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 | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 253 | 194 | 269 | 1536 | 574 | 0 | 0 | 29 | 0 |
N.S. |
1 | 0.96 | 0.73 | 1.02 | 5.82 | 2.17 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.570 | 0.377 | 1.234 | 0.051 | 0.161 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 338 | 356 | 282 | 379 | 2313 | 839 | 0 | 0 | 2831 | 0 |
N.S. |
1 | 1.05 | 0.83 | 1.12 | 6.84 | 2.48 | 0.00 | 0.00 | 8.38 | 0.00 |
time (sec) |
N/A | 0.801 | 0.658 | 1.477 | 0.057 | 0.126 | 0.000 | 0.000 | 5.747 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 284 | 248 | 197 | 456 | 177 | 0 | 206 | 35 | 0 |
N.S. |
1 | 0.90 | 0.79 | 0.63 | 1.45 | 0.56 | 0.00 | 0.65 | 0.11 | 0.00 |
time (sec) |
N/A | 0.768 | 1.379 | 0.964 | 0.142 | 0.106 | 0.000 | 0.133 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 208 | 202 | 150 | 308 | 139 | 0 | 156 | 35 | 0 |
N.S. |
1 | 0.89 | 0.87 | 0.64 | 1.32 | 0.60 | 0.00 | 0.67 | 0.15 | 0.00 |
time (sec) |
N/A | 0.616 | 0.692 | 0.626 | 0.126 | 0.141 | 0.000 | 0.124 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 180 | 162 | 113 | 161 | 106 | 0 | 114 | 35 | 0 |
N.S. |
1 | 1.05 | 0.95 | 0.66 | 0.94 | 0.62 | 0.00 | 0.67 | 0.20 | 0.00 |
time (sec) |
N/A | 0.569 | 0.376 | 0.478 | 0.114 | 0.133 | 0.000 | 0.129 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 121 | 131 | 87 | 97 | 79 | 0 | 76 | 33 | 0 |
N.S. |
1 | 1.10 | 1.19 | 0.79 | 0.88 | 0.72 | 0.00 | 0.69 | 0.30 | 0.00 |
time (sec) |
N/A | 0.442 | 0.171 | 0.386 | 0.110 | 0.109 | 0.000 | 0.123 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 65 | 28 | 69 | 35 | 60 | 0 | 52 | 32 | 0 |
N.S. |
1 | 1.25 | 0.54 | 1.33 | 0.67 | 1.15 | 0.00 | 1.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.358 | 0.023 | 0.306 | 0.103 | 0.149 | 0.000 | 0.122 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 111 | 142 | 260 | 0 | 144 | 0 | 113 | 35 | 0 |
N.S. |
1 | 1.25 | 1.60 | 2.92 | 0.00 | 1.62 | 0.00 | 1.27 | 0.39 | 0.00 |
time (sec) |
N/A | 0.456 | 0.102 | 0.310 | 0.000 | 0.147 | 0.000 | 0.182 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 119 | 93 | 0 | 224 | 0 | 145 | 39 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.72 | 0.00 | 1.72 | 0.00 | 1.12 | 0.30 | 0.00 |
time (sec) |
N/A | 0.433 | 0.098 | 0.464 | 0.000 | 0.140 | 0.000 | 0.175 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 198 | 154 | 187 | 0 | 452 | 0 | 471 | 29 | 0 |
N.S. |
1 | 0.99 | 0.77 | 0.93 | 0.00 | 2.25 | 0.00 | 2.34 | 0.14 | 0.00 |
time (sec) |
N/A | 0.518 | 0.190 | 0.478 | 0.000 | 0.150 | 0.000 | 0.178 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 294 | 233 | 281 | 0 | 690 | 0 | 884 | 29 | 0 |
N.S. |
1 | 1.04 | 0.82 | 0.99 | 0.00 | 2.44 | 0.00 | 3.12 | 0.10 | 0.00 |
time (sec) |
N/A | 0.654 | 0.486 | 0.938 | 0.000 | 0.153 | 0.000 | 0.170 | 200.017 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 95 | 125 | 105 | 105 | 114 | 215 | 153 | 165 |
N.S. |
1 | 1.00 | 0.96 | 1.26 | 1.06 | 1.06 | 1.15 | 2.17 | 1.55 | 1.67 |
time (sec) |
N/A | 0.476 | 0.089 | 0.219 | 0.044 | 0.121 | 0.221 | 0.141 | 0.171 | 0.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 77 | 85 | 73 | 77 | 76 | 158 | 153 | 129 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 0.95 | 1.00 | 0.99 | 2.05 | 1.99 | 1.68 |
time (sec) |
N/A | 0.425 | 0.076 | 0.200 | 0.036 | 0.111 | 0.187 | 0.122 | 0.183 | 23.417 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 55 | 59 | 53 | 53 | 49 | 109 | 153 | 90 |
N.S. |
1 | 1.00 | 0.93 | 1.00 | 0.90 | 0.90 | 0.83 | 1.85 | 2.59 | 1.53 |
time (sec) |
N/A | 0.388 | 0.044 | 0.151 | 0.031 | 0.110 | 0.144 | 0.114 | 0.193 | 23.231 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 40 | 39 | 36 | 35 | 29 | 72 | 149 | 51 |
N.S. |
1 | 1.00 | 1.00 | 0.98 | 0.90 | 0.88 | 0.72 | 1.80 | 3.72 | 1.28 |
time (sec) |
N/A | 0.348 | 0.030 | 0.144 | 0.027 | 0.069 | 0.109 | 0.136 | 0.160 | 23.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 32 | 22 | 19 | 22 | 15 | 37 | 143 | 21 |
N.S. |
1 | 1.00 | 1.39 | 0.96 | 0.83 | 0.96 | 0.65 | 1.61 | 6.22 | 0.91 |
time (sec) |
N/A | 0.301 | 0.013 | 0.089 | 0.032 | 0.069 | 0.078 | 0.136 | 0.169 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 34 | 42 | 47 | 27 | 99 | 68 | 157 | 34 |
N.S. |
1 | 1.00 | 0.83 | 1.02 | 1.15 | 0.66 | 2.41 | 1.66 | 3.83 | 0.83 |
time (sec) |
N/A | 0.361 | 0.030 | 0.165 | 0.028 | 0.077 | 0.422 | 0.138 | 0.174 | 23.359 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 42 | 69 | 110 | 40 | 158 | 95 | 176 | 100 |
N.S. |
1 | 1.00 | 0.68 | 1.11 | 1.77 | 0.65 | 2.55 | 1.53 | 2.84 | 1.61 |
time (sec) |
N/A | 0.381 | 0.035 | 0.191 | 0.037 | 0.076 | 0.296 | 0.131 | 0.162 | 23.357 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 81 | 66 | 109 | 160 | 69 | 226 | 142 | 191 | 156 |
N.S. |
1 | 0.98 | 0.80 | 1.31 | 1.93 | 0.83 | 2.72 | 1.71 | 2.30 | 1.88 |
time (sec) |
N/A | 0.417 | 0.049 | 0.216 | 0.037 | 0.115 | 0.427 | 0.137 | 0.171 | 23.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 102 | 91 | 150 | 218 | 94 | 286 | 183 | 197 | 199 |
N.S. |
1 | 0.98 | 0.88 | 1.44 | 2.10 | 0.90 | 2.75 | 1.76 | 1.89 | 1.91 |
time (sec) |
N/A | 0.445 | 0.062 | 0.243 | 0.038 | 0.087 | 0.573 | 0.140 | 0.173 | 23.434 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 360 | 342 | 299 | 445 | 1368 | 264 | 0 | 334 | 361 | 0 |
N.S. |
1 | 0.95 | 0.83 | 1.24 | 3.80 | 0.73 | 0.00 | 0.93 | 1.00 | 0.00 |
time (sec) |
N/A | 0.843 | 0.882 | 1.209 | 0.148 | 0.095 | 0.000 | 0.177 | 7.634 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 282 | 264 | 244 | 351 | 979 | 216 | 0 | 285 | 361 | 0 |
N.S. |
1 | 0.94 | 0.87 | 1.24 | 3.47 | 0.77 | 0.00 | 1.01 | 1.28 | 0.00 |
time (sec) |
N/A | 0.715 | 0.566 | 0.849 | 0.138 | 0.144 | 0.000 | 0.139 | 4.904 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 232 | 198 | 268 | 624 | 174 | 0 | 241 | 361 | 0 |
N.S. |
1 | 1.01 | 0.86 | 1.17 | 2.72 | 0.76 | 0.00 | 1.05 | 1.58 | 0.00 |
time (sec) |
N/A | 0.604 | 0.441 | 0.902 | 0.119 | 0.095 | 0.000 | 0.146 | 0.936 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 172 | 157 | 195 | 293 | 136 | 0 | 210 | 357 | 0 |
N.S. |
1 | 1.06 | 0.96 | 1.20 | 1.80 | 0.83 | 0.00 | 1.29 | 2.19 | 0.00 |
time (sec) |
N/A | 0.509 | 0.395 | 0.810 | 0.110 | 0.099 | 0.000 | 0.156 | 0.501 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 109 | 45 | 129 | 103 | 99 | 0 | 180 | 353 | 0 |
N.S. |
1 | 1.16 | 0.48 | 1.37 | 1.10 | 1.05 | 0.00 | 1.91 | 3.76 | 0.00 |
time (sec) |
N/A | 0.408 | 0.048 | 0.802 | 0.107 | 0.087 | 0.000 | 0.133 | 0.481 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 163 | 189 | 1067 | 0 | 356 | 0 | 252 | 29 | 0 |
N.S. |
1 | 1.22 | 1.41 | 7.96 | 0.00 | 2.66 | 0.00 | 1.88 | 0.22 | 0.00 |
time (sec) |
N/A | 0.577 | 0.762 | 0.793 | 0.000 | 0.148 | 0.000 | 0.253 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 187 | 145 | 187 | 0 | 389 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.05 | 0.81 | 1.05 | 0.00 | 2.19 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.498 | 0.198 | 1.487 | 0.000 | 0.144 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 255 | 194 | 282 | 0 | 574 | 0 | 0 | 29 | 0 |
N.S. |
1 | 0.97 | 0.73 | 1.07 | 0.00 | 2.17 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.587 | 0.282 | 1.451 | 0.000 | 0.164 | 0.000 | 0.000 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 339 | 363 | 275 | 392 | 0 | 839 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.07 | 0.81 | 1.16 | 0.00 | 2.47 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.801 | 0.486 | 2.716 | 0.000 | 0.161 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 391 | 414 | 121 | 0 | 0 | 554 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.06 | 0.31 | 0.00 | 0.00 | 1.42 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.888 | 0.107 | 0.000 | 0.000 | 0.155 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 314 | 355 | 81 | 0 | 0 | 415 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.13 | 0.26 | 0.00 | 0.00 | 1.32 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.766 | 0.056 | 0.000 | 0.000 | 0.142 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 299 | 45 | 0 | 0 | 255 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.22 | 0.18 | 0.00 | 0.00 | 1.04 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.659 | 0.020 | 0.000 | 0.000 | 0.143 | 0.000 | 0.000 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 319 | 437 | 124 | 0 | 0 | 414 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.37 | 0.39 | 0.00 | 0.00 | 1.30 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.894 | 0.116 | 0.000 | 0.000 | 0.143 | 0.000 | 0.000 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 261 | 110 | 0 | 0 | 598 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.27 | 0.54 | 0.00 | 0.00 | 2.92 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.518 | 0.035 | 0.000 | 0.000 | 0.157 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 391 | 414 | 121 | 0 | 0 | 561 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.06 | 0.31 | 0.00 | 0.00 | 1.43 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.889 | 0.117 | 0.000 | 0.000 | 0.141 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 314 | 355 | 79 | 0 | 0 | 431 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.13 | 0.25 | 0.00 | 0.00 | 1.37 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.773 | 0.051 | 0.000 | 0.000 | 0.131 | 0.000 | 0.000 | 200.025 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 299 | 45 | 0 | 0 | 268 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.22 | 0.18 | 0.00 | 0.00 | 1.09 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.680 | 0.019 | 0.000 | 0.000 | 0.132 | 0.000 | 0.000 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 344 | 427 | 122 | 0 | 0 | 690 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.24 | 0.35 | 0.00 | 0.00 | 2.01 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.963 | 0.094 | 0.000 | 0.000 | 0.098 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 224 | 106 | 0 | 0 | 694 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.06 | 0.50 | 0.00 | 0.00 | 3.29 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.563 | 0.031 | 0.000 | 0.000 | 0.093 | 0.000 | 0.000 | 200.033 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 391 | 414 | 99 | 0 | 0 | 561 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.06 | 0.25 | 0.00 | 0.00 | 1.43 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.947 | 0.114 | 0.000 | 0.000 | 0.096 | 0.000 | 0.000 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 314 | 355 | 84 | 0 | 0 | 421 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.13 | 0.27 | 0.00 | 0.00 | 1.34 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.803 | 0.050 | 0.000 | 0.000 | 0.093 | 0.000 | 0.000 | 200.024 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 299 | 45 | 0 | 0 | 266 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.22 | 0.18 | 0.00 | 0.00 | 1.09 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.677 | 0.021 | 0.000 | 0.000 | 0.113 | 0.000 | 0.000 | 200.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 319 | 437 | 126 | 0 | 0 | 470 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.37 | 0.39 | 0.00 | 0.00 | 1.47 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.886 | 0.040 | 0.000 | 0.000 | 0.098 | 0.000 | 0.000 | 200.027 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 210 | 261 | 107 | 0 | 0 | 707 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.24 | 0.51 | 0.00 | 0.00 | 3.37 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.524 | 0.037 | 0.000 | 0.000 | 0.088 | 0.000 | 0.000 | 200.028 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 391 | 414 | 98 | 0 | 0 | 555 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.06 | 0.25 | 0.00 | 0.00 | 1.42 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.982 | 0.114 | 0.000 | 0.000 | 0.131 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 314 | 355 | 84 | 0 | 0 | 433 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.13 | 0.27 | 0.00 | 0.00 | 1.38 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.797 | 0.048 | 0.000 | 0.000 | 0.144 | 0.000 | 0.000 | 200.026 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 299 | 43 | 0 | 0 | 255 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.22 | 0.18 | 0.00 | 0.00 | 1.04 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.671 | 0.022 | 0.000 | 0.000 | 0.129 | 0.000 | 0.000 | 200.040 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 344 | 427 | 128 | 0 | 0 | 629 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.24 | 0.37 | 0.00 | 0.00 | 1.83 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.961 | 0.041 | 0.000 | 0.000 | 0.165 | 0.000 | 0.000 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 226 | 107 | 0 | 0 | 613 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.07 | 0.51 | 0.00 | 0.00 | 2.91 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.569 | 0.034 | 0.000 | 0.000 | 0.141 | 0.000 | 0.000 | 200.020 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 140 | 0 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.04 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.470 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 320 | 266 | 272 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.83 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.683 | 0.393 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 226 | 160 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.03 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.592 | 0.199 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 128 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.00 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.454 | 0.163 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 60 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.00 | 0.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.338 | 0.047 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 203 | 170 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.06 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.495 | 0.049 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 125 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.434 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 205 | 173 | 0 | 0 | 0 | 0 | 0 | 362 | 0 |
N.S. |
1 | 0.99 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.75 | 0.00 |
time (sec) |
N/A | 0.593 | 0.095 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 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 | 102 | 102 | 102 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.536 | 0.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 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 | 63 | 63 | 63 | 0 | 0 | 0 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.363 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 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 | 61 | 61 | 61 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.344 | 0.018 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 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 | 60 | 60 | 45 | 0 | 0 | 0 | 0 | 0 | 8 | 0 |
N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.302 | 0.032 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 35 | 13 | 12 | 12 | 12 | 12 | 13 | 12 |
N.S. |
1 | 1.00 | 2.69 | 1.00 | 0.92 | 0.92 | 0.92 | 0.92 | 1.00 | 0.92 |
time (sec) |
N/A | 0.319 | 0.011 | 0.360 | 0.118 | 0.078 | 0.440 | 0.114 | 0.168 | 23.324 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 60 | 39 | 0 | 39 | 95 | 109 | 39 | 44 |
N.S. |
1 | 1.00 | 1.20 | 0.78 | 0.00 | 0.78 | 1.90 | 2.18 | 0.78 | 0.88 |
time (sec) |
N/A | 0.476 | 0.026 | 2.372 | 0.000 | 0.077 | 1.130 | 0.139 | 0.162 | 23.352 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 85 | 89 | 55 | 0 | 66 | 223 | 203 | 63 | 74 |
N.S. |
1 | 1.02 | 1.07 | 0.66 | 0.00 | 0.80 | 2.69 | 2.45 | 0.76 | 0.89 |
time (sec) |
N/A | 0.650 | 0.174 | 11.075 | 0.000 | 0.120 | 3.095 | 0.142 | 0.166 | 23.454 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 120 | 123 | 71 | 0 | 93 | 398 | 297 | 87 | 104 |
N.S. |
1 | 1.03 | 1.06 | 0.61 | 0.00 | 0.80 | 3.43 | 2.56 | 0.75 | 0.90 |
time (sec) |
N/A | 0.866 | 0.315 | 36.436 | 0.000 | 0.098 | 8.308 | 0.143 | 0.154 | 23.338 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 155 | 153 | 87 | 0 | 120 | 620 | 391 | 111 | 134 |
N.S. |
1 | 1.04 | 1.03 | 0.58 | 0.00 | 0.81 | 4.16 | 2.62 | 0.74 | 0.90 |
time (sec) |
N/A | 1.096 | 0.361 | 100.004 | 0.000 | 0.086 | 23.449 | 0.213 | 0.166 | 23.496 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 98 | 0 | 0 | 0 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.529 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 97 | 0 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.526 | 0.028 | 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 | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 93 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.551 | 0.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 35 | 37 | 0 | 42 | 0 | 64 | 42 | 33 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 0.00 | 1.20 | 0.00 | 1.83 | 1.20 | 0.94 |
time (sec) |
N/A | 0.351 | 0.020 | 0.064 | 0.000 | 0.134 | 0.000 | 0.188 | 0.165 | 0.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 60 | 54 | 0 | 70 | 0 | 107 | 67 | 78 |
N.S. |
1 | 1.00 | 0.83 | 0.75 | 0.00 | 0.97 | 0.00 | 1.49 | 0.93 | 1.08 |
time (sec) |
N/A | 0.543 | 0.045 | 0.063 | 0.000 | 0.119 | 0.000 | 0.169 | 0.162 | 0.255 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 116 | 79 | 70 | 0 | 97 | 0 | 250 | 91 | 120 |
N.S. |
1 | 1.07 | 0.73 | 0.65 | 0.00 | 0.90 | 0.00 | 2.31 | 0.84 | 1.11 |
time (sec) |
N/A | 0.753 | 0.047 | 0.069 | 0.000 | 0.146 | 0.000 | 0.191 | 0.191 | 23.555 |
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 | 90 | 90 | 90 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.540 | 0.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 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 | 53 | 53 | 53 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.369 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 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 | 51 | 51 | 51 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.343 | 0.018 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 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 | 46 | 46 | 37 | 0 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.00 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.306 | 0.037 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 34 | 16 | 15 | 15 | 15 | 15 | 16 | 15 |
N.S. |
1 | 1.00 | 1.89 | 0.89 | 0.83 | 0.83 | 0.83 | 0.83 | 0.89 | 0.83 |
time (sec) |
N/A | 0.329 | 0.012 | 0.367 | 0.120 | 0.112 | 0.449 | 0.117 | 0.153 | 23.269 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 55 | 40 | 0 | 40 | 99 | 119 | 40 | 46 |
N.S. |
1 | 1.00 | 1.04 | 0.75 | 0.00 | 0.75 | 1.87 | 2.25 | 0.75 | 0.87 |
time (sec) |
N/A | 0.514 | 0.027 | 2.622 | 0.000 | 0.131 | 1.185 | 0.127 | 0.172 | 23.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 90 | 86 | 57 | 0 | 68 | 231 | 221 | 65 | 79 |
N.S. |
1 | 1.02 | 0.98 | 0.65 | 0.00 | 0.77 | 2.62 | 2.51 | 0.74 | 0.90 |
time (sec) |
N/A | 0.665 | 0.157 | 11.234 | 0.000 | 0.131 | 3.240 | 0.154 | 0.158 | 23.414 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 127 | 122 | 73 | 0 | 95 | 410 | 323 | 89 | 111 |
N.S. |
1 | 1.03 | 0.99 | 0.59 | 0.00 | 0.77 | 3.33 | 2.63 | 0.72 | 0.90 |
time (sec) |
N/A | 0.897 | 0.320 | 36.803 | 0.000 | 0.154 | 8.580 | 0.161 | 0.152 | 23.626 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 88 | 0 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.531 | 0.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 87 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.527 | 0.025 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 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 | 87 | 87 | 87 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.522 | 0.026 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 39 | 0 | 44 | 0 | 70 | 44 | 35 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 0.00 | 1.19 | 0.00 | 1.89 | 1.19 | 0.95 |
time (sec) |
N/A | 0.360 | 0.021 | 0.059 | 0.000 | 0.087 | 0.000 | 0.194 | 0.163 | 23.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 62 | 56 | 0 | 72 | 0 | 170 | 69 | 80 |
N.S. |
1 | 1.00 | 0.82 | 0.74 | 0.00 | 0.95 | 0.00 | 2.24 | 0.91 | 1.05 |
time (sec) |
N/A | 0.542 | 0.045 | 0.062 | 0.000 | 0.082 | 0.000 | 0.141 | 0.158 | 0.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 122 | 81 | 72 | 0 | 99 | 0 | 272 | 93 | 122 |
N.S. |
1 | 1.07 | 0.71 | 0.63 | 0.00 | 0.87 | 0.00 | 2.39 | 0.82 | 1.07 |
time (sec) |
N/A | 0.763 | 0.047 | 0.063 | 0.000 | 0.092 | 0.000 | 0.165 | 0.194 | 22.954 |
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 | 101 | 101 | 102 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.530 | 0.035 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 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 | 63 | 63 | 63 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.356 | 0.022 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 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 | 61 | 61 | 61 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.340 | 0.018 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 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 | 60 | 60 | 45 | 0 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.304 | 0.034 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 36 | 16 | 23 | 15 | 15 | 15 | 16 | 15 |
N.S. |
1 | 1.00 | 2.25 | 1.00 | 1.44 | 0.94 | 0.94 | 0.94 | 1.00 | 0.94 |
time (sec) |
N/A | 0.328 | 0.013 | 0.549 | 0.043 | 0.111 | 3.165 | 0.113 | 0.151 | 22.878 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 60 | 41 | 0 | 41 | 116 | 98 | 41 | 47 |
N.S. |
1 | 1.00 | 1.11 | 0.76 | 0.00 | 0.76 | 2.15 | 1.81 | 0.76 | 0.87 |
time (sec) |
N/A | 0.506 | 0.028 | 3.535 | 0.000 | 0.114 | 19.748 | 0.140 | 0.160 | 23.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 91 | 91 | 57 | 0 | 68 | 291 | 182 | 237 | 80 |
N.S. |
1 | 1.02 | 1.02 | 0.64 | 0.00 | 0.76 | 3.27 | 2.04 | 2.66 | 0.90 |
time (sec) |
N/A | 0.692 | 0.191 | 14.631 | 0.000 | 0.116 | 90.233 | 0.135 | 0.155 | 23.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 128 | 127 | 73 | 0 | 95 | 0 | 266 | 369 | 112 |
N.S. |
1 | 1.03 | 1.02 | 0.59 | 0.00 | 0.77 | 0.00 | 2.15 | 2.98 | 0.90 |
time (sec) |
N/A | 0.885 | 0.433 | 46.457 | 0.000 | 0.108 | 0.000 | 0.151 | 0.163 | 23.260 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 98 | 0 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.531 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 97 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.517 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 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 | 93 | 93 | 93 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.522 | 0.026 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 37 | 39 | 0 | 44 | 0 | 94 | 44 | 35 |
N.S. |
1 | 1.00 | 0.97 | 1.03 | 0.00 | 1.16 | 0.00 | 2.47 | 1.16 | 0.92 |
time (sec) |
N/A | 0.362 | 0.026 | 0.059 | 0.000 | 0.141 | 0.000 | 0.184 | 0.162 | 23.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 62 | 56 | 0 | 72 | 0 | 105 | 77 | 81 |
N.S. |
1 | 1.00 | 0.81 | 0.73 | 0.00 | 0.94 | 0.00 | 1.36 | 1.00 | 1.05 |
time (sec) |
N/A | 0.558 | 0.053 | 0.062 | 0.000 | 0.130 | 0.000 | 0.170 | 0.174 | 23.295 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 123 | 81 | 72 | 0 | 99 | 0 | 224 | 101 | 123 |
N.S. |
1 | 1.07 | 0.70 | 0.63 | 0.00 | 0.86 | 0.00 | 1.95 | 0.88 | 1.07 |
time (sec) |
N/A | 0.847 | 0.058 | 0.065 | 0.000 | 0.103 | 0.000 | 0.178 | 0.168 | 22.969 |