Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 101 | 76 | 143 | 481 | 169 | 311 | 170 | 243 | 219 |
N.S. |
1 | 1.11 | 0.84 | 1.57 | 5.29 | 1.86 | 3.42 | 1.87 | 2.67 | 2.41 |
time (sec) |
N/A | 0.555 | 0.341 | 1.326 | 0.091 | 0.077 | 0.333 | 0.340 | 0.151 | 0.426 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 76 | 61 | 107 | 278 | 109 | 202 | 110 | 153 | 147 |
N.S. |
1 | 1.09 | 0.87 | 1.53 | 3.97 | 1.56 | 2.89 | 1.57 | 2.19 | 2.10 |
time (sec) |
N/A | 0.428 | 0.223 | 1.227 | 0.048 | 0.083 | 0.247 | 0.397 | 0.185 | 0.226 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 52 | 44 | 60 | 136 | 62 | 112 | 64 | 83 | 84 |
N.S. |
1 | 1.06 | 0.90 | 1.22 | 2.78 | 1.27 | 2.29 | 1.31 | 1.69 | 1.71 |
time (sec) |
N/A | 0.322 | 0.190 | 1.170 | 0.037 | 0.076 | 0.177 | 0.326 | 0.163 | 0.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 26 | 28 | 50 | 28 | 46 | 30 | 32 | 34 |
N.S. |
1 | 1.00 | 0.96 | 1.04 | 1.85 | 1.04 | 1.70 | 1.11 | 1.19 | 1.26 |
time (sec) |
N/A | 0.224 | 0.126 | 0.920 | 0.056 | 0.072 | 0.134 | 0.382 | 0.160 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 50 | 77 | 142 | 62 | 0 | 577 | 16 | 0 |
N.S. |
1 | 1.00 | 0.96 | 1.48 | 2.73 | 1.19 | 0.00 | 11.10 | 0.31 | 0.00 |
time (sec) |
N/A | 0.381 | 0.121 | 1.051 | 0.084 | 0.069 | 0.000 | 0.371 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 76 | 65 | 114 | 164 | 96 | 0 | 523 | 125 | 0 |
N.S. |
1 | 1.04 | 0.89 | 1.56 | 2.25 | 1.32 | 0.00 | 7.16 | 1.71 | 0.00 |
time (sec) |
N/A | 0.488 | 0.449 | 1.099 | 0.161 | 0.073 | 0.000 | 0.411 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 105 | 89 | 148 | 199 | 165 | 0 | 5518 | 274 | 0 |
N.S. |
1 | 1.01 | 0.86 | 1.42 | 1.91 | 1.59 | 0.00 | 53.06 | 2.63 | 0.00 |
time (sec) |
N/A | 0.596 | 0.719 | 1.302 | 0.148 | 0.075 | 0.000 | 0.531 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | B | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 134 | 144 | 184 | 249 | 235 | 0 | 8378 | 464 | 0 |
N.S. |
1 | 1.06 | 1.13 | 1.45 | 1.96 | 1.85 | 0.00 | 65.97 | 3.65 | 0.00 |
time (sec) |
N/A | 0.747 | 0.639 | 1.500 | 0.235 | 0.082 | 0.000 | 0.667 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 166 | 132 | 145 | 717 | 287 | 660 | 222 | 428 | 349 |
N.S. |
1 | 1.03 | 0.82 | 0.90 | 4.45 | 1.78 | 4.10 | 1.38 | 2.66 | 2.17 |
time (sec) |
N/A | 0.493 | 0.624 | 2.049 | 0.065 | 0.086 | 0.472 | 0.375 | 0.157 | 0.943 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 129 | 106 | 121 | 428 | 190 | 456 | 153 | 278 | 229 |
N.S. |
1 | 1.04 | 0.85 | 0.98 | 3.45 | 1.53 | 3.68 | 1.23 | 2.24 | 1.85 |
time (sec) |
N/A | 0.353 | 0.478 | 1.683 | 0.057 | 0.078 | 0.337 | 0.383 | 0.163 | 42.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 97 | 77 | 81 | 222 | 113 | 264 | 94 | 156 | 179 |
N.S. |
1 | 1.02 | 0.81 | 0.85 | 2.34 | 1.19 | 2.78 | 0.99 | 1.64 | 1.88 |
time (sec) |
N/A | 0.309 | 0.343 | 1.642 | 0.042 | 0.077 | 0.246 | 0.393 | 0.156 | 0.292 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 50 | 46 | 90 | 53 | 126 | 48 | 73 | 57 |
N.S. |
1 | 1.00 | 0.91 | 0.84 | 1.64 | 0.96 | 2.29 | 0.87 | 1.33 | 1.04 |
time (sec) |
N/A | 0.210 | 0.295 | 1.240 | 0.038 | 0.079 | 0.173 | 0.375 | 0.156 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 65 | 107 | 163 | 71 | 0 | 610 | 18 | 0 |
N.S. |
1 | 1.00 | 0.83 | 1.37 | 2.09 | 0.91 | 0.00 | 7.82 | 0.23 | 0.00 |
time (sec) |
N/A | 0.361 | 0.282 | 1.298 | 0.087 | 0.081 | 0.000 | 0.405 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 86 | 75 | 155 | 171 | 100 | 0 | 534 | 29 | 0 |
N.S. |
1 | 1.04 | 0.90 | 1.87 | 2.06 | 1.20 | 0.00 | 6.43 | 0.35 | 0.00 |
time (sec) |
N/A | 0.518 | 0.686 | 1.408 | 0.149 | 0.085 | 0.000 | 0.438 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 146 | 102 | 193 | 204 | 176 | 0 | 5136 | 40 | 0 |
N.S. |
1 | 1.30 | 0.91 | 1.72 | 1.82 | 1.57 | 0.00 | 45.86 | 0.36 | 0.00 |
time (sec) |
N/A | 0.488 | 1.111 | 1.652 | 0.177 | 0.087 | 0.000 | 0.589 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 304 | 385 | 173 | 925 | 350 | 772 | 351 | 568 | 532 |
N.S. |
1 | 1.35 | 1.71 | 0.77 | 4.11 | 1.56 | 3.43 | 1.56 | 2.52 | 2.36 |
time (sec) |
N/A | 1.804 | 1.085 | 3.338 | 0.100 | 0.089 | 0.619 | 0.385 | 0.675 | 46.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 216 | 121 | 224 | 535 | 227 | 495 | 231 | 364 | 364 |
N.S. |
1 | 1.23 | 0.69 | 1.28 | 3.06 | 1.30 | 2.83 | 1.32 | 2.08 | 2.08 |
time (sec) |
N/A | 1.119 | 1.072 | 2.814 | 0.054 | 0.087 | 0.438 | 0.343 | 0.165 | 47.123 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 137 | 93 | 128 | 267 | 128 | 284 | 137 | 195 | 173 |
N.S. |
1 | 1.11 | 0.76 | 1.04 | 2.17 | 1.04 | 2.31 | 1.11 | 1.59 | 1.41 |
time (sec) |
N/A | 0.619 | 0.672 | 2.680 | 0.051 | 0.080 | 0.328 | 0.383 | 0.164 | 44.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 74 | 52 | 61 | 103 | 60 | 126 | 69 | 79 | 77 |
N.S. |
1 | 0.99 | 0.69 | 0.81 | 1.37 | 0.80 | 1.68 | 0.92 | 1.05 | 1.03 |
time (sec) |
N/A | 0.351 | 0.238 | 2.303 | 0.041 | 0.075 | 0.219 | 0.367 | 0.182 | 43.796 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 103 | 171 | 278 | 123 | 0 | 6075 | 18 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.41 | 2.30 | 1.02 | 0.00 | 50.21 | 0.15 | 0.00 |
time (sec) |
N/A | 0.466 | 0.449 | 1.703 | 0.118 | 0.081 | 0.000 | 0.578 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 148 | 200 | 247 | 304 | 177 | 0 | 1000 | 29 | 0 |
N.S. |
1 | 1.02 | 1.38 | 1.70 | 2.10 | 1.22 | 0.00 | 6.90 | 0.20 | 0.00 |
time (sec) |
N/A | 0.457 | 0.795 | 1.902 | 0.247 | 0.087 | 0.000 | 0.470 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 243 | 221 | 316 | 339 | 289 | 0 | 115446 | 40 | 0 |
N.S. |
1 | 1.32 | 1.20 | 1.72 | 1.84 | 1.57 | 0.00 | 627.42 | 0.22 | 0.00 |
time (sec) |
N/A | 0.980 | 0.974 | 2.398 | 0.283 | 0.091 | 0.000 | 3.416 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 237 | 100 | 102 | 303 | 115 | 253 | 108 | 151 | 138 |
N.S. |
1 | 1.38 | 0.58 | 0.59 | 1.76 | 0.67 | 1.47 | 0.63 | 0.88 | 0.80 |
time (sec) |
N/A | 0.746 | 0.478 | 2.743 | 0.051 | 0.078 | 0.548 | 0.344 | 0.155 | 45.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 181 | 92 | 81 | 188 | 88 | 209 | 84 | 114 | 104 |
N.S. |
1 | 1.35 | 0.69 | 0.60 | 1.40 | 0.66 | 1.56 | 0.63 | 0.85 | 0.78 |
time (sec) |
N/A | 0.618 | 0.207 | 2.418 | 0.054 | 0.098 | 0.394 | 0.333 | 0.165 | 44.745 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 85 | 53 | 62 | 98 | 63 | 138 | 64 | 67 | 63 |
N.S. |
1 | 1.06 | 0.66 | 0.78 | 1.22 | 0.79 | 1.72 | 0.80 | 0.84 | 0.79 |
time (sec) |
N/A | 0.288 | 0.141 | 2.293 | 0.036 | 0.169 | 0.279 | 0.367 | 0.179 | 43.801 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 52 | 52 | 91 | 49 | 60 | 428 | 14 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.88 | 1.54 | 0.83 | 1.02 | 7.25 | 0.24 | 0.00 |
time (sec) |
N/A | 0.323 | 0.170 | 1.515 | 0.080 | 0.081 | 0.993 | 0.425 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 70 | 79 | 90 | 717 | 66 | 0 | 3220 | 14 | 0 |
N.S. |
1 | 1.06 | 1.20 | 1.36 | 10.86 | 1.00 | 0.00 | 48.79 | 0.21 | 0.00 |
time (sec) |
N/A | 0.334 | 0.247 | 1.642 | 0.107 | 0.086 | 0.000 | 0.417 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 138 | 119 | 124 | 790 | 100 | 0 | 3920 | 14 | 0 |
N.S. |
1 | 1.53 | 1.32 | 1.38 | 8.78 | 1.11 | 0.00 | 43.56 | 0.16 | 0.00 |
time (sec) |
N/A | 0.527 | 0.377 | 1.716 | 0.109 | 0.100 | 0.000 | 0.390 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 223 | 196 | 685 | 722 | 970 | 0 | 0 | 182 | 0 |
N.S. |
1 | 1.09 | 0.96 | 3.34 | 3.52 | 4.73 | 0.00 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.733 | 0.215 | 1.557 | 0.223 | 0.119 | 0.000 | 0.000 | 0.270 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 145 | 130 | 392 | 402 | 598 | 0 | 0 | 129 | 0 |
N.S. |
1 | 1.06 | 0.95 | 2.86 | 2.93 | 4.36 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.485 | 0.110 | 1.383 | 0.180 | 0.110 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 87 | 128 | 0 | 306 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.00 | 1.16 | 1.71 | 0.00 | 4.08 | 0.00 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.293 | 0.012 | 0.992 | 0.000 | 0.104 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 14 | 14 | 16 | 14 | 16 | 16 | 12 | 16 | 48 | 18 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.14 | 0.86 | 1.14 | 3.43 | 1.29 |
time (sec) |
N/A | 0.200 | 4.939 | 0.701 | 0.284 | 0.073 | 0.344 | 0.482 | 0.175 | 45.592 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 137 | 109 | 316 | 1059 | 790 | 0 | 0 | 1343 | 0 |
N.S. |
1 | 1.20 | 0.96 | 2.77 | 9.29 | 6.93 | 0.00 | 0.00 | 11.78 | 0.00 |
time (sec) |
N/A | 0.676 | 0.563 | 1.822 | 0.197 | 0.125 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 97 | 75 | 170 | 324 | 450 | 0 | 0 | 235 | 0 |
N.S. |
1 | 1.18 | 0.91 | 2.07 | 3.95 | 5.49 | 0.00 | 0.00 | 2.87 | 0.00 |
time (sec) |
N/A | 0.476 | 0.280 | 1.700 | 0.172 | 0.104 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 36 | 52 | 159 | 45 | 0 | 1404 | 95 | 55 |
N.S. |
1 | 1.00 | 1.29 | 1.86 | 5.68 | 1.61 | 0.00 | 50.14 | 3.39 | 1.96 |
time (sec) |
N/A | 0.262 | 0.019 | 1.284 | 0.113 | 0.081 | 0.000 | 0.520 | 0.182 | 43.496 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 16 | 16 | 18 | 16 | 290 | 18 | 14 | 18 | 56 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 18.12 | 1.12 | 0.88 | 1.12 | 3.50 | 1.12 |
time (sec) |
N/A | 0.218 | 6.739 | 0.446 | 0.268 | 0.075 | 0.355 | 0.410 | 0.235 | 42.783 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 337 | 358 | 311 | 1127 | 3831 | 1315 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.92 | 3.34 | 11.37 | 3.90 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.272 | 3.311 | 1.885 | 1.115 | 0.156 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 207 | 184 | 584 | 1891 | 795 | 0 | 0 | 884 | 0 |
N.S. |
1 | 1.07 | 0.95 | 3.03 | 9.80 | 4.12 | 0.00 | 0.00 | 4.58 | 0.00 |
time (sec) |
N/A | 0.741 | 1.096 | 1.698 | 0.427 | 0.130 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 118 | 389 | 267 | 0 | 435 | 0 | 0 | 398 | 0 |
N.S. |
1 | 1.01 | 3.32 | 2.28 | 0.00 | 3.72 | 0.00 | 0.00 | 3.40 | 0.00 |
time (sec) |
N/A | 0.410 | 4.437 | 1.384 | 0.000 | 0.107 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 16 | 16 | 18 | 16 | 290 | 18 | 14 | 18 | 56 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 18.12 | 1.12 | 0.88 | 1.12 | 3.50 | 1.12 |
time (sec) |
N/A | 0.214 | 1.820 | 0.020 | 0.259 | 0.093 | 0.361 | 0.403 | 0.203 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 202 | 124 | 232 | 263 | 190 | 0 | 1233 | 62 | 0 |
N.S. |
1 | 1.04 | 0.64 | 1.20 | 1.36 | 0.98 | 0.00 | 6.36 | 0.32 | 0.00 |
time (sec) |
N/A | 0.993 | 0.069 | 1.300 | 0.066 | 0.095 | 0.000 | 0.557 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 175 | 122 | 189 | 242 | 156 | 0 | 764 | 36 | 0 |
N.S. |
1 | 1.04 | 0.72 | 1.12 | 1.43 | 0.92 | 0.00 | 4.52 | 0.21 | 0.00 |
time (sec) |
N/A | 0.803 | 0.101 | 1.239 | 0.062 | 0.091 | 0.000 | 0.414 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 145 | 122 | 144 | 196 | 126 | 0 | 426 | 15 | 0 |
N.S. |
1 | 1.02 | 0.86 | 1.01 | 1.38 | 0.89 | 0.00 | 3.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.653 | 0.048 | 1.217 | 0.059 | 0.078 | 0.000 | 0.376 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 124 | 100 | 159 | 108 | 0 | 168 | 17 | 0 |
N.S. |
1 | 1.00 | 1.05 | 0.85 | 1.35 | 0.92 | 0.00 | 1.42 | 0.14 | 0.00 |
time (sec) |
N/A | 0.519 | 0.066 | 1.219 | 0.050 | 0.079 | 0.000 | 0.375 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 144 | 147 | 140 | 129 | 144 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.04 | 1.06 | 1.01 | 0.93 | 1.04 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.650 | 0.364 | 1.176 | 0.214 | 0.085 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 176 | 190 | 180 | 129 | 208 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.05 | 1.13 | 1.07 | 0.77 | 1.24 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.802 | 0.388 | 1.118 | 0.216 | 0.092 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 206 | 228 | 220 | 129 | 296 | 0 | 0 | 63 | 0 |
N.S. |
1 | 1.07 | 1.18 | 1.14 | 0.67 | 1.53 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.948 | 0.413 | 1.169 | 0.227 | 0.096 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 238 | 150 | 242 | 295 | 258 | 0 | 1310 | 68 | 0 |
N.S. |
1 | 1.03 | 0.65 | 1.05 | 1.28 | 1.12 | 0.00 | 5.67 | 0.29 | 0.00 |
time (sec) |
N/A | 0.696 | 0.894 | 1.896 | 0.141 | 0.095 | 0.000 | 0.609 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 210 | 150 | 197 | 274 | 195 | 0 | 797 | 40 | 0 |
N.S. |
1 | 1.03 | 0.74 | 0.97 | 1.35 | 0.96 | 0.00 | 3.93 | 0.20 | 0.00 |
time (sec) |
N/A | 0.626 | 0.677 | 1.695 | 0.139 | 0.095 | 0.000 | 0.518 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 158 | 150 | 150 | 229 | 148 | 0 | 436 | 17 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.95 | 1.45 | 0.94 | 0.00 | 2.76 | 0.11 | 0.00 |
time (sec) |
N/A | 0.466 | 0.258 | 1.676 | 0.130 | 0.096 | 0.000 | 0.446 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 145 | 108 | 187 | 114 | 0 | 167 | 19 | 0 |
N.S. |
1 | 1.00 | 1.12 | 0.83 | 1.44 | 0.88 | 0.00 | 1.28 | 0.15 | 0.00 |
time (sec) |
N/A | 0.408 | 0.264 | 1.575 | 0.126 | 0.118 | 0.000 | 0.378 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 140 | 175 | 146 | 135 | 136 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.04 | 1.30 | 1.08 | 1.00 | 1.01 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.688 | 0.700 | 1.724 | 0.228 | 0.089 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 213 | 181 | 189 | 136 | 206 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.25 | 1.06 | 1.11 | 0.80 | 1.21 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.575 | 1.532 | 1.768 | 0.218 | 0.101 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 223 | 237 | 230 | 136 | 323 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.03 | 1.10 | 1.06 | 0.63 | 1.50 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.989 | 0.898 | 1.759 | 0.222 | 0.106 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 296 | 237 | 273 | 136 | 417 | 0 | 0 | 82 | 0 |
N.S. |
1 | 1.20 | 0.96 | 1.11 | 0.55 | 1.69 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.787 | 0.954 | 1.715 | 0.222 | 0.129 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 410 | 576 | 236 | 474 | 547 | 368 | 0 | 2455 | 68 | 0 |
N.S. |
1 | 1.40 | 0.58 | 1.16 | 1.33 | 0.90 | 0.00 | 5.99 | 0.17 | 0.00 |
time (sec) |
N/A | 2.633 | 1.582 | 3.195 | 0.160 | 0.105 | 0.000 | 0.866 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 354 | 502 | 251 | 386 | 497 | 299 | 0 | 1522 | 40 | 0 |
N.S. |
1 | 1.42 | 0.71 | 1.09 | 1.40 | 0.84 | 0.00 | 4.30 | 0.11 | 0.00 |
time (sec) |
N/A | 2.169 | 1.137 | 2.129 | 0.170 | 0.097 | 0.000 | 0.674 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 304 | 304 | 234 | 294 | 424 | 245 | 0 | 848 | 17 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.97 | 1.39 | 0.81 | 0.00 | 2.79 | 0.06 | 0.00 |
time (sec) |
N/A | 0.818 | 0.338 | 2.144 | 0.147 | 0.094 | 0.000 | 0.528 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 257 | 236 | 212 | 377 | 213 | 0 | 332 | 19 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.82 | 1.47 | 0.83 | 0.00 | 1.29 | 0.07 | 0.00 |
time (sec) |
N/A | 0.643 | 0.369 | 1.997 | 0.135 | 0.082 | 0.000 | 0.399 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 286 | 293 | 286 | 253 | 265 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.06 | 1.08 | 1.06 | 0.93 | 0.98 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.662 | 1.500 | 2.003 | 0.287 | 0.096 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 445 | 268 | 368 | 253 | 367 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.52 | 0.92 | 1.26 | 0.87 | 1.26 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 1.555 | 2.204 | 1.969 | 0.309 | 0.111 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 356 | 506 | 448 | 450 | 254 | 528 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.42 | 1.26 | 1.26 | 0.71 | 1.48 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 1.789 | 1.601 | 1.958 | 0.282 | 0.124 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | A | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 55 | 34 | 74 | 35 | 83 | 69 | 24 | 0 |
N.S. |
1 | 1.00 | 1.12 | 0.69 | 1.51 | 0.71 | 1.69 | 1.41 | 0.49 | 0.00 |
time (sec) |
N/A | 0.331 | 0.019 | 0.748 | 0.117 | 0.082 | 2.428 | 0.379 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | A | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 48 | 27 | 67 | 26 | 61 | 53 | 7 | 26 |
N.S. |
1 | 1.00 | 1.33 | 0.75 | 1.86 | 0.72 | 1.69 | 1.47 | 0.19 | 0.72 |
time (sec) |
N/A | 0.264 | 0.010 | 0.694 | 0.123 | 0.073 | 0.485 | 0.346 | 0.175 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | A | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 51 | 19 | 60 | 18 | 37 | 35 | 9 | 18 |
N.S. |
1 | 1.00 | 2.12 | 0.79 | 2.50 | 0.75 | 1.54 | 1.46 | 0.38 | 0.75 |
time (sec) |
N/A | 0.202 | 0.011 | 0.645 | 0.116 | 0.098 | 0.418 | 0.379 | 0.161 | 41.217 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 63 | 28 | 21 | 31 | 61 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.80 | 0.80 | 0.60 | 0.89 | 1.74 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.264 | 0.053 | 0.684 | 0.135 | 0.077 | 0.834 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 192 | 122 | 0 | 235 | 174 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.05 | 0.67 | 0.00 | 1.28 | 0.95 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.575 | 0.122 | 0.000 | 0.212 | 0.085 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 159 | 122 | 0 | 186 | 140 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.05 | 0.80 | 0.00 | 1.22 | 0.92 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.444 | 0.052 | 0.000 | 0.206 | 0.090 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 159 | 122 | 0 | 186 | 140 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.05 | 0.80 | 0.00 | 1.22 | 0.92 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.442 | 0.055 | 0.000 | 0.201 | 0.083 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 124 | 0 | 137 | 118 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 1.01 | 0.87 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.330 | 0.063 | 0.000 | 0.203 | 0.087 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 124 | 0 | 138 | 118 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 1.02 | 0.87 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.334 | 0.067 | 0.000 | 0.198 | 0.089 | 0.000 | 0.000 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 158 | 121 | 0 | 138 | 169 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.05 | 0.80 | 0.00 | 0.91 | 1.12 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.425 | 0.056 | 0.000 | 0.206 | 0.088 | 0.000 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 162 | 121 | 0 | 138 | 169 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.06 | 0.79 | 0.00 | 0.90 | 1.10 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.437 | 0.058 | 0.000 | 0.266 | 0.106 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 193 | 125 | 0 | 137 | 259 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.06 | 0.69 | 0.00 | 0.75 | 1.42 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.543 | 0.053 | 0.000 | 0.211 | 0.115 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 12 | 12 | 14 | 10 | 12 | 0 | 12 | 12 | 11 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 1.00 | 0.00 | 1.00 | 1.00 | 0.92 | 1.00 |
time (sec) |
N/A | 0.182 | 27.252 | 0.194 | 0.343 | 0.000 | 5.727 | 0.395 | 0.189 | 41.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 133 | 0 | 57 | 0 | 0 | 9 | 15 |
N.S. |
1 | 1.00 | 1.00 | 8.31 | 0.00 | 3.56 | 0.00 | 0.00 | 0.56 | 0.94 |
time (sec) |
N/A | 0.166 | 0.008 | 1.322 | 0.000 | 0.085 | 0.000 | 0.000 | 0.184 | 41.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 14 | 14 | 16 | 12 | 14 | 0 | 12 | 14 | 13 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 1.00 | 0.00 | 0.86 | 1.00 | 0.93 | 1.00 |
time (sec) |
N/A | 0.186 | 0.908 | 0.220 | 0.304 | 0.000 | 2.831 | 0.316 | 0.172 | 41.445 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 12 | 12 | 14 | 10 | 12 | 0 | 12 | 12 | 17 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 1.00 | 0.00 | 1.00 | 1.00 | 1.42 | 1.00 |
time (sec) |
N/A | 0.275 | 2.589 | 0.196 | 0.343 | 0.000 | 78.331 | 9.511 | 0.176 | 41.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 36 | 179 | 0 | 68 | 0 | 0 | 16 | 35 |
N.S. |
1 | 1.00 | 0.86 | 4.26 | 0.00 | 1.62 | 0.00 | 0.00 | 0.38 | 0.83 |
time (sec) |
N/A | 0.226 | 0.029 | 2.023 | 0.000 | 0.103 | 0.000 | 0.000 | 0.221 | 40.942 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 14 | 14 | 16 | 12 | 14 | 0 | 12 | 14 | 19 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 1.00 | 0.00 | 0.86 | 1.00 | 1.36 | 1.00 |
time (sec) |
N/A | 0.184 | 8.241 | 0.202 | 0.324 | 0.000 | 32.673 | 0.357 | 0.183 | 41.237 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 40 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.200 | 1.117 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 10 | 10 | 12 | 8 | 10 | 0 | 10 | 10 | 11 | 10 |
N.S. |
1 | 1.00 | 1.20 | 0.80 | 1.00 | 0.00 | 1.00 | 1.00 | 1.10 | 1.00 |
time (sec) |
N/A | 0.299 | 6.272 | 0.142 | 0.178 | 0.000 | 41.476 | 0.392 | 0.161 | 40.873 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 12 | 12 | 14 | 10 | 12 | 0 | 12 | 12 | 19 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 1.00 | 0.00 | 1.00 | 1.00 | 1.58 | 1.00 |
time (sec) |
N/A | 0.177 | 0.303 | 0.190 | 0.343 | 0.000 | 2.756 | 0.459 | 0.182 | 41.338 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 18 | 0 | 51 | 0 | 0 | 18 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.12 | 0.00 | 3.19 | 0.00 | 0.00 | 1.12 | 0.94 |
time (sec) |
N/A | 0.167 | 0.010 | 0.267 | 0.000 | 0.088 | 0.000 | 0.000 | 0.172 | 40.836 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 14 | 14 | 16 | 12 | 14 | 0 | 14 | 14 | 21 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 1.00 | 0.00 | 1.00 | 1.00 | 1.50 | 1.00 |
time (sec) |
N/A | 0.188 | 0.404 | 0.190 | 0.306 | 0.000 | 8.328 | 0.430 | 0.167 | 41.310 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 12 | 12 | 14 | 10 | 12 | 0 | 12 | 12 | 19 | 12 |
N.S. |
1 | 1.00 | 1.17 | 0.83 | 1.00 | 0.00 | 1.00 | 1.00 | 1.58 | 1.00 |
time (sec) |
N/A | 0.270 | 2.995 | 0.195 | 0.348 | 0.000 | 11.618 | 0.440 | 0.159 | 41.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 182 | 0 | 93 | 0 | 0 | 18 | 42 |
N.S. |
1 | 1.00 | 1.00 | 4.79 | 0.00 | 2.45 | 0.00 | 0.00 | 0.47 | 1.11 |
time (sec) |
N/A | 0.227 | 0.051 | 0.855 | 0.000 | 0.081 | 0.000 | 0.000 | 0.185 | 41.239 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 14 | 14 | 16 | 12 | 14 | 0 | 14 | 14 | 21 | 14 |
N.S. |
1 | 1.00 | 1.14 | 0.86 | 1.00 | 0.00 | 1.00 | 1.00 | 1.50 | 1.00 |
time (sec) |
N/A | 0.190 | 11.408 | 0.188 | 0.360 | 0.000 | 30.648 | 0.358 | 0.176 | 41.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 33 | 0 | 0 | 0 | 0 | 0 | 31 | 51 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.82 | 1.34 |
time (sec) |
N/A | 0.205 | 1.215 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 41.331 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 17 | 0 | 0 | 0 | 0 | 0 | 19 | 15 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.95 | 0.75 |
time (sec) |
N/A | 0.181 | 0.141 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 41.392 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 17 | 0 | 0 | 15 | 0 | 0 | 25 | 16 |
N.S. |
1 | 1.00 | 0.71 | 0.00 | 0.00 | 0.62 | 0.00 | 0.00 | 1.04 | 0.67 |
time (sec) |
N/A | 0.185 | 0.119 | 0.000 | 0.000 | 0.080 | 0.000 | 0.000 | 0.191 | 0.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 33 | 0 | 0 | 0 | 0 | 0 | 21 | 31 |
N.S. |
1 | 1.00 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.66 |
time (sec) |
N/A | 0.204 | 0.193 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 41.379 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 29 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.220 | 0.209 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 17 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.215 | 0.097 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 17 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.211 | 0.283 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 45 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.231 | 0.143 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 51 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.294 | 0.108 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 18 | 18 | 20 | 18 | 20 | 20 | 17 | 20 | 22 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.94 | 1.11 | 1.22 | 1.11 |
time (sec) |
N/A | 0.213 | 1.209 | 0.496 | 0.383 | 0.086 | 8.364 | 1.278 | 0.172 | 41.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 275 | 275 | 253 | 0 | 0 | 188 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.538 | 0.204 | 0.000 | 0.000 | 0.092 | 0.000 | 0.000 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 162 | 150 | 0 | 0 | 136 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.421 | 0.228 | 0.000 | 0.000 | 0.115 | 0.000 | 0.000 | 0.202 | 0.000 |