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 | B | F | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 474 | 342 | 559 | 1860 | 0 | 3576 | 0 | 978 | 1220 | 0 |
N.S. |
1 | 0.72 | 1.18 | 3.92 | 0.00 | 7.54 | 0.00 | 2.06 | 2.57 | 0.00 |
time (sec) |
N/A | 0.739 | 4.839 | 1.522 | 0.000 | 0.787 | 0.000 | 0.226 | 0.236 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 549 | 378 | 720 | 2282 | 0 | 4815 | 0 | 1161 | 1814 | 0 |
N.S. |
1 | 0.69 | 1.31 | 4.16 | 0.00 | 8.77 | 0.00 | 2.11 | 3.30 | 0.00 |
time (sec) |
N/A | 0.771 | 6.033 | 1.542 | 0.000 | 2.060 | 0.000 | 0.262 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 234 | 208 | 1958 | 957 | 2274 | 28048 | 4377 | 1728 | 2117 |
N.S. |
1 | 1.00 | 0.89 | 8.37 | 4.09 | 9.72 | 119.86 | 18.71 | 7.38 | 9.05 |
time (sec) |
N/A | 0.761 | 0.388 | 1.407 | 0.094 | 0.112 | 5.942 | 0.844 | 0.228 | 12.485 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 122 | 576 | 364 | 660 | 6186 | 1261 | 546 | 676 |
N.S. |
1 | 1.00 | 0.88 | 4.17 | 2.64 | 4.78 | 44.83 | 9.14 | 3.96 | 4.90 |
time (sec) |
N/A | 0.517 | 0.201 | 0.799 | 0.057 | 0.098 | 1.624 | 0.178 | 0.218 | 11.497 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 112 | 99 | 0 | 0 | 0 | 0 | 0 | 94 | 0 |
N.S. |
1 | 1.08 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.426 | 0.140 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 125 | 109 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.435 | 0.173 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-2) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 471 | 310 | 269 | 3931 | 1864 | 3485 | 0 | 8705 | 2686 | 0 |
N.S. |
1 | 0.66 | 0.57 | 8.35 | 3.96 | 7.40 | 0.00 | 18.48 | 5.70 | 0.00 |
time (sec) |
N/A | 0.902 | 0.556 | 1.414 | 0.069 | 0.147 | 0.000 | 0.388 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-2) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 321 | 214 | 183 | 1286 | 756 | 1282 | 0 | 3203 | 1028 | 0 |
N.S. |
1 | 0.67 | 0.57 | 4.01 | 2.36 | 3.99 | 0.00 | 9.98 | 3.20 | 0.00 |
time (sec) |
N/A | 0.668 | 0.408 | 1.450 | 0.066 | 0.099 | 0.000 | 0.255 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 118 | 121 | 205 | 177 | 256 | 0 | 652 | 241 | 312 |
N.S. |
1 | 0.69 | 0.71 | 1.20 | 1.04 | 1.50 | 0.00 | 3.81 | 1.41 | 1.82 |
time (sec) |
N/A | 0.473 | 0.193 | 0.781 | 0.042 | 0.106 | 0.000 | 0.194 | 0.223 | 11.857 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 111 | 94 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 0.82 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.398 | 0.187 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 149 | 120 | 0 | 0 | 0 | 0 | 0 | 1218 | 0 |
N.S. |
1 | 0.93 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 7.61 | 0.00 |
time (sec) |
N/A | 0.468 | 0.236 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 187 | 125 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.12 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.610 | 0.187 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.333 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 126 | 97 | 174 | 0 | 348 | 0 | 1316 | 180 | 375 |
N.S. |
1 | 1.06 | 0.82 | 1.46 | 0.00 | 2.92 | 0.00 | 11.06 | 1.51 | 3.15 |
time (sec) |
N/A | 0.474 | 0.187 | 2.056 | 0.000 | 0.103 | 0.000 | 0.232 | 0.233 | 12.296 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 189 | 366 | 748 | 0 | 361 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.06 | 2.04 | 4.18 | 0.00 | 2.02 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.606 | 0.355 | 1.665 | 0.000 | 0.086 | 0.000 | 0.000 | 200.034 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 229 | 242 | 231 | 231 | 279 | 280 | 280 | 238 |
N.S. |
1 | 1.00 | 1.85 | 1.95 | 1.86 | 1.86 | 2.25 | 2.26 | 2.26 | 1.92 |
time (sec) |
N/A | 0.641 | 0.090 | 0.680 | 0.044 | 0.072 | 0.041 | 0.188 | 0.222 | 12.011 |
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 | 124 | 124 | 175 | 183 | 174 | 174 | 211 | 211 | 213 | 179 |
N.S. |
1 | 1.00 | 1.41 | 1.48 | 1.40 | 1.40 | 1.70 | 1.70 | 1.72 | 1.44 |
time (sec) |
N/A | 0.580 | 0.067 | 0.737 | 0.028 | 0.064 | 0.034 | 0.207 | 0.326 | 0.073 |
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 | 124 | 124 | 133 | 128 | 126 | 126 | 146 | 146 | 146 | 124 |
N.S. |
1 | 1.00 | 1.07 | 1.03 | 1.02 | 1.02 | 1.18 | 1.18 | 1.18 | 1.00 |
time (sec) |
N/A | 0.545 | 0.046 | 0.685 | 0.041 | 0.070 | 0.028 | 0.218 | 0.211 | 0.050 |
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 | 79 | 79 | 79 | 72 | 73 | 73 | 82 | 80 | 79 | 71 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.92 | 0.92 | 1.04 | 1.01 | 1.00 | 0.90 |
time (sec) |
N/A | 0.412 | 0.021 | 0.270 | 0.033 | 0.076 | 0.022 | 0.225 | 0.210 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 21 | 15 | 14 | 32 | 31 | 25 | 32 | 32 |
N.S. |
1 | 1.00 | 1.31 | 0.94 | 0.88 | 2.00 | 1.94 | 1.56 | 2.00 | 2.00 |
time (sec) |
N/A | 0.245 | 0.006 | 0.260 | 0.037 | 0.062 | 0.022 | 0.189 | 0.216 | 0.042 |
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 | 104 | 104 | 95 | 115 | 116 | 117 | 100 | 123 | 145 | 121 |
N.S. |
1 | 1.00 | 0.91 | 1.11 | 1.12 | 1.12 | 0.96 | 1.18 | 1.39 | 1.16 |
time (sec) |
N/A | 0.494 | 0.046 | 0.879 | 0.042 | 0.067 | 0.207 | 0.237 | 0.211 | 11.872 |
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 | 102 | 102 | 97 | 115 | 117 | 172 | 126 | 180 | 221 | 127 |
N.S. |
1 | 1.00 | 0.95 | 1.13 | 1.15 | 1.69 | 1.24 | 1.76 | 2.17 | 1.25 |
time (sec) |
N/A | 0.500 | 0.070 | 0.757 | 0.038 | 0.078 | 0.365 | 0.225 | 0.235 | 0.075 |
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 | 111 | 111 | 118 | 121 | 128 | 187 | 139 | 120 | 206 | 135 |
N.S. |
1 | 1.00 | 1.06 | 1.09 | 1.15 | 1.68 | 1.25 | 1.08 | 1.86 | 1.22 |
time (sec) |
N/A | 0.501 | 0.053 | 0.849 | 0.031 | 0.071 | 0.858 | 0.192 | 0.232 | 11.765 |
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 | 119 | 119 | 111 | 122 | 146 | 179 | 158 | 127 | 194 | 144 |
N.S. |
1 | 1.00 | 0.93 | 1.03 | 1.23 | 1.50 | 1.33 | 1.07 | 1.63 | 1.21 |
time (sec) |
N/A | 0.507 | 0.053 | 0.760 | 0.037 | 0.074 | 1.747 | 0.214 | 0.226 | 0.117 |
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 | 122 | 122 | 100 | 118 | 150 | 150 | 170 | 176 | 131 | 151 |
N.S. |
1 | 1.00 | 0.82 | 0.97 | 1.23 | 1.23 | 1.39 | 1.44 | 1.07 | 1.24 |
time (sec) |
N/A | 0.486 | 0.050 | 0.772 | 0.062 | 0.076 | 3.335 | 0.212 | 0.239 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 240 | 240 | 433 | 473 | 430 | 430 | 552 | 561 | 565 | 454 |
N.S. |
1 | 1.00 | 1.80 | 1.97 | 1.79 | 1.79 | 2.30 | 2.34 | 2.35 | 1.89 |
time (sec) |
N/A | 1.087 | 0.180 | 1.313 | 0.029 | 0.072 | 0.059 | 0.209 | 0.322 | 0.167 |
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 | 240 | 240 | 351 | 363 | 343 | 343 | 430 | 429 | 433 | 349 |
N.S. |
1 | 1.00 | 1.46 | 1.51 | 1.43 | 1.43 | 1.79 | 1.79 | 1.80 | 1.45 |
time (sec) |
N/A | 0.943 | 0.136 | 1.231 | 0.037 | 0.073 | 0.048 | 0.233 | 0.379 | 11.636 |
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 | 240 | 240 | 244 | 254 | 241 | 241 | 294 | 298 | 301 | 242 |
N.S. |
1 | 1.00 | 1.02 | 1.06 | 1.00 | 1.00 | 1.22 | 1.24 | 1.25 | 1.01 |
time (sec) |
N/A | 0.858 | 0.091 | 1.279 | 0.033 | 0.066 | 0.040 | 0.228 | 0.313 | 11.335 |
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 | 153 | 153 | 153 | 145 | 151 | 151 | 168 | 167 | 169 | 144 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.99 | 0.99 | 1.10 | 1.09 | 1.10 | 0.94 |
time (sec) |
N/A | 0.614 | 0.049 | 1.141 | 0.035 | 0.066 | 0.029 | 0.231 | 0.293 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 36 | 15 | 14 | 67 | 65 | 40 | 73 | 62 |
N.S. |
1 | 1.00 | 2.25 | 0.94 | 0.88 | 4.19 | 4.06 | 2.50 | 4.56 | 3.88 |
time (sec) |
N/A | 0.256 | 0.012 | 1.174 | 0.025 | 0.069 | 0.029 | 0.210 | 0.310 | 11.188 |
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 | 229 | 229 | 228 | 320 | 307 | 308 | 280 | 360 | 405 | 326 |
N.S. |
1 | 1.00 | 1.00 | 1.40 | 1.34 | 1.34 | 1.22 | 1.57 | 1.77 | 1.42 |
time (sec) |
N/A | 0.863 | 0.126 | 1.438 | 0.043 | 0.070 | 0.410 | 0.210 | 0.338 | 11.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 223 | 241 | 331 | 310 | 444 | 325 | 437 | 577 | 387 |
N.S. |
1 | 1.00 | 1.08 | 1.48 | 1.39 | 1.99 | 1.46 | 1.96 | 2.59 | 1.74 |
time (sec) |
N/A | 0.856 | 0.216 | 1.448 | 0.040 | 0.085 | 0.993 | 0.229 | 0.432 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 219 | 233 | 326 | 317 | 487 | 360 | 340 | 630 | 358 |
N.S. |
1 | 1.00 | 1.06 | 1.49 | 1.45 | 2.22 | 1.64 | 1.55 | 2.88 | 1.63 |
time (sec) |
N/A | 0.807 | 0.088 | 1.380 | 0.038 | 0.082 | 3.043 | 0.208 | 0.319 | 11.373 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 217 | 300 | 319 | 327 | 487 | 379 | 337 | 601 | 349 |
N.S. |
1 | 1.00 | 1.38 | 1.47 | 1.51 | 2.24 | 1.75 | 1.55 | 2.77 | 1.61 |
time (sec) |
N/A | 0.771 | 0.144 | 1.415 | 0.038 | 0.080 | 9.257 | 0.226 | 0.338 | 11.443 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 227 | 292 | 329 | 338 | 458 | 401 | 526 | 494 | 369 |
N.S. |
1 | 1.00 | 1.29 | 1.45 | 1.49 | 2.02 | 1.77 | 2.32 | 2.18 | 1.63 |
time (sec) |
N/A | 0.790 | 0.197 | 1.344 | 0.040 | 0.080 | 29.157 | 0.209 | 0.287 | 11.525 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 411 | 411 | 735 | 783 | 729 | 729 | 935 | 936 | 940 | 768 |
N.S. |
1 | 1.00 | 1.79 | 1.91 | 1.77 | 1.77 | 2.27 | 2.28 | 2.29 | 1.87 |
time (sec) |
N/A | 1.796 | 0.269 | 1.086 | 0.035 | 0.079 | 0.087 | 0.235 | 0.298 | 11.337 |
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 | 411 | 411 | 562 | 603 | 565 | 565 | 726 | 719 | 723 | 589 |
N.S. |
1 | 1.00 | 1.37 | 1.47 | 1.37 | 1.37 | 1.77 | 1.75 | 1.76 | 1.43 |
time (sec) |
N/A | 1.521 | 0.217 | 1.267 | 0.056 | 0.078 | 0.064 | 0.223 | 0.299 | 0.203 |
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 | 411 | 411 | 413 | 423 | 417 | 417 | 503 | 502 | 506 | 414 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.01 | 1.01 | 1.22 | 1.22 | 1.23 | 1.01 |
time (sec) |
N/A | 1.365 | 0.147 | 1.358 | 0.034 | 0.079 | 0.060 | 0.214 | 0.320 | 11.424 |
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 | 251 | 251 | 251 | 244 | 261 | 261 | 291 | 286 | 289 | 243 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 1.04 | 1.04 | 1.16 | 1.14 | 1.15 | 0.97 |
time (sec) |
N/A | 0.853 | 0.069 | 1.129 | 0.031 | 0.090 | 0.039 | 0.218 | 0.290 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 51 | 15 | 14 | 121 | 121 | 56 | 128 | 112 |
N.S. |
1 | 1.00 | 3.19 | 0.94 | 0.88 | 7.56 | 7.56 | 3.50 | 8.00 | 7.00 |
time (sec) |
N/A | 0.260 | 0.021 | 1.166 | 0.031 | 0.062 | 0.039 | 0.228 | 0.209 | 11.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 399 | 399 | 483 | 695 | 644 | 645 | 641 | 795 | 871 | 697 |
N.S. |
1 | 1.00 | 1.21 | 1.74 | 1.61 | 1.62 | 1.61 | 1.99 | 2.18 | 1.75 |
time (sec) |
N/A | 1.494 | 0.266 | 1.443 | 0.044 | 0.076 | 0.737 | 0.217 | 0.233 | 11.298 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 396 | 396 | 637 | 709 | 649 | 903 | 688 | 870 | 1163 | 1090 |
N.S. |
1 | 1.00 | 1.61 | 1.79 | 1.64 | 2.28 | 1.74 | 2.20 | 2.94 | 2.75 |
time (sec) |
N/A | 1.442 | 0.262 | 1.319 | 0.039 | 0.082 | 1.998 | 0.229 | 1.665 | 11.281 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 390 | 390 | 403 | 702 | 656 | 990 | 733 | 747 | 1320 | 936 |
N.S. |
1 | 1.00 | 1.03 | 1.80 | 1.68 | 2.54 | 1.88 | 1.92 | 3.38 | 2.40 |
time (sec) |
N/A | 1.381 | 0.176 | 1.438 | 0.055 | 0.087 | 7.852 | 0.214 | 0.217 | 11.314 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 396 | 396 | 404 | 703 | 670 | 1031 | 821 | 731 | 1380 | 807 |
N.S. |
1 | 1.00 | 1.02 | 1.78 | 1.69 | 2.60 | 2.07 | 1.85 | 3.48 | 2.04 |
time (sec) |
N/A | 1.376 | 0.159 | 1.417 | 0.055 | 0.091 | 36.266 | 0.201 | 0.228 | 11.335 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 389 | 389 | 614 | 701 | 679 | 1017 | 0 | 1066 | 1248 | 763 |
N.S. |
1 | 1.00 | 1.58 | 1.80 | 1.75 | 2.61 | 0.00 | 2.74 | 3.21 | 1.96 |
time (sec) |
N/A | 1.379 | 0.301 | 1.339 | 0.050 | 0.085 | 0.000 | 0.263 | 0.219 | 11.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 299 | 297 | 474 | 0 | 709 | 1056 | 424 | 604 | 726 |
N.S. |
1 | 1.00 | 0.99 | 1.59 | 0.00 | 2.37 | 3.53 | 1.42 | 2.02 | 2.43 |
time (sec) |
N/A | 1.051 | 0.227 | 1.552 | 0.000 | 0.105 | 7.078 | 0.212 | 0.232 | 0.406 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 188 | 177 | 290 | 0 | 458 | 561 | 262 | 362 | 433 |
N.S. |
1 | 1.00 | 0.94 | 1.54 | 0.00 | 2.44 | 2.98 | 1.39 | 1.93 | 2.30 |
time (sec) |
N/A | 0.725 | 0.188 | 1.465 | 0.000 | 0.089 | 2.667 | 0.226 | 0.214 | 0.312 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 111 | 163 | 0 | 282 | 335 | 146 | 180 | 230 |
N.S. |
1 | 1.00 | 0.97 | 1.43 | 0.00 | 2.47 | 2.94 | 1.28 | 1.58 | 2.02 |
time (sec) |
N/A | 0.518 | 0.099 | 1.432 | 0.000 | 0.085 | 0.972 | 0.241 | 0.219 | 0.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 72 | 88 | 0 | 176 | 134 | 77 | 76 | 129 |
N.S. |
1 | 1.00 | 1.03 | 1.26 | 0.00 | 2.51 | 1.91 | 1.10 | 1.09 | 1.84 |
time (sec) |
N/A | 0.408 | 0.073 | 1.177 | 0.000 | 0.101 | 0.421 | 0.241 | 0.208 | 0.324 |
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 | 11 | 11 | 10 | 12 | 11 | 11 | 10 | 12 | 11 | 11 |
N.S. |
1 | 1.00 | 0.91 | 1.09 | 1.00 | 1.00 | 0.91 | 1.09 | 1.00 | 1.00 |
time (sec) |
N/A | 0.241 | 0.003 | 1.187 | 0.043 | 0.093 | 0.091 | 0.214 | 0.220 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 116 | 151 | 0 | 229 | 0 | 146 | 107 | 515 |
N.S. |
1 | 1.00 | 0.89 | 1.16 | 0.00 | 1.76 | 0.00 | 1.12 | 0.82 | 3.96 |
time (sec) |
N/A | 0.601 | 0.124 | 1.504 | 0.000 | 0.137 | 0.000 | 0.228 | 0.229 | 13.925 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 210 | 177 | 276 | 0 | 745 | 0 | 368 | 619 | 1637 |
N.S. |
1 | 1.00 | 0.84 | 1.31 | 0.00 | 3.55 | 0.00 | 1.75 | 2.95 | 7.80 |
time (sec) |
N/A | 0.824 | 0.293 | 1.832 | 0.000 | 1.083 | 0.000 | 0.222 | 0.217 | 13.761 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 303 | 303 | 268 | 452 | 0 | 1961 | 0 | 750 | 1810 | 2608 |
N.S. |
1 | 1.00 | 0.88 | 1.49 | 0.00 | 6.47 | 0.00 | 2.48 | 5.97 | 8.61 |
time (sec) |
N/A | 1.182 | 0.358 | 1.602 | 0.000 | 8.020 | 0.000 | 0.227 | 0.222 | 21.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 176 | 241 | 306 | 0 | 1701 | 1071 | 304 | 1706 | 358 |
N.S. |
1 | 1.02 | 1.40 | 1.78 | 0.00 | 9.89 | 6.23 | 1.77 | 9.92 | 2.08 |
time (sec) |
N/A | 0.673 | 0.274 | 1.432 | 0.000 | 0.108 | 10.343 | 0.193 | 0.222 | 0.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 161 | 187 | 0 | 1050 | 733 | 182 | 1048 | 226 |
N.S. |
1 | 1.00 | 1.28 | 1.48 | 0.00 | 8.33 | 5.82 | 1.44 | 8.32 | 1.79 |
time (sec) |
N/A | 0.568 | 0.181 | 1.455 | 0.000 | 0.092 | 4.702 | 0.229 | 0.216 | 11.577 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 91 | 98 | 110 | 0 | 573 | 340 | 116 | 517 | 248 |
N.S. |
1 | 1.05 | 1.13 | 1.26 | 0.00 | 6.59 | 3.91 | 1.33 | 5.94 | 2.85 |
time (sec) |
N/A | 0.431 | 0.126 | 1.175 | 0.000 | 0.087 | 1.881 | 0.225 | 0.224 | 0.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 58 | 58 | 0 | 269 | 158 | 55 | 211 | 73 |
N.S. |
1 | 1.00 | 1.05 | 1.05 | 0.00 | 4.89 | 2.87 | 1.00 | 3.84 | 1.33 |
time (sec) |
N/A | 0.311 | 0.038 | 1.368 | 0.000 | 0.094 | 0.546 | 0.214 | 0.319 | 11.100 |
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 | 14 | 14 | 13 | 15 | 14 | 14 | 12 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 0.93 | 1.07 | 1.00 | 1.00 | 0.86 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.240 | 0.005 | 1.172 | 0.031 | 0.067 | 0.203 | 0.214 | 0.217 | 11.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 253 | 173 | 249 | 0 | 1834 | 0 | 375 | 1651 | 1833 |
N.S. |
1 | 1.22 | 0.83 | 1.20 | 0.00 | 8.82 | 0.00 | 1.80 | 7.94 | 8.81 |
time (sec) |
N/A | 0.944 | 0.259 | 1.649 | 0.000 | 1.621 | 0.000 | 0.217 | 0.219 | 18.937 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 344 | 275 | 429 | 0 | 4494 | 0 | 767 | 5554 | 3631 |
N.S. |
1 | 1.15 | 0.92 | 1.43 | 0.00 | 15.03 | 0.00 | 2.57 | 18.58 | 12.14 |
time (sec) |
N/A | 1.146 | 0.624 | 1.686 | 0.000 | 23.840 | 0.000 | 0.252 | 0.239 | 19.341 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 354 | 296 | 480 | 753 | 0 | 3618 | 0 | 672 | 4047 | 1148 |
N.S. |
1 | 0.84 | 1.36 | 2.13 | 0.00 | 10.22 | 0.00 | 1.90 | 11.43 | 3.24 |
time (sec) |
N/A | 1.144 | 0.796 | 1.445 | 0.000 | 0.205 | 0.000 | 0.246 | 0.249 | 13.776 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 212 | 334 | 518 | 0 | 2400 | 1545 | 459 | 2558 | 753 |
N.S. |
1 | 1.08 | 1.70 | 2.63 | 0.00 | 12.18 | 7.84 | 2.33 | 12.98 | 3.82 |
time (sec) |
N/A | 0.828 | 0.529 | 1.350 | 0.000 | 0.109 | 64.156 | 0.249 | 0.221 | 12.974 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 128 | 216 | 300 | 0 | 1455 | 762 | 300 | 1447 | 412 |
N.S. |
1 | 1.02 | 1.71 | 2.38 | 0.00 | 11.55 | 6.05 | 2.38 | 11.48 | 3.27 |
time (sec) |
N/A | 0.489 | 0.289 | 1.277 | 0.000 | 0.097 | 17.108 | 0.230 | 0.222 | 0.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 113 | 143 | 197 | 0 | 1004 | 530 | 183 | 925 | 284 |
N.S. |
1 | 1.01 | 1.28 | 1.76 | 0.00 | 8.96 | 4.73 | 1.63 | 8.26 | 2.54 |
time (sec) |
N/A | 0.451 | 0.190 | 1.326 | 0.000 | 0.090 | 5.263 | 0.196 | 0.234 | 12.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 93 | 93 | 146 | 0 | 681 | 377 | 116 | 539 | 213 |
N.S. |
1 | 0.99 | 0.99 | 1.55 | 0.00 | 7.24 | 4.01 | 1.23 | 5.73 | 2.27 |
time (sec) |
N/A | 0.409 | 0.128 | 1.213 | 0.000 | 0.087 | 1.486 | 0.167 | 0.224 | 0.185 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 15 | 15 | 14 | 39 | 44 | 14 | 45 | 43 |
N.S. |
1 | 1.00 | 0.94 | 0.94 | 0.88 | 2.44 | 2.75 | 0.88 | 2.81 | 2.69 |
time (sec) |
N/A | 0.246 | 0.008 | 1.288 | 0.031 | 0.070 | 0.448 | 0.221 | 0.215 | 0.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 369 | 463 | 356 | 875 | 0 | 6667 | 0 | 1183 | 6517 | 2461 |
N.S. |
1 | 1.25 | 0.96 | 2.37 | 0.00 | 18.07 | 0.00 | 3.21 | 17.66 | 6.67 |
time (sec) |
N/A | 1.662 | 1.054 | 1.733 | 0.000 | 46.653 | 0.000 | 0.249 | 0.257 | 15.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 111 | 94 | 121 | 272 | 643 | 1026 | 318 | 118 |
N.S. |
1 | 1.00 | 0.84 | 0.71 | 0.92 | 2.06 | 4.87 | 7.77 | 2.41 | 0.89 |
time (sec) |
N/A | 0.498 | 0.152 | 1.717 | 0.029 | 0.075 | 0.440 | 0.187 | 0.214 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 109 | 94 | 121 | 220 | 173 | 673 | 251 | 118 |
N.S. |
1 | 1.00 | 0.83 | 0.71 | 0.92 | 1.67 | 1.31 | 5.10 | 1.90 | 0.89 |
time (sec) |
N/A | 0.476 | 0.139 | 1.431 | 0.039 | 0.070 | 1.223 | 0.187 | 0.223 | 11.611 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 132 | 132 | 110 | 97 | 121 | 167 | 173 | 380 | 184 | 118 |
N.S. |
1 | 1.00 | 0.83 | 0.73 | 0.92 | 1.27 | 1.31 | 2.88 | 1.39 | 0.89 |
time (sec) |
N/A | 0.467 | 0.125 | 1.455 | 0.028 | 0.075 | 1.038 | 0.447 | 0.205 | 0.069 |
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 | 130 | 130 | 109 | 97 | 121 | 116 | 172 | 159 | 121 | 118 |
N.S. |
1 | 1.00 | 0.84 | 0.75 | 0.93 | 0.89 | 1.32 | 1.22 | 0.93 | 0.91 |
time (sec) |
N/A | 0.459 | 0.119 | 1.353 | 0.033 | 0.072 | 0.965 | 0.200 | 0.217 | 0.068 |
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 | 126 | 126 | 106 | 97 | 129 | 126 | 150 | 166 | 123 | 133 |
N.S. |
1 | 1.00 | 0.84 | 0.77 | 1.02 | 1.00 | 1.19 | 1.32 | 0.98 | 1.06 |
time (sec) |
N/A | 0.467 | 0.125 | 0.849 | 0.035 | 0.075 | 3.010 | 0.176 | 0.211 | 12.086 |
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 | 128 | 128 | 108 | 99 | 126 | 137 | 536 | 153 | 130 | 139 |
N.S. |
1 | 1.00 | 0.84 | 0.77 | 0.98 | 1.07 | 4.19 | 1.20 | 1.02 | 1.09 |
time (sec) |
N/A | 0.483 | 0.143 | 0.793 | 0.041 | 0.076 | 0.365 | 0.215 | 0.210 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 252 | 291 | 240 | 308 | 590 | 423 | 2306 | 749 | 267 |
N.S. |
1 | 1.00 | 1.15 | 0.95 | 1.22 | 2.34 | 1.68 | 9.15 | 2.97 | 1.06 |
time (sec) |
N/A | 0.762 | 0.337 | 2.026 | 0.041 | 0.080 | 1.631 | 0.224 | 0.218 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 252 | 291 | 234 | 308 | 495 | 423 | 1556 | 617 | 267 |
N.S. |
1 | 1.00 | 1.15 | 0.93 | 1.22 | 1.96 | 1.68 | 6.17 | 2.45 | 1.06 |
time (sec) |
N/A | 0.700 | 0.335 | 1.941 | 0.044 | 0.073 | 1.666 | 0.220 | 0.220 | 11.862 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 252 | 291 | 237 | 308 | 399 | 423 | 914 | 485 | 267 |
N.S. |
1 | 1.00 | 1.15 | 0.94 | 1.22 | 1.58 | 1.68 | 3.63 | 1.92 | 1.06 |
time (sec) |
N/A | 0.650 | 0.303 | 1.944 | 0.036 | 0.075 | 1.434 | 0.173 | 0.220 | 12.008 |
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 | 250 | 250 | 290 | 240 | 308 | 306 | 422 | 400 | 357 | 267 |
N.S. |
1 | 1.00 | 1.16 | 0.96 | 1.23 | 1.22 | 1.69 | 1.60 | 1.43 | 1.07 |
time (sec) |
N/A | 0.694 | 0.282 | 2.091 | 0.036 | 0.074 | 1.419 | 0.200 | 0.318 | 11.828 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 248 | 287 | 245 | 316 | 316 | 342 | 467 | 359 | 333 |
N.S. |
1 | 1.00 | 1.16 | 0.99 | 1.27 | 1.27 | 1.38 | 1.88 | 1.45 | 1.34 |
time (sec) |
N/A | 0.650 | 0.323 | 1.410 | 0.039 | 0.075 | 15.293 | 0.203 | 0.215 | 11.565 |
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 | 246 | 246 | 289 | 247 | 314 | 327 | 298 | 444 | 366 | 329 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.28 | 1.33 | 1.21 | 1.80 | 1.49 | 1.34 |
time (sec) |
N/A | 0.680 | 0.303 | 1.509 | 0.035 | 0.079 | 15.257 | 0.790 | 0.212 | 11.387 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 427 | 427 | 600 | 494 | 645 | 1113 | 862 | 4281 | 1440 | 444 |
N.S. |
1 | 1.00 | 1.41 | 1.16 | 1.51 | 2.61 | 2.02 | 10.03 | 3.37 | 1.04 |
time (sec) |
N/A | 1.167 | 0.710 | 2.228 | 0.049 | 0.085 | 2.166 | 0.247 | 0.239 | 0.157 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 427 | 427 | 600 | 500 | 645 | 958 | 862 | 2941 | 1223 | 444 |
N.S. |
1 | 1.00 | 1.41 | 1.17 | 1.51 | 2.24 | 2.02 | 6.89 | 2.86 | 1.04 |
time (sec) |
N/A | 1.099 | 0.645 | 2.244 | 0.036 | 0.088 | 2.108 | 0.210 | 0.222 | 11.283 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 427 | 427 | 601 | 504 | 645 | 802 | 862 | 1769 | 1006 | 444 |
N.S. |
1 | 1.00 | 1.41 | 1.18 | 1.51 | 1.88 | 2.02 | 4.14 | 2.36 | 1.04 |
time (sec) |
N/A | 1.017 | 0.589 | 2.214 | 0.037 | 0.080 | 1.869 | 0.209 | 0.222 | 0.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 425 | 425 | 599 | 500 | 645 | 648 | 860 | 795 | 793 | 444 |
N.S. |
1 | 1.00 | 1.41 | 1.18 | 1.52 | 1.52 | 2.02 | 1.87 | 1.87 | 1.04 |
time (sec) |
N/A | 0.999 | 0.597 | 2.300 | 0.038 | 0.080 | 1.945 | 1.407 | 0.213 | 11.528 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 421 | 421 | 594 | 510 | 653 | 657 | 702 | 1012 | 795 | 581 |
N.S. |
1 | 1.00 | 1.41 | 1.21 | 1.55 | 1.56 | 1.67 | 2.40 | 1.89 | 1.38 |
time (sec) |
N/A | 1.006 | 0.658 | 1.602 | 0.047 | 0.080 | 68.386 | 0.206 | 0.217 | 11.506 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 421 | 421 | 598 | 517 | 651 | 669 | 585 | 981 | 802 | 677 |
N.S. |
1 | 1.00 | 1.42 | 1.23 | 1.55 | 1.59 | 1.39 | 2.33 | 1.90 | 1.61 |
time (sec) |
N/A | 1.006 | 0.678 | 1.493 | 0.038 | 0.088 | 66.121 | 0.222 | 0.236 | 11.687 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 425 | 654 | 526 | 0 | 7259 | 0 | 1071 | 2881 | 13848 |
N.S. |
1 | 1.65 | 2.53 | 2.04 | 0.00 | 28.14 | 0.00 | 4.15 | 11.17 | 53.67 |
time (sec) |
N/A | 1.997 | 4.110 | 1.950 | 0.000 | 1.301 | 0.000 | 0.261 | 0.566 | 1.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | B | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 428 | 464 | 436 | 0 | 2909 | 0 | 819 | 1391 | 6933 |
N.S. |
1 | 2.04 | 2.21 | 2.08 | 0.00 | 13.85 | 0.00 | 3.90 | 6.62 | 33.01 |
time (sec) |
N/A | 1.554 | 2.514 | 1.784 | 0.000 | 0.150 | 0.000 | 0.275 | 0.431 | 0.991 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 274 | 332 | 322 | 0 | 368 | 0 | 617 | 437 | 2611 |
N.S. |
1 | 1.47 | 1.78 | 1.73 | 0.00 | 1.98 | 0.00 | 3.32 | 2.35 | 14.04 |
time (sec) |
N/A | 0.904 | 1.378 | 1.806 | 0.000 | 0.096 | 0.000 | 0.253 | 0.300 | 11.844 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 1 | 161 | 155 | 0 | 1317 | 0 | 338 | 453 | 205 |
N.S. |
1 | 0.01 | 0.92 | 0.89 | 0.00 | 7.53 | 0.00 | 1.93 | 2.59 | 1.17 |
time (sec) |
N/A | 0.461 | 0.869 | 1.599 | 0.000 | 0.098 | 0.000 | 0.230 | 0.264 | 12.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 354 | 339 | 350 | 362 | 0 | 8557 | 0 | 1398 | 2515 | 33147 |
N.S. |
1 | 0.96 | 0.99 | 1.02 | 0.00 | 24.17 | 0.00 | 3.95 | 7.10 | 93.64 |
time (sec) |
N/A | 1.064 | 1.739 | 1.686 | 0.000 | 0.361 | 0.000 | 0.317 | 2.421 | 19.272 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 523 | 478 | 509 | 0 | 21310 | 0 | 3189 | 9427 | 50695 |
N.S. |
1 | 1.93 | 1.76 | 1.88 | 0.00 | 78.63 | 0.00 | 11.77 | 34.79 | 187.07 |
time (sec) |
N/A | 1.583 | 3.397 | 2.094 | 0.000 | 3.223 | 0.000 | 0.520 | 29.210 | 21.868 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 350 | 329 | 715 | 452 | 0 | 2928 | 0 | 930 | 8709 | 8776 |
N.S. |
1 | 0.94 | 2.04 | 1.29 | 0.00 | 8.37 | 0.00 | 2.66 | 24.88 | 25.07 |
time (sec) |
N/A | 1.068 | 9.023 | 2.009 | 0.000 | 0.199 | 0.000 | 0.340 | 79.734 | 1.455 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 259 | 543 | 309 | 0 | 828 | 0 | 505 | 4248 | 841 |
N.S. |
1 | 1.16 | 2.42 | 1.38 | 0.00 | 3.70 | 0.00 | 2.25 | 18.96 | 3.75 |
time (sec) |
N/A | 0.500 | 4.882 | 1.832 | 0.000 | 0.094 | 0.000 | 0.341 | 7.133 | 0.483 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 223 | 232 | 247 | 219 | 0 | 2750 | 0 | 478 | 7327 | 4814 |
N.S. |
1 | 1.04 | 1.11 | 0.98 | 0.00 | 12.33 | 0.00 | 2.14 | 32.86 | 21.59 |
time (sec) |
N/A | 0.354 | 2.033 | 1.701 | 0.000 | 0.117 | 0.000 | 0.305 | 6.333 | 12.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 336 | 344 | 295 | 348 | 0 | 11482 | 0 | 1574 | 13710 | 18615 |
N.S. |
1 | 1.02 | 0.88 | 1.04 | 0.00 | 34.17 | 0.00 | 4.68 | 40.80 | 55.40 |
time (sec) |
N/A | 0.667 | 2.295 | 1.803 | 0.000 | 0.315 | 0.000 | 0.400 | 17.773 | 14.693 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 441 | 480 | 429 | 500 | 0 | 26583 | 0 | 3464 | 28 | 58573 |
N.S. |
1 | 1.09 | 0.97 | 1.13 | 0.00 | 60.28 | 0.00 | 7.85 | 0.06 | 132.82 |
time (sec) |
N/A | 0.918 | 6.179 | 2.024 | 0.000 | 4.077 | 0.000 | 0.758 | 200.047 | 20.681 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 486 | 471 | 1403 | 651 | 0 | 5701 | 0 | 1739 | 28 | 22151 |
N.S. |
1 | 0.97 | 2.89 | 1.34 | 0.00 | 11.73 | 0.00 | 3.58 | 0.06 | 45.58 |
time (sec) |
N/A | 1.048 | 17.372 | 2.627 | 0.000 | 0.517 | 0.000 | 1.099 | 200.040 | 15.850 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 398 | 381 | 1197 | 532 | 0 | 2773 | 0 | 1411 | 28 | 12750 |
N.S. |
1 | 0.96 | 3.01 | 1.34 | 0.00 | 6.97 | 0.00 | 3.55 | 0.07 | 32.04 |
time (sec) |
N/A | 0.749 | 16.989 | 2.279 | 0.000 | 0.145 | 0.000 | 0.710 | 200.044 | 17.675 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 322 | 314 | 1069 | 430 | 0 | 6728 | 0 | 1169 | 28 | 16393 |
N.S. |
1 | 0.98 | 3.32 | 1.34 | 0.00 | 20.89 | 0.00 | 3.63 | 0.09 | 50.91 |
time (sec) |
N/A | 0.624 | 16.724 | 1.875 | 0.000 | 0.227 | 0.000 | 0.683 | 200.048 | 17.507 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 463 | 461 | 1080 | 571 | 0 | 21401 | 0 | 3127 | 28 | 46559 |
N.S. |
1 | 1.00 | 2.33 | 1.23 | 0.00 | 46.22 | 0.00 | 6.75 | 0.06 | 100.56 |
time (sec) |
N/A | 0.898 | 16.593 | 2.398 | 0.000 | 2.250 | 0.000 | 0.948 | 200.066 | 19.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 645 | 647 | 1033 | 871 | 0 | 41435 | 0 | 5956 | 28 | 84064 |
N.S. |
1 | 1.00 | 1.60 | 1.35 | 0.00 | 64.24 | 0.00 | 9.23 | 0.04 | 130.33 |
time (sec) |
N/A | 1.439 | 16.322 | 21.882 | 0.000 | 28.908 | 0.000 | 1.572 | 200.035 | 21.784 |