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 | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 125 | 73 | 67 | 54 | 75 | 0 | 77 | 48 | 95 |
N.S. |
1 | 1.11 | 0.65 | 0.59 | 0.48 | 0.66 | 0.00 | 0.68 | 0.42 | 0.84 |
time (sec) |
N/A | 0.387 | 0.903 | 0.371 | 0.047 | 0.114 | 0.000 | 0.120 | 0.251 | 9.291 |
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 | 69 | 80 | 52 | 46 | 36 | 54 | 0 | 38 | 27 | 65 |
N.S. |
1 | 1.16 | 0.75 | 0.67 | 0.52 | 0.78 | 0.00 | 0.55 | 0.39 | 0.94 |
time (sec) |
N/A | 0.342 | 0.827 | 0.363 | 0.046 | 0.082 | 0.000 | 0.119 | 0.250 | 9.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 99 | 107 | 115 | 0 | 303 | 0 | 71 | 145 | 0 |
N.S. |
1 | 1.00 | 1.08 | 1.16 | 0.00 | 3.06 | 0.00 | 0.72 | 1.46 | 0.00 |
time (sec) |
N/A | 0.359 | 0.972 | 0.357 | 0.000 | 0.099 | 0.000 | 0.137 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 147 | 125 | 204 | 0 | 457 | 0 | 111 | 304 | 0 |
N.S. |
1 | 0.99 | 0.84 | 1.38 | 0.00 | 3.09 | 0.00 | 0.75 | 2.05 | 0.00 |
time (sec) |
N/A | 0.424 | 1.262 | 0.356 | 0.000 | 0.109 | 0.000 | 0.129 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 191 | 151 | 310 | 0 | 525 | 0 | 139 | 491 | 0 |
N.S. |
1 | 1.22 | 0.96 | 1.97 | 0.00 | 3.34 | 0.00 | 0.89 | 3.13 | 0.00 |
time (sec) |
N/A | 0.493 | 1.482 | 0.365 | 0.000 | 0.098 | 0.000 | 0.130 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 234 | 173 | 414 | 0 | 713 | 0 | 187 | 676 | 0 |
N.S. |
1 | 1.16 | 0.86 | 2.06 | 0.00 | 3.55 | 0.00 | 0.93 | 3.36 | 0.00 |
time (sec) |
N/A | 0.570 | 1.920 | 0.368 | 0.000 | 0.110 | 0.000 | 0.138 | 0.220 | 0.000 |
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 | 156 | 161 | 95 | 90 | 97 | 116 | 0 | 113 | 80 | 142 |
N.S. |
1 | 1.03 | 0.61 | 0.58 | 0.62 | 0.74 | 0.00 | 0.72 | 0.51 | 0.91 |
time (sec) |
N/A | 0.451 | 1.222 | 0.386 | 0.053 | 0.088 | 0.000 | 0.130 | 0.245 | 9.636 |
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 | 110 | 123 | 72 | 66 | 76 | 92 | 0 | 75 | 56 | 113 |
N.S. |
1 | 1.12 | 0.65 | 0.60 | 0.69 | 0.84 | 0.00 | 0.68 | 0.51 | 1.03 |
time (sec) |
N/A | 0.387 | 1.155 | 0.388 | 0.057 | 0.078 | 0.000 | 0.123 | 0.239 | 9.657 |
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 | 71 | 87 | 45 | 46 | 57 | 71 | 0 | 39 | 35 | 82 |
N.S. |
1 | 1.23 | 0.63 | 0.65 | 0.80 | 1.00 | 0.00 | 0.55 | 0.49 | 1.15 |
time (sec) |
N/A | 0.341 | 0.981 | 0.365 | 0.050 | 0.093 | 0.000 | 0.122 | 0.236 | 9.579 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 146 | 126 | 206 | 0 | 461 | 0 | 108 | 307 | 0 |
N.S. |
1 | 0.99 | 0.85 | 1.39 | 0.00 | 3.11 | 0.00 | 0.73 | 2.07 | 0.00 |
time (sec) |
N/A | 0.420 | 1.387 | 0.369 | 0.000 | 0.103 | 0.000 | 0.129 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 189 | 150 | 238 | 0 | 457 | 0 | 134 | 353 | 0 |
N.S. |
1 | 1.23 | 0.97 | 1.55 | 0.00 | 2.97 | 0.00 | 0.87 | 2.29 | 0.00 |
time (sec) |
N/A | 0.492 | 1.595 | 0.378 | 0.000 | 0.096 | 0.000 | 0.140 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 233 | 172 | 414 | 0 | 683 | 0 | 175 | 676 | 0 |
N.S. |
1 | 1.20 | 0.89 | 2.13 | 0.00 | 3.52 | 0.00 | 0.90 | 3.48 | 0.00 |
time (sec) |
N/A | 0.558 | 1.835 | 0.359 | 0.000 | 0.102 | 0.000 | 0.136 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 276 | 192 | 438 | 0 | 803 | 0 | 206 | 701 | 0 |
N.S. |
1 | 1.35 | 0.94 | 2.15 | 0.00 | 3.94 | 0.00 | 1.01 | 3.44 | 0.00 |
time (sec) |
N/A | 0.648 | 2.352 | 0.363 | 0.000 | 0.121 | 0.000 | 0.132 | 0.239 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 302 | 0 | 0 | 0 | 971 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 2.40 | 0.00 | 0.00 | 0.00 | 7.71 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.428 | 1.125 | 0.000 | 0.000 | 0.000 | 3.708 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 123 | 169 | 0 | 0 | 0 | 576 | 0 | 1696 | 0 |
N.S. |
1 | 1.02 | 1.40 | 0.00 | 0.00 | 0.00 | 4.76 | 0.00 | 14.02 | 0.00 |
time (sec) |
N/A | 0.427 | 0.837 | 0.000 | 0.000 | 0.000 | 2.853 | 0.000 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 135 | 143 | 0 | 0 | 0 | 175 | 0 | 1193 | 0 |
N.S. |
1 | 1.10 | 1.16 | 0.00 | 0.00 | 0.00 | 1.42 | 0.00 | 9.70 | 0.00 |
time (sec) |
N/A | 0.412 | 0.467 | 0.000 | 0.000 | 0.000 | 1.941 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 120 | 0 | 0 | 0 | 82 | 0 | 320 | 79 |
N.S. |
1 | 1.00 | 1.43 | 0.00 | 0.00 | 0.00 | 0.98 | 0.00 | 3.81 | 0.94 |
time (sec) |
N/A | 0.319 | 0.270 | 0.000 | 0.000 | 0.000 | 1.148 | 0.000 | 0.219 | 10.988 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 129 | 160 | 0 | 0 | 0 | 763 | 0 | 385 | 0 |
N.S. |
1 | 1.11 | 1.38 | 0.00 | 0.00 | 0.00 | 6.58 | 0.00 | 3.32 | 0.00 |
time (sec) |
N/A | 0.424 | 0.628 | 0.000 | 0.000 | 0.000 | 26.964 | 0.000 | 0.224 | 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 | 114 | 138 | 114 | 0 | 0 | 0 | 0 | 0 | 297 | 0 |
N.S. |
1 | 1.21 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.61 | 0.00 |
time (sec) |
N/A | 0.450 | 0.826 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.229 | 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 | 128 | 142 | 114 | 0 | 0 | 0 | 0 | 0 | 1519 | 0 |
N.S. |
1 | 1.11 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 11.87 | 0.00 |
time (sec) |
N/A | 0.468 | 0.997 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.269 | 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 | 145 | 141 | 127 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.506 | 2.045 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.396 | 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 | 144 | 140 | 138 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.500 | 1.909 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.345 | 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 | 146 | 142 | 135 | 0 | 0 | 0 | 0 | 0 | 1022 | 0 |
N.S. |
1 | 0.97 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 7.00 | 0.00 |
time (sec) |
N/A | 0.480 | 1.635 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.292 | 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 | 146 | 143 | 147 | 0 | 0 | 0 | 0 | 0 | 428 | 0 |
N.S. |
1 | 0.98 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.93 | 0.00 |
time (sec) |
N/A | 0.486 | 1.706 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.358 | 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 | 147 | 157 | 155 | 0 | 0 | 0 | 0 | 0 | 1077 | 0 |
N.S. |
1 | 1.07 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 7.33 | 0.00 |
time (sec) |
N/A | 0.517 | 1.885 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.348 | 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 | 147 | 156 | 134 | 0 | 0 | 0 | 0 | 0 | 1634 | 0 |
N.S. |
1 | 1.06 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 11.12 | 0.00 |
time (sec) |
N/A | 0.552 | 1.986 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.358 | 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 | 145 | 140 | 131 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.97 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.472 | 0.262 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.250 | 0.000 |
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 | 27 | 27 | 33 | 34 | 45 | 39 | 60 | 70 | 37 | 27 |
N.S. |
1 | 1.00 | 1.22 | 1.26 | 1.67 | 1.44 | 2.22 | 2.59 | 1.37 | 1.00 |
time (sec) |
N/A | 0.260 | 0.220 | 1.057 | 0.085 | 0.113 | 0.844 | 0.133 | 0.216 | 8.948 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 317 | 249 | 444 | 460 | 285 | 619 | 302 | 425 | 0 |
N.S. |
1 | 1.03 | 0.81 | 1.44 | 1.49 | 0.93 | 2.01 | 0.98 | 1.38 | 0.00 |
time (sec) |
N/A | 1.740 | 2.019 | 0.501 | 0.122 | 0.092 | 0.739 | 0.148 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 250 | 215 | 334 | 301 | 237 | 437 | 248 | 351 | 0 |
N.S. |
1 | 0.99 | 0.85 | 1.33 | 1.19 | 0.94 | 1.73 | 0.98 | 1.39 | 0.00 |
time (sec) |
N/A | 1.123 | 1.427 | 0.389 | 0.114 | 0.093 | 0.757 | 0.134 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 162 | 140 | 202 | 162 | 139 | 212 | 135 | 213 | 0 |
N.S. |
1 | 1.02 | 0.88 | 1.27 | 1.02 | 0.87 | 1.33 | 0.85 | 1.34 | 0.00 |
time (sec) |
N/A | 0.639 | 0.979 | 0.317 | 0.119 | 0.091 | 0.441 | 0.129 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 213 | 152 | 385 | 276 | 158 | 0 | 165 | 157 | 0 |
N.S. |
1 | 1.06 | 0.76 | 1.92 | 1.37 | 0.79 | 0.00 | 0.82 | 0.78 | 0.00 |
time (sec) |
N/A | 1.033 | 0.923 | 0.413 | 0.147 | 0.090 | 0.000 | 0.146 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 207 | 158 | 382 | 311 | 262 | 0 | 542 | 396 | 0 |
N.S. |
1 | 1.02 | 0.78 | 1.88 | 1.53 | 1.29 | 0.00 | 2.67 | 1.95 | 0.00 |
time (sec) |
N/A | 0.974 | 1.071 | 0.431 | 0.136 | 0.099 | 0.000 | 0.171 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 212 | 163 | 358 | 0 | 354 | 0 | 380 | 493 | 0 |
N.S. |
1 | 1.04 | 0.80 | 1.76 | 0.00 | 1.74 | 0.00 | 1.87 | 2.43 | 0.00 |
time (sec) |
N/A | 0.976 | 1.440 | 0.440 | 0.000 | 0.092 | 0.000 | 0.141 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-1) | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 261 | 167 | 396 | 0 | 427 | 0 | 613 | 525 | 0 |
N.S. |
1 | 1.25 | 0.80 | 1.89 | 0.00 | 2.04 | 0.00 | 2.93 | 2.51 | 0.00 |
time (sec) |
N/A | 1.094 | 1.441 | 0.474 | 0.000 | 0.117 | 0.000 | 0.143 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 234 | 373 | 188 | 463 | 0 | 478 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.59 | 0.80 | 1.98 | 0.00 | 2.04 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.985 | 1.582 | 0.523 | 0.000 | 0.131 | 0.000 | 0.000 | 200.078 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 278 | 155 | 195 | 2090 | 497 | 0 | 895 | 510 | 0 |
N.S. |
1 | 1.16 | 0.65 | 0.82 | 8.74 | 2.08 | 0.00 | 3.74 | 2.13 | 0.00 |
time (sec) |
N/A | 1.049 | 1.579 | 0.596 | 0.075 | 0.166 | 0.000 | 0.148 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 322 | 189 | 243 | 2890 | 591 | 0 | 1200 | 768 | 0 |
N.S. |
1 | 1.08 | 0.63 | 0.81 | 9.67 | 1.98 | 0.00 | 4.01 | 2.57 | 0.00 |
time (sec) |
N/A | 1.123 | 2.214 | 0.671 | 0.087 | 0.284 | 0.000 | 0.143 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 359 | 358 | 216 | 291 | 3800 | 687 | 0 | 1470 | 901 | 0 |
N.S. |
1 | 1.00 | 0.60 | 0.81 | 10.58 | 1.91 | 0.00 | 4.09 | 2.51 | 0.00 |
time (sec) |
N/A | 1.148 | 2.979 | 0.772 | 0.104 | 0.462 | 0.000 | 0.144 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 416 | 413 | 344 | 711 | 809 | 410 | 1331 | 439 | 647 | 0 |
N.S. |
1 | 0.99 | 0.83 | 1.71 | 1.94 | 0.99 | 3.20 | 1.06 | 1.56 | 0.00 |
time (sec) |
N/A | 2.488 | 3.162 | 0.629 | 0.121 | 0.103 | 0.883 | 0.152 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 362 | 346 | 311 | 513 | 554 | 366 | 1044 | 392 | 573 | 0 |
N.S. |
1 | 0.96 | 0.86 | 1.42 | 1.53 | 1.01 | 2.88 | 1.08 | 1.58 | 0.00 |
time (sec) |
N/A | 1.731 | 2.753 | 0.501 | 0.114 | 0.100 | 0.791 | 0.149 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 309 | 281 | 279 | 403 | 376 | 323 | 782 | 345 | 499 | 0 |
N.S. |
1 | 0.91 | 0.90 | 1.30 | 1.22 | 1.05 | 2.53 | 1.12 | 1.61 | 0.00 |
time (sec) |
N/A | 1.163 | 2.158 | 0.388 | 0.110 | 0.097 | 0.825 | 0.143 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 191 | 169 | 248 | 207 | 186 | 394 | 196 | 311 | 0 |
N.S. |
1 | 0.98 | 0.87 | 1.27 | 1.06 | 0.95 | 2.02 | 1.01 | 1.59 | 0.00 |
time (sec) |
N/A | 0.688 | 0.987 | 0.350 | 0.114 | 0.091 | 0.516 | 0.139 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 242 | 215 | 535 | 638 | 239 | 651 | 250 | 282 | 0 |
N.S. |
1 | 0.94 | 0.83 | 2.07 | 2.47 | 0.93 | 2.52 | 0.97 | 1.09 | 0.00 |
time (sec) |
N/A | 1.087 | 1.324 | 0.411 | 0.145 | 0.106 | 2.289 | 0.148 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 240 | 186 | 543 | 682 | 202 | 0 | 778 | 277 | 0 |
N.S. |
1 | 0.94 | 0.73 | 2.13 | 2.67 | 0.79 | 0.00 | 3.05 | 1.09 | 0.00 |
time (sec) |
N/A | 1.047 | 1.099 | 0.418 | 0.142 | 0.100 | 0.000 | 0.200 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 254 | 189 | 689 | 756 | 313 | 0 | 235 | 517 | 0 |
N.S. |
1 | 0.99 | 0.74 | 2.68 | 2.94 | 1.22 | 0.00 | 0.91 | 2.01 | 0.00 |
time (sec) |
N/A | 1.074 | 1.380 | 0.423 | 0.154 | 0.099 | 0.000 | 0.147 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 249 | 187 | 902 | 894 | 396 | 0 | 415 | 650 | 0 |
N.S. |
1 | 0.97 | 0.72 | 3.50 | 3.47 | 1.53 | 0.00 | 1.61 | 2.52 | 0.00 |
time (sec) |
N/A | 1.153 | 1.629 | 0.476 | 0.161 | 0.130 | 0.000 | 0.148 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 241 | 192 | 812 | 1207 | 484 | 0 | 550 | 822 | 0 |
N.S. |
1 | 0.96 | 0.76 | 3.22 | 4.79 | 1.92 | 0.00 | 2.18 | 3.26 | 0.00 |
time (sec) |
N/A | 1.085 | 2.001 | 0.519 | 0.145 | 0.114 | 0.000 | 0.187 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 296 | 202 | 718 | 1755 | 546 | 0 | 885 | 39 | 0 |
N.S. |
1 | 1.20 | 0.82 | 2.91 | 7.11 | 2.21 | 0.00 | 3.58 | 0.16 | 0.00 |
time (sec) |
N/A | 1.136 | 2.051 | 0.585 | 0.149 | 0.174 | 0.000 | 0.153 | 200.081 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 403 | 221 | 624 | 2467 | 587 | 0 | 1056 | 881 | 0 |
N.S. |
1 | 1.53 | 0.84 | 2.36 | 9.34 | 2.22 | 0.00 | 4.00 | 3.34 | 0.00 |
time (sec) |
N/A | 1.031 | 2.093 | 0.660 | 0.183 | 0.208 | 0.000 | 0.158 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 278 | 156 | 195 | 3298 | 590 | 0 | 1200 | 768 | 0 |
N.S. |
1 | 1.16 | 0.65 | 0.82 | 13.80 | 2.47 | 0.00 | 5.02 | 3.21 | 0.00 |
time (sec) |
N/A | 1.089 | 2.075 | 0.763 | 0.118 | 0.301 | 0.000 | 0.167 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 326 | 191 | 243 | 4251 | 686 | 0 | 1470 | 912 | 0 |
N.S. |
1 | 1.09 | 0.64 | 0.81 | 14.22 | 2.29 | 0.00 | 4.92 | 3.05 | 0.00 |
time (sec) |
N/A | 1.191 | 3.385 | 0.878 | 0.130 | 0.571 | 0.000 | 0.169 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 359 | 364 | 221 | 291 | 5316 | 782 | 0 | 1705 | 1032 | 0 |
N.S. |
1 | 1.01 | 0.62 | 0.81 | 14.81 | 2.18 | 0.00 | 4.75 | 2.87 | 0.00 |
time (sec) |
N/A | 1.183 | 4.072 | 0.993 | 0.144 | 0.807 | 0.000 | 0.163 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 416 | 375 | 377 | 582 | 648 | 453 | 1457 | 485 | 721 | 0 |
N.S. |
1 | 0.90 | 0.91 | 1.40 | 1.56 | 1.09 | 3.50 | 1.17 | 1.73 | 0.00 |
time (sec) |
N/A | 1.819 | 3.605 | 0.517 | 0.126 | 0.112 | 0.902 | 0.157 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 363 | 310 | 343 | 472 | 451 | 408 | 1238 | 436 | 647 | 0 |
N.S. |
1 | 0.85 | 0.94 | 1.30 | 1.24 | 1.12 | 3.41 | 1.20 | 1.78 | 0.00 |
time (sec) |
N/A | 1.235 | 3.850 | 0.398 | 0.114 | 0.118 | 0.890 | 0.148 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 220 | 196 | 294 | 252 | 236 | 627 | 252 | 409 | 0 |
N.S. |
1 | 0.95 | 0.85 | 1.27 | 1.09 | 1.02 | 2.71 | 1.09 | 1.77 | 0.00 |
time (sec) |
N/A | 0.723 | 1.184 | 0.326 | 0.117 | 0.096 | 0.588 | 0.140 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 312 | 273 | 279 | 683 | 733 | 325 | 1459 | 347 | 406 | 0 |
N.S. |
1 | 0.88 | 0.89 | 2.19 | 2.35 | 1.04 | 4.68 | 1.11 | 1.30 | 0.00 |
time (sec) |
N/A | 1.134 | 2.169 | 0.415 | 0.174 | 0.103 | 4.084 | 0.152 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 311 | 269 | 249 | 702 | 797 | 285 | 1047 | 1041 | 425 | 0 |
N.S. |
1 | 0.86 | 0.80 | 2.26 | 2.56 | 0.92 | 3.37 | 3.35 | 1.37 | 0.00 |
time (sec) |
N/A | 1.095 | 1.961 | 0.427 | 0.175 | 0.111 | 5.092 | 0.233 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 286 | 216 | 881 | 978 | 243 | 0 | 255 | 351 | 0 |
N.S. |
1 | 0.93 | 0.70 | 2.86 | 3.18 | 0.79 | 0.00 | 0.83 | 1.14 | 0.00 |
time (sec) |
N/A | 1.200 | 1.379 | 0.441 | 0.201 | 0.092 | 0.000 | 0.145 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 310 | 281 | 222 | 1127 | 1173 | 358 | 0 | 280 | 630 | 0 |
N.S. |
1 | 0.91 | 0.72 | 3.64 | 3.78 | 1.15 | 0.00 | 0.90 | 2.03 | 0.00 |
time (sec) |
N/A | 1.097 | 1.468 | 0.478 | 0.151 | 0.103 | 0.000 | 0.144 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 278 | 221 | 1334 | 1447 | 450 | 0 | 910 | 798 | 0 |
N.S. |
1 | 0.88 | 0.70 | 4.23 | 4.59 | 1.43 | 0.00 | 2.89 | 2.53 | 0.00 |
time (sec) |
N/A | 1.296 | 1.673 | 0.568 | 0.148 | 0.110 | 0.000 | 0.207 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 289 | 219 | 1541 | 1825 | 534 | 0 | 717 | 1136 | 0 |
N.S. |
1 | 0.92 | 0.70 | 4.89 | 5.79 | 1.70 | 0.00 | 2.28 | 3.61 | 0.00 |
time (sec) |
N/A | 1.156 | 2.315 | 0.698 | 0.172 | 0.139 | 0.000 | 0.152 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 272 | 225 | 1292 | 2371 | 612 | 0 | 857 | 39 | 0 |
N.S. |
1 | 0.91 | 0.75 | 4.32 | 7.93 | 2.05 | 0.00 | 2.87 | 0.13 | 0.00 |
time (sec) |
N/A | 1.101 | 2.656 | 0.859 | 0.184 | 0.151 | 0.000 | 0.165 | 200.028 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 333 | 231 | 1038 | 3095 | 667 | 0 | 1153 | 939 | 0 |
N.S. |
1 | 1.17 | 0.81 | 3.64 | 10.86 | 2.34 | 0.00 | 4.05 | 3.29 | 0.00 |
time (sec) |
N/A | 1.195 | 2.567 | 1.115 | 0.208 | 0.309 | 0.000 | 0.160 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 296 | 435 | 249 | 784 | 3960 | 692 | 0 | 1327 | 1087 | 0 |
N.S. |
1 | 1.47 | 0.84 | 2.65 | 13.38 | 2.34 | 0.00 | 4.48 | 3.67 | 0.00 |
time (sec) |
N/A | 1.083 | 2.853 | 1.517 | 0.225 | 0.336 | 0.000 | 0.161 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 278 | 156 | 195 | 4892 | 687 | 0 | 1470 | 912 | 0 |
N.S. |
1 | 1.16 | 0.65 | 0.82 | 20.47 | 2.87 | 0.00 | 6.15 | 3.82 | 0.00 |
time (sec) |
N/A | 1.057 | 2.748 | 2.110 | 0.145 | 0.490 | 0.000 | 0.185 | 0.280 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 326 | 191 | 243 | 5999 | 782 | 0 | 1740 | 1056 | 0 |
N.S. |
1 | 1.09 | 0.64 | 0.81 | 20.06 | 2.62 | 0.00 | 5.82 | 3.53 | 0.00 |
time (sec) |
N/A | 1.198 | 3.953 | 2.838 | 0.171 | 0.909 | 0.000 | 0.170 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 359 | 367 | 218 | 291 | 7218 | 877 | 0 | 2010 | 1189 | 0 |
N.S. |
1 | 1.02 | 0.61 | 0.81 | 20.11 | 2.44 | 0.00 | 5.60 | 3.31 | 0.00 |
time (sec) |
N/A | 1.208 | 5.572 | 4.045 | 0.189 | 1.380 | 0.000 | 0.182 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 306 | 353 | 216 | 527 | 546 | 242 | 556 | 254 | 351 | 0 |
N.S. |
1 | 1.15 | 0.71 | 1.72 | 1.78 | 0.79 | 1.82 | 0.83 | 1.15 | 0.00 |
time (sec) |
N/A | 2.377 | 1.493 | 0.641 | 0.118 | 0.100 | 0.761 | 0.143 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 286 | 185 | 375 | 365 | 200 | 377 | 208 | 277 | 0 |
N.S. |
1 | 1.13 | 0.73 | 1.49 | 1.45 | 0.79 | 1.50 | 0.83 | 1.10 | 0.00 |
time (sec) |
N/A | 1.749 | 1.238 | 0.504 | 0.121 | 0.129 | 0.701 | 0.139 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 221 | 152 | 265 | 225 | 157 | 235 | 164 | 203 | 0 |
N.S. |
1 | 1.11 | 0.76 | 1.33 | 1.13 | 0.79 | 1.18 | 0.82 | 1.02 | 0.00 |
time (sec) |
N/A | 1.112 | 1.030 | 0.389 | 0.109 | 0.086 | 0.710 | 0.137 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 131 | 98 | 156 | 116 | 92 | 153 | 87 | 105 | 207 |
N.S. |
1 | 1.08 | 0.81 | 1.29 | 0.96 | 0.76 | 1.26 | 0.72 | 0.87 | 1.71 |
time (sec) |
N/A | 0.609 | 0.645 | 0.315 | 0.113 | 0.100 | 0.396 | 0.126 | 0.192 | 10.269 |
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 | 156 | 170 | 132 | 261 | 227 | 227 | 0 | 149 | 264 | 0 |
N.S. |
1 | 1.09 | 0.85 | 1.67 | 1.46 | 1.46 | 0.00 | 0.96 | 1.69 | 0.00 |
time (sec) |
N/A | 0.908 | 0.810 | 0.431 | 0.131 | 0.088 | 0.000 | 0.129 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 216 | 134 | 267 | 467 | 305 | 0 | 275 | 355 | 0 |
N.S. |
1 | 1.25 | 0.77 | 1.54 | 2.70 | 1.76 | 0.00 | 1.59 | 2.05 | 0.00 |
time (sec) |
N/A | 0.980 | 1.024 | 0.448 | 0.129 | 0.103 | 0.000 | 0.159 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 341 | 157 | 365 | 880 | 373 | 0 | 516 | 392 | 0 |
N.S. |
1 | 1.67 | 0.77 | 1.79 | 4.31 | 1.83 | 0.00 | 2.53 | 1.92 | 0.00 |
time (sec) |
N/A | 0.945 | 1.180 | 0.439 | 0.135 | 0.106 | 0.000 | 0.146 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 273 | 148 | 189 | 1448 | 400 | 0 | 660 | 173 | 0 |
N.S. |
1 | 1.14 | 0.62 | 0.79 | 6.06 | 1.67 | 0.00 | 2.76 | 0.72 | 0.00 |
time (sec) |
N/A | 1.034 | 1.135 | 0.486 | 0.134 | 0.114 | 0.000 | 0.137 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 269 | 293 | 190 | 500 | 544 | 314 | 0 | 232 | 516 | 0 |
N.S. |
1 | 1.09 | 0.71 | 1.86 | 2.02 | 1.17 | 0.00 | 0.86 | 1.92 | 0.00 |
time (sec) |
N/A | 1.846 | 1.365 | 0.631 | 0.114 | 0.096 | 0.000 | 0.150 | 0.212 | 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 | 213 | 238 | 160 | 351 | 362 | 264 | 0 | 185 | 396 | 0 |
N.S. |
1 | 1.12 | 0.75 | 1.65 | 1.70 | 1.24 | 0.00 | 0.87 | 1.86 | 0.00 |
time (sec) |
N/A | 1.285 | 1.120 | 0.498 | 0.118 | 0.102 | 0.000 | 0.143 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 163 | 133 | 246 | 226 | 227 | 558 | 146 | 278 | 0 |
N.S. |
1 | 1.09 | 0.89 | 1.65 | 1.52 | 1.52 | 3.74 | 0.98 | 1.87 | 0.00 |
time (sec) |
N/A | 0.738 | 0.791 | 0.385 | 0.116 | 0.097 | 9.588 | 0.146 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 105 | 111 | 142 | 119 | 167 | 223 | 110 | 82 | 127 |
N.S. |
1 | 1.11 | 1.17 | 1.49 | 1.25 | 1.76 | 2.35 | 1.16 | 0.86 | 1.34 |
time (sec) |
N/A | 0.443 | 0.677 | 0.320 | 0.111 | 0.086 | 6.061 | 0.137 | 0.192 | 9.225 |
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 | 155 | 229 | 156 | 280 | 337 | 366 | 0 | 0 | 550 | 0 |
N.S. |
1 | 1.48 | 1.01 | 1.81 | 2.17 | 2.36 | 0.00 | 0.00 | 3.55 | 0.00 |
time (sec) |
N/A | 0.790 | 0.944 | 0.437 | 0.134 | 0.109 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 220 | 149 | 195 | 752 | 345 | 0 | 577 | 346 | 0 |
N.S. |
1 | 1.22 | 0.82 | 1.08 | 4.15 | 1.91 | 0.00 | 3.19 | 1.91 | 0.00 |
time (sec) |
N/A | 0.955 | 0.943 | 0.448 | 0.059 | 0.109 | 0.000 | 0.174 | 0.209 | 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 | 233 | 276 | 189 | 243 | 1454 | 500 | 0 | 0 | 466 | 0 |
N.S. |
1 | 1.18 | 0.81 | 1.04 | 6.24 | 2.15 | 0.00 | 0.00 | 2.00 | 0.00 |
time (sec) |
N/A | 1.077 | 1.495 | 0.466 | 0.073 | 0.128 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 293 | 317 | 215 | 291 | 2453 | 540 | 0 | 0 | 255 | 0 |
N.S. |
1 | 1.08 | 0.73 | 0.99 | 8.37 | 1.84 | 0.00 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 1.141 | 1.736 | 0.503 | 0.088 | 0.181 | 0.000 | 0.000 | 0.273 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 271 | 187 | 679 | 836 | 396 | 0 | 413 | 651 | 0 |
N.S. |
1 | 1.04 | 0.72 | 2.60 | 3.20 | 1.52 | 0.00 | 1.58 | 2.49 | 0.00 |
time (sec) |
N/A | 1.278 | 1.652 | 0.776 | 0.123 | 0.104 | 0.000 | 0.167 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 220 | 162 | 539 | 623 | 354 | 0 | 380 | 494 | 0 |
N.S. |
1 | 1.09 | 0.81 | 2.68 | 3.10 | 1.76 | 0.00 | 1.89 | 2.46 | 0.00 |
time (sec) |
N/A | 1.073 | 1.355 | 0.602 | 0.125 | 0.095 | 0.000 | 0.163 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 181 | 135 | 394 | 415 | 304 | 0 | 342 | 359 | 0 |
N.S. |
1 | 1.07 | 0.80 | 2.33 | 2.46 | 1.80 | 0.00 | 2.02 | 2.12 | 0.00 |
time (sec) |
N/A | 0.947 | 1.074 | 0.496 | 0.120 | 0.118 | 0.000 | 0.152 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | C | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 154 | 156 | 285 | 281 | 369 | 1550 | 0 | 577 | 0 |
N.S. |
1 | 1.05 | 1.06 | 1.94 | 1.91 | 2.51 | 10.54 | 0.00 | 3.93 | 0.00 |
time (sec) |
N/A | 0.707 | 0.928 | 0.384 | 0.116 | 0.101 | 9.038 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 105 | 94 | 80 | 153 | 166 | 529 | 97 | 173 | 113 |
N.S. |
1 | 1.05 | 0.94 | 0.80 | 1.53 | 1.66 | 5.29 | 0.97 | 1.73 | 1.13 |
time (sec) |
N/A | 0.441 | 0.579 | 0.325 | 0.034 | 0.087 | 7.182 | 0.137 | 0.200 | 9.919 |
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 | 183 | 214 | 182 | 236 | 418 | 491 | 0 | 0 | 347 | 0 |
N.S. |
1 | 1.17 | 0.99 | 1.29 | 2.28 | 2.68 | 0.00 | 0.00 | 1.90 | 0.00 |
time (sec) |
N/A | 0.982 | 0.974 | 0.441 | 0.065 | 0.120 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 255 | 213 | 289 | 846 | 588 | 0 | 803 | 502 | 0 |
N.S. |
1 | 1.09 | 0.91 | 1.23 | 3.60 | 2.50 | 0.00 | 3.42 | 2.14 | 0.00 |
time (sec) |
N/A | 1.025 | 1.353 | 0.440 | 0.076 | 0.173 | 0.000 | 0.190 | 0.210 | 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 | 286 | 308 | 252 | 339 | 1548 | 684 | 0 | 0 | 706 | 0 |
N.S. |
1 | 1.08 | 0.88 | 1.19 | 5.41 | 2.39 | 0.00 | 0.00 | 2.47 | 0.00 |
time (sec) |
N/A | 1.097 | 1.827 | 0.447 | 0.092 | 0.367 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 368 | 312 | 198 | 251 | 345 | 281 | 0 | 1346 | 196 | 0 |
N.S. |
1 | 0.85 | 0.54 | 0.68 | 0.94 | 0.76 | 0.00 | 3.66 | 0.53 | 0.00 |
time (sec) |
N/A | 1.203 | 0.699 | 0.371 | 0.082 | 0.095 | 0.000 | 0.124 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 306 | 274 | 168 | 203 | 301 | 239 | 0 | 1170 | 161 | 0 |
N.S. |
1 | 0.90 | 0.55 | 0.66 | 0.98 | 0.78 | 0.00 | 3.82 | 0.53 | 0.00 |
time (sec) |
N/A | 1.119 | 0.591 | 0.363 | 0.082 | 0.084 | 0.000 | 0.129 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 236 | 133 | 155 | 257 | 197 | 0 | 502 | 126 | 0 |
N.S. |
1 | 0.97 | 0.55 | 0.64 | 1.05 | 0.81 | 0.00 | 2.06 | 0.52 | 0.00 |
time (sec) |
N/A | 1.064 | 0.479 | 0.358 | 0.073 | 0.084 | 0.000 | 0.124 | 0.292 | 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 | 184 | 198 | 101 | 111 | 154 | 154 | 0 | 192 | 91 | 0 |
N.S. |
1 | 1.08 | 0.55 | 0.60 | 0.84 | 0.84 | 0.00 | 1.04 | 0.49 | 0.00 |
time (sec) |
N/A | 0.999 | 0.394 | 0.356 | 0.060 | 0.092 | 0.000 | 0.123 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 249 | 175 | 304 | 0 | 479 | 0 | 211 | 189 | 0 |
N.S. |
1 | 0.97 | 0.68 | 1.18 | 0.00 | 1.86 | 0.00 | 0.82 | 0.74 | 0.00 |
time (sec) |
N/A | 1.124 | 0.729 | 0.361 | 0.000 | 0.096 | 0.000 | 0.128 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 256 | 263 | 177 | 436 | 0 | 621 | 0 | 213 | 369 | 0 |
N.S. |
1 | 1.03 | 0.69 | 1.70 | 0.00 | 2.43 | 0.00 | 0.83 | 1.44 | 0.00 |
time (sec) |
N/A | 1.120 | 0.908 | 0.356 | 0.000 | 0.109 | 0.000 | 0.133 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 274 | 257 | 189 | 582 | 0 | 753 | 0 | 231 | 555 | 0 |
N.S. |
1 | 0.94 | 0.69 | 2.12 | 0.00 | 2.75 | 0.00 | 0.84 | 2.03 | 0.00 |
time (sec) |
N/A | 1.178 | 1.114 | 0.362 | 0.000 | 0.107 | 0.000 | 0.132 | 0.839 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 298 | 210 | 750 | 0 | 901 | 0 | 307 | 39 | 0 |
N.S. |
1 | 1.02 | 0.72 | 2.57 | 0.00 | 3.09 | 0.00 | 1.05 | 0.13 | 0.00 |
time (sec) |
N/A | 1.195 | 1.233 | 0.402 | 0.000 | 0.116 | 0.000 | 0.135 | 200.030 | 0.000 |