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 | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 153 | 151 | 150 | 0 | 864 | 0 | 318 | 1275 | 0 |
N.S. |
1 | 1.07 | 1.06 | 1.05 | 0.00 | 6.04 | 0.00 | 2.22 | 8.92 | 0.00 |
time (sec) |
N/A | 0.277 | 0.559 | 0.706 | 0.000 | 0.327 | 0.000 | 0.434 | 0.320 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 250 | 1392 | 222 | 0 | 1482 | 0 | 643 | 3380 | 0 |
N.S. |
1 | 1.17 | 6.50 | 1.04 | 0.00 | 6.93 | 0.00 | 3.00 | 15.79 | 0.00 |
time (sec) |
N/A | 0.364 | 13.038 | 0.787 | 0.000 | 0.761 | 0.000 | 0.683 | 5.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 274 | 202 | 201 | 392 | 684 | 0 | 237 | 769 | 0 |
N.S. |
1 | 1.51 | 1.11 | 1.10 | 2.15 | 3.76 | 0.00 | 1.30 | 4.23 | 0.00 |
time (sec) |
N/A | 0.427 | 0.357 | 0.659 | 0.038 | 0.215 | 0.000 | 0.139 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 187 | 143 | 145 | 254 | 486 | 0 | 158 | 519 | 0 |
N.S. |
1 | 1.38 | 1.05 | 1.07 | 1.87 | 3.57 | 0.00 | 1.16 | 3.82 | 0.00 |
time (sec) |
N/A | 0.334 | 0.243 | 0.583 | 0.035 | 0.137 | 0.000 | 0.137 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 115 | 91 | 96 | 147 | 318 | 0 | 103 | 300 | 0 |
N.S. |
1 | 1.16 | 0.92 | 0.97 | 1.48 | 3.21 | 0.00 | 1.04 | 3.03 | 0.00 |
time (sec) |
N/A | 0.227 | 0.168 | 0.454 | 0.037 | 0.110 | 0.000 | 0.138 | 0.251 | 0.000 |
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 | 61 | 47 | 37 | 34 | 68 | 54 | 144 | 40 | 141 | 33 |
N.S. |
1 | 0.77 | 0.61 | 0.56 | 1.11 | 0.89 | 2.36 | 0.66 | 2.31 | 0.54 |
time (sec) |
N/A | 0.161 | 0.075 | 0.340 | 0.031 | 0.102 | 3.778 | 0.128 | 0.204 | 0.358 |
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 | 39 | 39 | 29 | 26 | 31 | 47 | 95 | 27 | 84 | 28 |
N.S. |
1 | 1.00 | 0.74 | 0.67 | 0.79 | 1.21 | 2.44 | 0.69 | 2.15 | 0.72 |
time (sec) |
N/A | 0.150 | 0.002 | 0.322 | 0.025 | 0.110 | 0.442 | 0.124 | 0.191 | 0.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 139 | 130 | 124 | 0 | 764 | 0 | 320 | 768 | 0 |
N.S. |
1 | 1.14 | 1.07 | 1.02 | 0.00 | 6.26 | 0.00 | 2.62 | 6.30 | 0.00 |
time (sec) |
N/A | 0.260 | 0.336 | 0.696 | 0.000 | 0.321 | 0.000 | 0.138 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 228 | 219 | 210 | 0 | 1440 | 0 | 620 | 2710 | 0 |
N.S. |
1 | 1.13 | 1.08 | 1.04 | 0.00 | 7.13 | 0.00 | 3.07 | 13.42 | 0.00 |
time (sec) |
N/A | 0.361 | 1.067 | 0.831 | 0.000 | 0.722 | 0.000 | 0.415 | 2.425 | 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 | 292 | 353 | 367 | 302 | 0 | 2250 | 0 | 1010 | 21 | 0 |
N.S. |
1 | 1.21 | 1.26 | 1.03 | 0.00 | 7.71 | 0.00 | 3.46 | 0.07 | 0.00 |
time (sec) |
N/A | 0.504 | 2.891 | 0.841 | 0.000 | 2.645 | 0.000 | 0.431 | 200.031 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 187 | 163 | 150 | 465 | 229 | 0 | 218 | 738 | 326 |
N.S. |
1 | 0.76 | 0.67 | 0.61 | 1.90 | 0.93 | 0.00 | 0.89 | 3.01 | 1.33 |
time (sec) |
N/A | 0.258 | 0.306 | 0.456 | 0.042 | 0.245 | 0.000 | 0.125 | 0.234 | 0.745 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 150 | 107 | 96 | 249 | 151 | 0 | 138 | 449 | 176 |
N.S. |
1 | 0.93 | 0.66 | 0.59 | 1.54 | 0.93 | 0.00 | 0.85 | 2.77 | 1.09 |
time (sec) |
N/A | 0.237 | 0.173 | 0.425 | 0.042 | 0.138 | 0.000 | 0.134 | 0.212 | 0.540 |
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 | 91 | 88 | 60 | 52 | 103 | 87 | 566 | 72 | 223 | 87 |
N.S. |
1 | 0.97 | 0.66 | 0.57 | 1.13 | 0.96 | 6.22 | 0.79 | 2.45 | 0.96 |
time (sec) |
N/A | 0.188 | 0.102 | 0.351 | 0.026 | 0.099 | 9.987 | 0.128 | 0.198 | 0.409 |
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 | 39 | 39 | 29 | 26 | 31 | 47 | 95 | 27 | 84 | 28 |
N.S. |
1 | 1.00 | 0.74 | 0.67 | 0.79 | 1.21 | 2.44 | 0.69 | 2.15 | 0.72 |
time (sec) |
N/A | 0.152 | 0.047 | 0.324 | 0.024 | 0.103 | 0.444 | 0.133 | 0.211 | 0.305 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 99 | 71 | 0 | 442 | 0 | 107 | 507 | 0 |
N.S. |
1 | 1.00 | 1.25 | 0.90 | 0.00 | 5.59 | 0.00 | 1.35 | 6.42 | 0.00 |
time (sec) |
N/A | 0.206 | 0.216 | 0.687 | 0.000 | 0.210 | 0.000 | 0.137 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 122 | 88 | 0 | 459 | 0 | 225 | 830 | 0 |
N.S. |
1 | 1.00 | 1.22 | 0.88 | 0.00 | 4.59 | 0.00 | 2.25 | 8.30 | 0.00 |
time (sec) |
N/A | 0.221 | 0.267 | 0.671 | 0.000 | 0.175 | 0.000 | 0.139 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 148 | 151 | 121 | 0 | 698 | 0 | 487 | 2314 | 0 |
N.S. |
1 | 1.07 | 1.09 | 0.88 | 0.00 | 5.06 | 0.00 | 3.53 | 16.77 | 0.00 |
time (sec) |
N/A | 0.260 | 0.667 | 0.728 | 0.000 | 0.218 | 0.000 | 0.323 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 185 | 179 | 179 | 0 | 972 | 0 | 919 | 3307 | 0 |
N.S. |
1 | 0.93 | 0.90 | 0.90 | 0.00 | 4.88 | 0.00 | 4.62 | 16.62 | 0.00 |
time (sec) |
N/A | 0.275 | 15.168 | 0.716 | 0.000 | 0.389 | 0.000 | 0.702 | 0.500 | 0.000 |
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 | 20 | 20 | 20 | 19 | 0 | 27 | 0 | 18 | 39 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.00 | 1.35 | 0.00 | 0.90 | 1.95 | 0.90 |
time (sec) |
N/A | 0.145 | 0.030 | 0.423 | 0.000 | 0.091 | 0.000 | 0.137 | 0.227 | 0.488 |
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 | 25 | 25 | 25 | 24 | 0 | 27 | 0 | 51 | 52 | 79 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.00 | 1.08 | 0.00 | 2.04 | 2.08 | 3.16 |
time (sec) |
N/A | 0.149 | 0.052 | 0.356 | 0.000 | 0.081 | 0.000 | 0.130 | 0.205 | 0.628 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 70 | 41 | 0 | 241 | 0 | 70 | 159 | 0 |
N.S. |
1 | 1.00 | 1.43 | 0.84 | 0.00 | 4.92 | 0.00 | 1.43 | 3.24 | 0.00 |
time (sec) |
N/A | 0.163 | 0.092 | 0.611 | 0.000 | 0.120 | 0.000 | 0.132 | 0.202 | 0.000 |
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 | 15 | 15 | 29 | 14 | 13 | 44 | 31 | 25 | 46 | 27 |
N.S. |
1 | 1.00 | 1.93 | 0.93 | 0.87 | 2.93 | 2.07 | 1.67 | 3.07 | 1.80 |
time (sec) |
N/A | 0.138 | 0.034 | 0.344 | 0.102 | 0.083 | 1.956 | 0.117 | 0.183 | 0.269 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 58 | 57 | 94 | 70 | 315 | 0 | 0 | 80 | 0 |
N.S. |
1 | 0.73 | 0.72 | 1.19 | 0.89 | 3.99 | 0.00 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.178 | 0.084 | 0.386 | 0.040 | 0.129 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 58 | 54 | 94 | 0 | 303 | 0 | 0 | 80 | 0 |
N.S. |
1 | 0.78 | 0.73 | 1.27 | 0.00 | 4.09 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.176 | 0.066 | 0.346 | 0.000 | 0.113 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 58 | 57 | 94 | 0 | 314 | 0 | 0 | 80 | 0 |
N.S. |
1 | 0.76 | 0.75 | 1.24 | 0.00 | 4.13 | 0.00 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 0.172 | 0.083 | 0.340 | 0.000 | 0.117 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 78 | 82 | 0 | 95 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.18 | 1.24 | 0.00 | 1.44 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.182 | 0.563 | 0.757 | 0.000 | 0.098 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 80 | 99 | 0 | 96 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 0.59 | 0.73 | 0.00 | 0.71 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.264 | 0.508 | 0.668 | 0.000 | 0.085 | 0.000 | 0.000 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 122 | 62 | 113 | 0 | 67 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.14 | 0.58 | 1.06 | 0.00 | 0.63 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.216 | 0.142 | 3.335 | 0.000 | 0.081 | 0.000 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 82 | 61 | 101 | 0 | 57 | 0 | 0 | 55 | 0 |
N.S. |
1 | 1.17 | 0.87 | 1.44 | 0.00 | 0.81 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.188 | 0.060 | 0.785 | 0.000 | 0.092 | 0.000 | 0.000 | 0.252 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 49 | 61 | 57 | 0 | 22 | 94 | 0 | 34 | 0 |
N.S. |
1 | 1.17 | 1.45 | 1.36 | 0.00 | 0.52 | 2.24 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.169 | 0.070 | 3.740 | 0.000 | 0.086 | 10.326 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 85 | 65 | 87 | 0 | 69 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.13 | 0.87 | 1.16 | 0.00 | 0.92 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.188 | 0.146 | 8.092 | 0.000 | 0.090 | 0.000 | 0.000 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 122 | 85 | 132 | 0 | 97 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.14 | 0.79 | 1.23 | 0.00 | 0.91 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.216 | 0.178 | 18.824 | 0.000 | 0.093 | 0.000 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 44 | 27 | 0 | 6 | 61 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 1.63 | 1.00 | 0.00 | 0.22 | 2.26 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.137 | 0.170 | 0.907 | 0.000 | 0.087 | 9.873 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | C | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 37 | 59 | 44 | 0 | 11 | 71 | 0 | 34 | 0 |
N.S. |
1 | 1.06 | 1.69 | 1.26 | 0.00 | 0.31 | 2.03 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.156 | 0.329 | 1.919 | 0.000 | 0.090 | 9.820 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 330 | 312 | 243 | 412 | 0 | 232 | 0 | 0 | 330 | 0 |
N.S. |
1 | 0.95 | 0.74 | 1.25 | 0.00 | 0.70 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.459 | 2.168 | 3.605 | 0.000 | 0.101 | 0.000 | 0.000 | 0.517 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 249 | 242 | 198 | 279 | 0 | 153 | 0 | 0 | 167 | 0 |
N.S. |
1 | 0.97 | 0.80 | 1.12 | 0.00 | 0.61 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.334 | 1.012 | 1.836 | 0.000 | 0.093 | 0.000 | 0.000 | 0.370 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 206 | 86 | 101 | 0 | 114 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.06 | 0.44 | 0.52 | 0.00 | 0.59 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.290 | 0.761 | 0.926 | 0.000 | 0.101 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 133 | 181 | 0 | 122 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.00 | 1.58 | 2.15 | 0.00 | 1.45 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.179 | 1.823 | 1.358 | 0.000 | 0.090 | 0.000 | 0.000 | 0.348 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 240 | 243 | 418 | 0 | 333 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.02 | 1.03 | 1.78 | 0.00 | 1.42 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.299 | 2.598 | 1.341 | 0.000 | 0.107 | 0.000 | 0.000 | 0.654 | 0.000 |
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 | 307 | 330 | 285 | 570 | 0 | 689 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.07 | 0.93 | 1.86 | 0.00 | 2.24 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.412 | 2.826 | 1.335 | 0.000 | 0.134 | 0.000 | 0.000 | 0.802 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 404 | 392 | 302 | 566 | 0 | 316 | 0 | 0 | 536 | 0 |
N.S. |
1 | 0.97 | 0.75 | 1.40 | 0.00 | 0.78 | 0.00 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.564 | 3.956 | 5.201 | 0.000 | 0.096 | 0.000 | 0.000 | 0.698 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 325 | 314 | 246 | 411 | 0 | 233 | 0 | 0 | 330 | 0 |
N.S. |
1 | 0.97 | 0.76 | 1.26 | 0.00 | 0.72 | 0.00 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.459 | 2.188 | 3.464 | 0.000 | 0.097 | 0.000 | 0.000 | 0.507 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 263 | 264 | 199 | 310 | 0 | 166 | 0 | 0 | 225 | 0 |
N.S. |
1 | 1.00 | 0.76 | 1.18 | 0.00 | 0.63 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.347 | 1.872 | 4.240 | 0.000 | 0.095 | 0.000 | 0.000 | 0.413 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 258 | 191 | 332 | 0 | 226 | 0 | 0 | 345 | 0 |
N.S. |
1 | 1.25 | 0.93 | 1.61 | 0.00 | 1.10 | 0.00 | 0.00 | 1.67 | 0.00 |
time (sec) |
N/A | 0.352 | 3.580 | 4.759 | 0.000 | 0.101 | 0.000 | 0.000 | 0.621 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 233 | 232 | 421 | 0 | 294 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 1.04 | 1.88 | 0.00 | 1.31 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.318 | 4.342 | 5.694 | 0.000 | 0.094 | 0.000 | 0.000 | 0.888 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 310 | 323 | 285 | 552 | 0 | 635 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.92 | 1.78 | 0.00 | 2.05 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.436 | 4.541 | 5.822 | 0.000 | 0.102 | 0.000 | 0.000 | 1.395 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 398 | 427 | 373 | 716 | 0 | 1097 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.94 | 1.80 | 0.00 | 2.76 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.536 | 4.976 | 5.815 | 0.000 | 0.122 | 0.000 | 0.000 | 1.803 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 539 | 507 | 378 | 738 | 0 | 427 | 0 | 0 | 775 | 0 |
N.S. |
1 | 0.94 | 0.70 | 1.37 | 0.00 | 0.79 | 0.00 | 0.00 | 1.44 | 0.00 |
time (sec) |
N/A | 0.678 | 5.361 | 7.206 | 0.000 | 0.098 | 0.000 | 0.000 | 0.936 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 425 | 404 | 310 | 564 | 0 | 322 | 0 | 0 | 535 | 0 |
N.S. |
1 | 0.95 | 0.73 | 1.33 | 0.00 | 0.76 | 0.00 | 0.00 | 1.26 | 0.00 |
time (sec) |
N/A | 0.567 | 2.835 | 5.249 | 0.000 | 0.098 | 0.000 | 0.000 | 0.667 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 345 | 339 | 245 | 435 | 0 | 241 | 0 | 0 | 393 | 0 |
N.S. |
1 | 0.98 | 0.71 | 1.26 | 0.00 | 0.70 | 0.00 | 0.00 | 1.14 | 0.00 |
time (sec) |
N/A | 0.463 | 2.694 | 6.883 | 0.000 | 0.094 | 0.000 | 0.000 | 0.555 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 279 | 330 | 251 | 510 | 0 | 347 | 0 | 0 | 884 | 0 |
N.S. |
1 | 1.18 | 0.90 | 1.83 | 0.00 | 1.24 | 0.00 | 0.00 | 3.17 | 0.00 |
time (sec) |
N/A | 0.443 | 4.313 | 17.004 | 0.000 | 0.103 | 0.000 | 0.000 | 0.895 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 290 | 342 | 259 | 505 | 0 | 482 | 0 | 0 | 1315 | 0 |
N.S. |
1 | 1.18 | 0.89 | 1.74 | 0.00 | 1.66 | 0.00 | 0.00 | 4.53 | 0.00 |
time (sec) |
N/A | 0.487 | 4.932 | 6.946 | 0.000 | 0.109 | 0.000 | 0.000 | 1.428 | 0.000 |
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 | 290 | 311 | 279 | 580 | 0 | 588 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.96 | 2.00 | 0.00 | 2.03 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.426 | 5.151 | 13.901 | 0.000 | 0.109 | 0.000 | 0.000 | 2.336 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 403 | 427 | 378 | 718 | 0 | 1046 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.94 | 1.78 | 0.00 | 2.60 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.571 | 5.422 | 13.894 | 0.000 | 0.133 | 0.000 | 0.000 | 2.899 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 510 | 549 | 480 | 899 | 0 | 1632 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.08 | 0.94 | 1.76 | 0.00 | 3.20 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.697 | 5.723 | 8.002 | 0.000 | 0.179 | 0.000 | 0.000 | 4.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 628 | 682 | 597 | 1074 | 0 | 2362 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.95 | 1.71 | 0.00 | 3.76 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.854 | 6.110 | 8.023 | 0.000 | 0.251 | 0.000 | 0.000 | 5.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 218 | 140 | 183 | 0 | 128 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.06 | 0.68 | 0.89 | 0.00 | 0.62 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.349 | 1.879 | 1.378 | 0.000 | 0.094 | 0.000 | 0.000 | 0.389 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 86 | 100 | 0 | 42 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.00 | 0.99 | 1.15 | 0.00 | 0.48 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.181 | 0.555 | 3.572 | 0.000 | 0.101 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 258 | 112 | 248 | 0 | 187 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.33 | 0.58 | 1.28 | 0.00 | 0.96 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.337 | 1.733 | 5.973 | 0.000 | 0.096 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 269 | 261 | 445 | 0 | 441 | 0 | 0 | 91 | 0 |
N.S. |
1 | 1.05 | 1.02 | 1.74 | 0.00 | 1.72 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.338 | 2.834 | 14.497 | 0.000 | 0.112 | 0.000 | 0.000 | 0.630 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 335 | 365 | 301 | 573 | 0 | 845 | 0 | 0 | 115 | 0 |
N.S. |
1 | 1.09 | 0.90 | 1.71 | 0.00 | 2.52 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.466 | 3.141 | 17.038 | 0.000 | 0.117 | 0.000 | 0.000 | 1.010 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 261 | 112 | 144 | 0 | 159 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.35 | 0.58 | 0.74 | 0.00 | 0.82 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.350 | 1.780 | 6.050 | 0.000 | 0.102 | 0.000 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 242 | 254 | 224 | 354 | 0 | 407 | 0 | 0 | 108 | 0 |
N.S. |
1 | 1.05 | 0.93 | 1.46 | 0.00 | 1.68 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.322 | 4.008 | 8.203 | 0.000 | 0.101 | 0.000 | 0.000 | 0.580 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 344 | 337 | 561 | 0 | 856 | 0 | 0 | 149 | 0 |
N.S. |
1 | 1.06 | 1.04 | 1.73 | 0.00 | 2.64 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.438 | 5.295 | 16.475 | 0.000 | 0.126 | 0.000 | 0.000 | 0.613 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 271 | 246 | 440 | 0 | 402 | 0 | 0 | 91 | 0 |
N.S. |
1 | 1.05 | 0.95 | 1.71 | 0.00 | 1.56 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.332 | 2.799 | 8.244 | 0.000 | 0.105 | 0.000 | 0.000 | 0.637 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 324 | 344 | 329 | 560 | 0 | 861 | 0 | 0 | 149 | 0 |
N.S. |
1 | 1.06 | 1.02 | 1.73 | 0.00 | 2.66 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.423 | 5.125 | 16.778 | 0.000 | 0.127 | 0.000 | 0.000 | 0.627 | 0.000 |
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 | 408 | 445 | 355 | 861 | 0 | 1456 | 0 | 0 | 207 | 0 |
N.S. |
1 | 1.09 | 0.87 | 2.11 | 0.00 | 3.57 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.533 | 5.660 | 19.540 | 0.000 | 0.173 | 0.000 | 0.000 | 1.051 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 230 | 127 | 252 | 0 | 149 | 0 | 0 | 156 | 0 |
N.S. |
1 | 0.99 | 0.55 | 1.08 | 0.00 | 0.64 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.332 | 0.864 | 1.440 | 0.000 | 0.099 | 0.000 | 0.000 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 22 | 75 | 0 | 41 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.00 | 0.58 | 1.97 | 0.00 | 1.08 | 0.00 | 0.00 | 1.39 | 0.00 |
time (sec) |
N/A | 0.163 | 0.070 | 0.573 | 0.000 | 0.088 | 0.000 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 19 | 15 | 38 | 0 | 38 | 17 | 17 | 12 | 0 |
N.S. |
1 | 0.95 | 0.75 | 1.90 | 0.00 | 1.90 | 0.85 | 0.85 | 0.60 | 0.00 |
time (sec) |
N/A | 0.160 | 0.002 | 0.304 | 0.000 | 0.086 | 1.172 | 0.128 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 87 | 104 | 0 | 130 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 0.00 | 1.49 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.207 | 0.749 | 1.023 | 0.000 | 0.098 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 90 | 168 | 0 | 131 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.87 | 0.00 | 1.46 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.208 | 0.747 | 0.961 | 0.000 | 0.090 | 0.000 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 88 | 167 | 0 | 128 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.90 | 0.00 | 1.45 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.205 | 0.573 | 1.340 | 0.000 | 0.096 | 0.000 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 91 | 108 | 0 | 133 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.19 | 0.00 | 1.46 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.202 | 0.523 | 1.342 | 0.000 | 0.087 | 0.000 | 0.000 | 0.260 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 88 | 105 | 0 | 113 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.19 | 0.00 | 1.28 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.204 | 0.779 | 0.973 | 0.000 | 0.084 | 0.000 | 0.000 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 89 | 161 | 0 | 116 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.81 | 0.00 | 1.30 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.200 | 0.759 | 0.970 | 0.000 | 0.084 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 89 | 162 | 0 | 115 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.82 | 0.00 | 1.29 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.204 | 0.536 | 1.380 | 0.000 | 0.089 | 0.000 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 90 | 107 | 0 | 114 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.19 | 0.00 | 1.27 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.199 | 0.497 | 1.328 | 0.000 | 0.090 | 0.000 | 0.000 | 0.253 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 203 | 86 | 158 | 0 | 130 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.05 | 0.44 | 0.81 | 0.00 | 0.67 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.274 | 0.749 | 0.931 | 0.000 | 0.085 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 213 | 89 | 104 | 0 | 135 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.05 | 0.44 | 0.51 | 0.00 | 0.67 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.297 | 0.763 | 0.940 | 0.000 | 0.081 | 0.000 | 0.000 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 212 | 89 | 108 | 0 | 134 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.04 | 0.44 | 0.53 | 0.00 | 0.66 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.295 | 0.587 | 1.326 | 0.000 | 0.088 | 0.000 | 0.000 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 222 | 92 | 165 | 0 | 135 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.05 | 0.43 | 0.78 | 0.00 | 0.64 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.313 | 0.555 | 1.311 | 0.000 | 0.089 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 189 | 89 | 161 | 0 | 115 | 0 | 0 | 29 | 0 |
N.S. |
1 | 0.99 | 0.47 | 0.85 | 0.00 | 0.61 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.312 | 0.737 | 0.958 | 0.000 | 0.110 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 191 | 90 | 107 | 0 | 114 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.99 | 0.47 | 0.56 | 0.00 | 0.59 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.310 | 0.718 | 0.973 | 0.000 | 0.130 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 194 | 92 | 109 | 0 | 117 | 0 | 0 | 32 | 0 |
N.S. |
1 | 0.99 | 0.47 | 0.56 | 0.00 | 0.60 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.324 | 0.505 | 1.328 | 0.000 | 0.099 | 0.000 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 198 | 198 | 93 | 166 | 0 | 120 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 0.47 | 0.84 | 0.00 | 0.61 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.320 | 0.568 | 1.340 | 0.000 | 0.095 | 0.000 | 0.000 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 87 | 104 | 0 | 130 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 0.00 | 1.49 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.199 | 0.761 | 0.957 | 0.000 | 0.095 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 90 | 168 | 0 | 131 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.87 | 0.00 | 1.46 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.199 | 0.757 | 0.937 | 0.000 | 0.096 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 88 | 167 | 0 | 128 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.90 | 0.00 | 1.45 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.197 | 0.604 | 1.316 | 0.000 | 0.098 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 91 | 108 | 0 | 133 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.19 | 0.00 | 1.46 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.199 | 0.533 | 1.542 | 0.000 | 0.097 | 0.000 | 0.000 | 0.260 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 88 | 160 | 0 | 127 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.82 | 0.00 | 1.44 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.195 | 0.790 | 1.003 | 0.000 | 0.109 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 89 | 106 | 0 | 130 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.19 | 0.00 | 1.46 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.196 | 0.765 | 0.979 | 0.000 | 0.110 | 0.000 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 89 | 106 | 0 | 129 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.19 | 0.00 | 1.45 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.193 | 0.655 | 1.319 | 0.000 | 0.097 | 0.000 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 90 | 163 | 0 | 128 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.81 | 0.00 | 1.42 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.195 | 0.539 | 1.366 | 0.000 | 0.093 | 0.000 | 0.000 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 206 | 86 | 101 | 0 | 114 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.06 | 0.44 | 0.52 | 0.00 | 0.59 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.274 | 0.023 | 0.937 | 0.000 | 0.095 | 0.000 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 217 | 89 | 161 | 0 | 119 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.07 | 0.44 | 0.79 | 0.00 | 0.59 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.287 | 0.760 | 0.977 | 0.000 | 0.124 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 216 | 89 | 162 | 0 | 118 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.06 | 0.44 | 0.80 | 0.00 | 0.58 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.304 | 0.756 | 1.341 | 0.000 | 0.097 | 0.000 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 225 | 92 | 111 | 0 | 119 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.06 | 0.43 | 0.52 | 0.00 | 0.56 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.309 | 0.709 | 1.322 | 0.000 | 0.093 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 189 | 89 | 161 | 0 | 115 | 0 | 0 | 29 | 0 |
N.S. |
1 | 0.99 | 0.47 | 0.85 | 0.00 | 0.61 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.314 | 0.751 | 0.951 | 0.000 | 0.089 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 191 | 90 | 107 | 0 | 114 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.99 | 0.47 | 0.56 | 0.00 | 0.59 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.333 | 0.720 | 0.951 | 0.000 | 0.087 | 0.000 | 0.000 | 0.225 | 0.000 |