 | 0.000 | 0.292 | 0.165 | 0.309 | 8.390 |
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 | 36 | 36 | 38 | 35 | 0 | 120 | 124 | 34 | 46 |
N.S. |
1 | 1.00 | 1.06 | 0.97 | 0.00 | 3.33 | 3.44 | 0.94 | 1.28 |
time (sec) |
N/A | 0.022 | 0.007 | 0.037 | 0.000 | 0.297 | 0.107 | 0.286 | 0.026 |
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 | 62 | 62 | 61 | 61 | 0 | 211 | 564 | 62 | 213 |
N.S. |
1 | 1.00 | 0.98 | 0.98 | 0.00 | 3.40 | 9.10 | 1.00 | 3.44 |
time (sec) |
N/A | 0.035 | 0.052 | 0.069 | 0.000 | 0.291 | 4.462 | 0.324 | 0.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 77 | 81 | 0 | 269 | 0 | 79 | 339 |
N.S. |
1 | 1.00 | 0.95 | 1.00 | 0.00 | 3.32 | 0.00 | 0.98 | 4.19 |
time (sec) |
N/A | 0.066 | 0.066 | 0.056 | 0.000 | 0.295 | 0.000 | 0.302 | 8.619 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 102 | 128 | 0 | 358 | 0 | 105 | 447 |
N.S. |
1 | 1.00 | 0.98 | 1.23 | 0.00 | 3.44 | 0.00 | 1.01 | 4.30 |
time (sec) |
N/A | 0.101 | 0.096 | 0.121 | 0.000 | 0.315 | 0.000 | 0.310 | 8.586 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 137 | 131 | 157 | 0 | 445 | 0 | 136 | 524 |
N.S. |
1 | 1.00 | 0.96 | 1.15 | 0.00 | 3.25 | 0.00 | 0.99 | 3.82 |
time (sec) |
N/A | 0.127 | 0.076 | 0.119 | 0.000 | 0.328 | 0.000 | 0.298 | 8.599 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 196 | 196 | 163 | 238 | 0 | 1029 | 1012 | 188 | 382 |
N.S. |
1 | 1.00 | 0.83 | 1.21 | 0.00 | 5.25 | 5.16 | 0.96 | 1.95 |
time (sec) |
N/A | 0.141 | 0.183 | 0.174 | 0.000 | 0.292 | 1.347 | 0.330 | 8.686 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 150 | 150 | 132 | 198 | 0 | 837 | 842 | 161 | 261 |
N.S. |
1 | 1.00 | 0.88 | 1.32 | 0.00 | 5.58 | 5.61 | 1.07 | 1.74 |
time (sec) |
N/A | 0.098 | 0.128 | 0.159 | 0.000 | 0.298 | 1.072 | 0.280 | 8.471 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 109 | 169 | 0 | 635 | 729 | 125 | 279 |
N.S. |
1 | 1.00 | 0.96 | 1.48 | 0.00 | 5.57 | 6.39 | 1.10 | 2.45 |
time (sec) |
N/A | 0.066 | 0.100 | 0.106 | 0.000 | 0.316 | 0.758 | 0.297 | 8.523 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 81 | 97 | 0 | 387 | 280 | 88 | 135 |
N.S. |
1 | 1.00 | 1.14 | 1.37 | 0.00 | 5.45 | 3.94 | 1.24 | 1.90 |
time (sec) |
N/A | 0.026 | 0.069 | 0.075 | 0.000 | 0.277 | 0.317 | 0.288 | 8.310 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 69 | 70 | 0 | 338 | 253 | 76 | 110 |
N.S. |
1 | 1.00 | 1.05 | 1.06 | 0.00 | 5.12 | 3.83 | 1.15 | 1.67 |
time (sec) |
N/A | 0.021 | 0.052 | 0.068 | 0.000 | 0.296 | 0.294 | 0.293 | 0.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 70 | 68 | 0 | 341 | 265 | 76 | 119 |
N.S. |
1 | 1.00 | 1.06 | 1.03 | 0.00 | 5.17 | 4.02 | 1.15 | 1.80 |
time (sec) |
N/A | 0.021 | 0.050 | 0.066 | 0.000 | 0.275 | 0.309 | 0.303 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 107 | 177 | 0 | 781 | 0 | 126 | 620 |
N.S. |
1 | 1.00 | 0.99 | 1.64 | 0.00 | 7.23 | 0.00 | 1.17 | 5.74 |
time (sec) |
N/A | 0.096 | 0.122 | 0.132 | 0.000 | 0.343 | 0.000 | 0.297 | 8.703 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 148 | 148 | 131 | 205 | 0 | 975 | 0 | 171 | 775 |
N.S. |
1 | 1.00 | 0.89 | 1.39 | 0.00 | 6.59 | 0.00 | 1.16 | 5.24 |
time (sec) |
N/A | 0.124 | 0.177 | 0.089 | 0.000 | 0.401 | 0.000 | 0.308 | 8.847 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 202 | 202 | 175 | 255 | 0 | 1226 | 0 | 229 | 914 |
N.S. |
1 | 1.00 | 0.87 | 1.26 | 0.00 | 6.07 | 0.00 | 1.13 | 4.52 |
time (sec) |
N/A | 0.169 | 0.259 | 0.184 | 0.000 | 0.458 | 0.000 | 0.314 | 9.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 238 | 238 | 260 | 401 | 0 | 1926 | 1714 | 282 | 705 |
N.S. |
1 | 1.00 | 1.09 | 1.68 | 0.00 | 8.09 | 7.20 | 1.18 | 2.96 |
time (sec) |
N/A | 0.212 | 0.238 | 0.200 | 0.000 | 0.294 | 3.038 | 0.330 | 8.593 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 190 | 190 | 221 | 357 | 0 | 1603 | 1510 | 245 | 620 |
N.S. |
1 | 1.00 | 1.16 | 1.88 | 0.00 | 8.44 | 7.95 | 1.29 | 3.26 |
time (sec) |
N/A | 0.187 | 0.197 | 0.154 | 0.000 | 0.287 | 1.868 | 0.295 | 8.820 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 174 | 260 | 0 | 953 | 547 | 202 | 343 |
N.S. |
1 | 1.00 | 1.57 | 2.34 | 0.00 | 8.59 | 4.93 | 1.82 | 3.09 |
time (sec) |
N/A | 0.047 | 0.118 | 0.099 | 0.000 | 0.292 | 0.822 | 0.308 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 126 | 223 | 0 | 872 | 513 | 163 | 271 |
N.S. |
1 | 1.00 | 1.18 | 2.08 | 0.00 | 8.15 | 4.79 | 1.52 | 2.53 |
time (sec) |
N/A | 0.039 | 0.138 | 0.096 | 0.000 | 0.286 | 0.663 | 0.286 | 8.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 131 | 210 | 0 | 887 | 570 | 154 | 313 |
N.S. |
1 | 1.00 | 1.14 | 1.83 | 0.00 | 7.71 | 4.96 | 1.34 | 2.72 |
time (sec) |
N/A | 0.046 | 0.092 | 0.106 | 0.000 | 0.280 | 0.755 | 0.287 | 8.410 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 102 | 118 | 0 | 788 | 481 | 135 | 253 |
N.S. |
1 | 1.00 | 0.99 | 1.15 | 0.00 | 7.65 | 4.67 | 1.31 | 2.46 |
time (sec) |
N/A | 0.028 | 0.064 | 0.092 | 0.000 | 0.286 | 0.604 | 0.289 | 8.392 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 101 | 97 | 116 | 0 | 785 | 474 | 136 | 285 |
N.S. |
1 | 0.98 | 0.94 | 1.13 | 0.00 | 7.62 | 4.60 | 1.32 | 2.77 |
time (sec) |
N/A | 0.028 | 0.069 | 0.093 | 0.000 | 0.263 | 0.697 | 0.297 | 8.492 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 185 | 178 | 352 | 0 | 1985 | 0 | 239 | 1089 |
N.S. |
1 | 1.00 | 0.96 | 1.90 | 0.00 | 10.73 | 0.00 | 1.29 | 5.89 |
time (sec) |
N/A | 0.148 | 0.233 | 0.185 | 0.000 | 0.524 | 0.000 | 0.293 | 8.990 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 239 | 239 | 221 | 404 | 0 | 2280 | 0 | 309 | 1255 |
N.S. |
1 | 1.00 | 0.92 | 1.69 | 0.00 | 9.54 | 0.00 | 1.29 | 5.25 |
time (sec) |
N/A | 0.192 | 0.259 | 0.133 | 0.000 | 0.674 | 0.000 | 0.298 | 9.079 |
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 | 40 | 40 | 40 | 27 | 30 | 30 | 34 | 32 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.68 | 0.75 | 0.75 | 0.85 | 0.80 | 0.65 |
time (sec) |
N/A | 0.015 | 0.006 | 0.034 | 0.183 | 0.249 | 0.060 | 0.295 | 0.025 |
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 | 33 | 33 | 33 | 22 | 25 | 25 | 27 | 27 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.76 | 0.76 | 0.82 | 0.82 | 0.64 |
time (sec) |
N/A | 0.013 | 0.004 | 0.033 | 0.184 | 0.231 | 0.059 | 0.307 | 8.287 |
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 | 26 | 26 | 26 | 17 | 20 | 20 | 20 | 22 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.65 | 0.77 | 0.77 | 0.77 | 0.85 | 0.62 |
time (sec) |
N/A | 0.009 | 0.004 | 0.031 | 0.182 | 0.245 | 0.060 | 0.279 | 0.042 |
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 | 21 | 21 | 21 | 14 | 17 | 17 | 17 | 19 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.81 | 0.81 | 0.81 | 0.90 | 0.62 |
time (sec) |
N/A | 0.008 | 0.004 | 0.027 | 0.186 | 0.248 | 0.066 | 0.282 | 0.036 |
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 | 23 | 23 | 21 | 14 | 17 | 17 | 15 | 19 | 8 |
N.S. |
1 | 1.00 | 0.91 | 0.61 | 0.74 | 0.74 | 0.65 | 0.83 | 0.35 |
time (sec) |
N/A | 0.009 | 0.003 | 0.031 | 0.185 | 0.248 | 0.046 | 0.307 | 8.486 |
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 | 27 | 27 | 18 | 21 | 21 | 24 | 24 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.78 | 0.78 | 0.89 | 0.89 | 0.63 |
time (sec) |
N/A | 0.011 | 0.014 | 0.042 | 0.226 | 0.298 | 0.066 | 0.289 | 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 | 34 | 34 | 34 | 27 | 26 | 30 | 31 | 29 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.76 | 0.88 | 0.91 | 0.85 | 0.65 |
time (sec) |
N/A | 0.021 | 0.004 | 0.048 | 0.196 | 0.254 | 0.072 | 0.275 | 0.025 |
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 | 41 | 41 | 41 | 31 | 31 | 39 | 36 | 34 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.76 | 0.95 | 0.88 | 0.83 | 0.63 |
time (sec) |
N/A | 0.023 | 0.005 | 0.047 | 0.189 | 0.261 | 0.075 | 0.323 | 8.552 |
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 | 48 | 48 | 48 | 36 | 36 | 44 | 41 | 39 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.75 | 0.92 | 0.85 | 0.81 | 0.67 |
time (sec) |
N/A | 0.030 | 0.006 | 0.050 | 0.181 | 0.275 | 0.087 | 0.310 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 204 | 204 | 208 | 249 | 0 | 959 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 1.22 | 0.00 | 4.70 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.154 | 1.375 | 0.147 | 0.000 | 0.426 | 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(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 158 | 179 | 0 | 709 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.09 | 1.23 | 0.00 | 4.89 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.091 | 0.584 | 0.067 | 0.000 | 0.323 | 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(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 131 | 121 | 0 | 590 | 0 | 0 | 100 |
N.S. |
1 | 1.00 | 1.25 | 1.15 | 0.00 | 5.62 | 0.00 | 0.00 | 0.95 |
time (sec) |
N/A | 0.055 | 0.194 | 0.038 | 0.000 | 0.320 | 0.000 | 0.000 | 8.525 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 89 | 88 | 0 | 171 | 0 | 0 | 53 |
N.S. |
1 | 1.00 | 1.33 | 1.31 | 0.00 | 2.55 | 0.00 | 0.00 | 0.79 |
time (sec) |
N/A | 0.027 | 0.153 | 0.048 | 0.000 | 0.275 | 0.000 | 0.000 | 8.578 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 133 | 133 | 140 | 197 | 0 | 465 | 0 | 231 | 0 |
N.S. |
1 | 1.00 | 1.05 | 1.48 | 0.00 | 3.50 | 0.00 | 1.74 | 0.00 |
time (sec) |
N/A | 0.068 | 0.461 | 0.083 | 0.000 | 0.310 | 0.000 | 0.410 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 220 | 220 | 246 | 376 | 0 | 1081 | 0 | 499 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.71 | 0.00 | 4.91 | 0.00 | 2.27 | 0.00 |
time (sec) |
N/A | 0.134 | 1.199 | 0.151 | 0.000 | 0.407 | 0.000 | 0.374 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 32 | 40 | 8 | 8 | 0 | 29 | 134 |
N.S. |
1 | 1.00 | 0.44 | 0.55 | 0.11 | 0.11 | 0.00 | 0.40 | 1.84 |
time (sec) |
N/A | 0.025 | 1.016 | 0.069 | 0.192 | 0.251 | 0.000 | 0.318 | 8.388 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 179 | 202 | 57 | 0 | 1059 | 129 | 2109 | 3026 |
N.S. |
1 | 1.00 | 1.13 | 0.32 | 0.00 | 5.92 | 0.72 | 11.78 | 16.91 |
time (sec) |
N/A | 0.175 | 0.110 | 0.048 | 0.000 | 0.277 | 1.233 | 0.786 | 8.733 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 631 | 631 | 70 | 59 | 0 | 2882 | 196 | 0 | 2280 |
N.S. |
1 | 1.00 | 0.11 | 0.09 | 0.00 | 4.57 | 0.31 | 0.00 | 3.61 |
time (sec) |
N/A | 0.749 | 0.041 | 0.059 | 0.000 | 0.388 | 54.067 | 0.000 | 10.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | B | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 376 | 376 | 70 | 59 | 0 | 4001 | 0 | 0 | 10382 |
N.S. |
1 | 1.00 | 0.19 | 0.16 | 0.00 | 10.64 | 0.00 | 0.00 | 27.61 |
time (sec) |
N/A | 0.373 | 0.040 | 0.047 | 0.000 | 0.456 | 0.000 | 0.000 | 9.601 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F(-1) | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 106 | 105 | 84 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.060 | 0.204 | 0.032 | 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 | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 55 | 50 | 54 | 53 | 51 | 49 | 44 |
N.S. |
1 | 1.00 | 1.38 | 1.25 | 1.35 | 1.32 | 1.28 | 1.22 | 1.10 |
time (sec) |
N/A | 0.014 | 0.030 | 0.079 | 0.188 | 0.285 | 0.162 | 0.282 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 50 | 41 | 23 | 0 | 124 | 45 | 0 |
N.S. |
1 | 1.00 | 0.67 | 0.55 | 0.31 | 0.00 | 1.65 | 0.60 | 0.00 |
time (sec) |
N/A | 0.027 | 0.028 | 0.091 | 0.198 | 0.000 | 0.397 | 0.289 | 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 | 137 | 137 | 117 | 98 | 114 | 84 | 233 | 140 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.72 | 0.83 | 0.61 | 1.70 | 1.02 | 0.00 |
time (sec) |
N/A | 0.054 | 0.057 | 0.075 | 0.190 | 0.262 | 5.616 | 0.309 | 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 | 137 | 137 | 93 | 76 | 114 | 61 | 204 | 102 | 0 |
N.S. |
1 | 1.00 | 0.68 | 0.55 | 0.83 | 0.45 | 1.49 | 0.74 | 0.00 |
time (sec) |
N/A | 0.047 | 0.022 | 0.020 | 0.185 | 0.284 | 1.431 | 0.295 | 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 | 137 | 137 | 67 | 54 | 114 | 32 | 175 | 64 | 0 |
N.S. |
1 | 1.00 | 0.49 | 0.39 | 0.83 | 0.23 | 1.28 | 0.47 | 0.00 |
time (sec) |
N/A | 0.040 | 0.018 | 0.023 | 0.199 | 0.258 | 0.616 | 0.292 | 0.000 |
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 | No | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 43 | 42 | 114 | 10 | 146 | 26 | 71 |
N.S. |
1 | 1.00 | 0.49 | 0.48 | 1.30 | 0.11 | 1.66 | 0.30 | 0.81 |
time (sec) |
N/A | 0.028 | 0.008 | 0.086 | 0.184 | 0.245 | 0.478 | 0.277 | 8.736 |
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 | 147 | 147 | 65 | 52 | 36 | 33 | 170 | 61 | 0 |
N.S. |
1 | 1.00 | 0.44 | 0.35 | 0.24 | 0.22 | 1.16 | 0.41 | 0.00 |
time (sec) |
N/A | 0.048 | 0.023 | 0.041 | 0.183 | 0.262 | 0.432 | 0.319 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 72 | 81 | 55 | 113 | 0 | 64 | 0 |
N.S. |
1 | 1.00 | 0.55 | 0.62 | 0.42 | 0.87 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.052 | 0.029 | 0.115 | 0.190 | 0.270 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 56 | 43 | 53 | 136 | 0 | 43 | 53 |
N.S. |
1 | 1.00 | 0.41 | 0.32 | 0.39 | 1.01 | 0.00 | 0.32 | 0.39 |
time (sec) |
N/A | 0.050 | 0.055 | 0.263 | 0.188 | 0.278 | 0.000 | 0.314 | 9.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 137 | 56 | 43 | 53 | 209 | 0 | 43 | 53 |
N.S. |
1 | 1.00 | 0.41 | 0.31 | 0.39 | 1.53 | 0.00 | 0.31 | 0.39 |
time (sec) |
N/A | 0.053 | 0.052 | 0.493 | 0.186 | 0.338 | 0.000 | 0.291 | 9.485 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 137 | 56 | 43 | 53 | 275 | 0 | 43 | 53 |
N.S. |
1 | 1.00 | 0.41 | 0.31 | 0.39 | 2.01 | 0.00 | 0.31 | 0.39 |
time (sec) |
N/A | 0.053 | 0.055 | 0.779 | 0.185 | 0.410 | 0.000 | 0.289 | 9.598 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 137 | 56 | 43 | 53 | 343 | 0 | 43 | 53 |
N.S. |
1 | 1.00 | 0.41 | 0.31 | 0.39 | 2.50 | 0.00 | 0.31 | 0.39 |
time (sec) |
N/A | 0.053 | 0.054 | 1.184 | 0.191 | 0.577 | 0.000 | 0.290 | 10.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 68 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.025 | 0.139 | 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 | F | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 468 | 468 | 207 | 0 | 362 | 579 | 0 | 1564 | 777 |
N.S. |
1 | 1.00 | 0.44 | 0.00 | 0.77 | 1.24 | 0.00 | 3.34 | 1.66 |
time (sec) |
N/A | 0.153 | 0.308 | 0.000 | 0.201 | 0.425 | 0.000 | 0.323 | 9.607 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 315 | 315 | 143 | 0 | 198 | 297 | 0 | 745 | 390 |
N.S. |
1 | 1.00 | 0.45 | 0.00 | 0.63 | 0.94 | 0.00 | 2.37 | 1.24 |
time (sec) |
N/A | 0.094 | 0.240 | 0.000 | 0.199 | 0.330 | 0.000 | 0.317 | 8.760 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | A | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 142 | 142 | 83 | 0 | 77 | 110 | 0 | 229 | 138 |
N.S. |
1 | 1.00 | 0.58 | 0.00 | 0.54 | 0.77 | 0.00 | 1.61 | 0.97 |
time (sec) |
N/A | 0.048 | 0.137 | 0.000 | 0.197 | 0.302 | 0.000 | 0.341 | 8.439 |
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 | 69 | 69 | 58 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.020 | 0.106 | 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 | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 61 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.023 | 0.104 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | C | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 146 | 162 | 101 | 0 | 0 | 82 | 0 | 0 | 69 |
N.S. |
1 | 1.11 | 0.69 | 0.00 | 0.00 | 0.56 | 0.00 | 0.00 | 0.47 |
time (sec) |
N/A | 0.067 | 0.333 | 0.000 | 0.000 | 0.338 | 0.000 | 0.000 | 8.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 176 | 176 | 93 | 103 | 114 | 147 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.53 | 0.59 | 0.65 | 0.84 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.066 | 0.093 | 0.256 | 0.198 | 1.994 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 268 | 268 | 121 | 163 | 119 | 0 | 0 | 105 | 0 |
N.S. |
1 | 1.00 | 0.45 | 0.61 | 0.44 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.097 | 0.129 | 5.449 | 0.199 | 0.000 | 0.000 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F(-1) | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 179 | 66 | 65 | 0 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.00 | 0.37 | 0.36 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.062 | 0.046 | 0.170 | 0.000 | 0.000 | 0.000 | 0.443 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 391 | 391 | 125 | 113 | 79 | 0 | 0 | 173 | 0 |
N.S. |
1 | 1.00 | 0.32 | 0.29 | 0.20 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.126 | 0.070 | 0.126 | 0.209 | 0.000 | 0.000 | 0.325 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 291 | 291 | 99 | 91 | 57 | 0 | 0 | 128 | 0 |
N.S. |
1 | 1.00 | 0.34 | 0.31 | 0.20 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.093 | 0.060 | 0.036 | 0.193 | 0.000 | 0.000 | 0.331 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 189 | 189 | 75 | 69 | 30 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.00 | 0.40 | 0.37 | 0.16 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.067 | 0.044 | 0.030 | 0.196 | 0.000 | 0.000 | 0.312 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 49 | 47 | 10 | 0 | 0 | 34 | 39 |
N.S. |
1 | 1.00 | 0.56 | 0.53 | 0.11 | 0.00 | 0.00 | 0.39 | 0.44 |
time (sec) |
N/A | 0.039 | 0.024 | 0.023 | 0.196 | 0.000 | 0.000 | 0.306 | 8.479 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 190 | 190 | 86 | 78 | 44 | 0 | 0 | 77 | 0 |
N.S. |
1 | 1.00 | 0.45 | 0.41 | 0.23 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.082 | 0.040 | 0.026 | 0.240 | 0.000 | 0.000 | 0.337 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 300 | 300 | 126 | 141 | 97 | 0 | 0 | 127 | 0 |
N.S. |
1 | 1.00 | 0.42 | 0.47 | 0.32 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.130 | 0.097 | 0.038 | 0.227 | 0.000 | 0.000 | 0.312 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 410 | 410 | 152 | 199 | 139 | 0 | 0 | 147 | 0 |
N.S. |
1 | 1.00 | 0.37 | 0.49 | 0.34 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.176 | 0.096 | 0.037 | 0.188 | 0.000 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 289 | 289 | 98 | 91 | 57 | 0 | 0 | 126 | 0 |
N.S. |
1 | 1.00 | 0.34 | 0.31 | 0.20 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.096 | 0.057 | 0.153 | 0.181 | 0.000 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 291 | 291 | 101 | 91 | 52 | 0 | 0 | 125 | 0 |
N.S. |
1 | 1.00 | 0.35 | 0.31 | 0.18 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.092 | 0.062 | 0.136 | 0.188 | 0.000 | 0.000 | 0.314 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 222 | 222 | 98 | 141 | 99 | 302 | 0 | 84 | 0 |
N.S. |
1 | 1.00 | 0.44 | 0.64 | 0.45 | 1.36 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.088 | 0.088 | 1.248 | 0.187 | 0.390 | 0.000 | 0.314 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 391 | 391 | 124 | 117 | 79 | 0 | 0 | 172 | 0 |
N.S. |
1 | 1.00 | 0.32 | 0.30 | 0.20 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.121 | 0.067 | 0.058 | 0.179 | 0.000 | 0.000 | 0.427 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 38 | 47 | 45 | 38 | 63 | 0 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.02 | 0.98 | 0.83 | 1.37 | 0.00 | 0.00 |
time (sec) |
N/A | 0.026 | 0.051 | 0.663 | 0.178 | 0.271 | 22.442 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 27 | 31 | 32 | 24 | 48 | 0 | 0 |
N.S. |
1 | 1.00 | 0.96 | 1.11 | 1.14 | 0.86 | 1.71 | 0.00 | 0.00 |
time (sec) |
N/A | 0.017 | 0.043 | 0.650 | 0.173 | 0.270 | 8.957 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 18 | 19 | 15 | 46 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 1.27 | 1.00 | 3.07 | 0.00 | 0.00 |
time (sec) |
N/A | 0.009 | 0.024 | 0.627 | 0.174 | 0.258 | 1.745 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 25 | 26 | 27 | 22 | 54 | 25 | 20 |
N.S. |
1 | 1.00 | 1.09 | 1.13 | 1.17 | 0.96 | 2.35 | 1.09 | 0.87 |
time (sec) |
N/A | 0.013 | 0.037 | 0.642 | 0.182 | 0.272 | 1.744 | 0.276 | 8.710 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 48 | 58 | 58 | 59 | 100 | 0 | 0 |
N.S. |
1 | 1.00 | 0.84 | 1.02 | 1.02 | 1.04 | 1.75 | 0.00 | 0.00 |
time (sec) |
N/A | 0.029 | 0.078 | 0.625 | 0.180 | 0.287 | 29.315 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 63 | 75 | 71 | 72 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.99 | 0.93 | 0.95 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.033 | 0.091 | 0.615 | 0.174 | 0.276 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 76 | 90 | 84 | 85 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.97 | 0.90 | 0.91 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.036 | 0.103 | 0.628 | 0.179 | 0.264 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 236 | 236 | 34 | 54 | 0 | 270 | 0 | 203 | 0 |
N.S. |
1 | 1.00 | 0.14 | 0.23 | 0.00 | 1.14 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.144 | 0.040 | 0.691 | 0.000 | 0.266 | 0.000 | 0.321 | 0.000 |