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 | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 121 | 121 | 111 | 0 | 0 | 0 | 252 | 57 | 0 |
N.S. |
1 | 0.84 | 0.84 | 0.77 | 0.00 | 0.00 | 0.00 | 1.75 | 0.40 | 0.00 |
time (sec) |
N/A | 0.457 | 0.305 | 0.198 | 0.000 | 0.000 | 0.000 | 0.164 | 0.276 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 28 | 26 | 0 | 58 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.00 | 0.93 | 0.00 | 2.07 | 1.00 |
time (sec) |
N/A | 0.928 | 2.124 | 0.357 | 0.328 | 0.095 | 2.044 | 0.000 | 0.259 | 0.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 32 | 27 | 28 | 90 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.14 | 0.96 | 1.00 | 3.21 | 1.00 |
time (sec) |
N/A | 0.802 | 1.919 | 0.414 | 0.266 | 0.104 | 1.623 | 0.355 | 0.284 | 0.196 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 32 | 27 | 0 | 64 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.14 | 0.96 | 0.00 | 2.29 | 1.00 |
time (sec) |
N/A | 0.332 | 3.852 | 1.196 | 0.348 | 0.088 | 2.085 | 0.000 | 0.309 | 0.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 204 | 180 | 185 | 0 | 0 | 0 | 746 | 91 | 0 |
N.S. |
1 | 0.83 | 0.73 | 0.76 | 0.00 | 0.00 | 0.00 | 3.04 | 0.37 | 0.00 |
time (sec) |
N/A | 0.762 | 0.773 | 0.191 | 0.000 | 0.000 | 0.000 | 0.170 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 221 | 209 | 203 | 0 | 0 | 0 | 757 | 91 | 0 |
N.S. |
1 | 0.82 | 0.78 | 0.76 | 0.00 | 0.00 | 0.00 | 2.82 | 0.34 | 0.00 |
time (sec) |
N/A | 0.771 | 0.726 | 0.181 | 0.000 | 0.000 | 0.000 | 0.165 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 204 | 180 | 185 | 0 | 0 | 0 | 614 | 89 | 0 |
N.S. |
1 | 0.83 | 0.73 | 0.76 | 0.00 | 0.00 | 0.00 | 2.51 | 0.36 | 0.00 |
time (sec) |
N/A | 0.580 | 0.642 | 0.177 | 0.000 | 0.000 | 0.000 | 0.171 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 206 | 171 | 165 | 157 | 0 | 0 | 0 | 472 | 88 | 0 |
N.S. |
1 | 0.83 | 0.80 | 0.76 | 0.00 | 0.00 | 0.00 | 2.29 | 0.43 | 0.00 |
time (sec) |
N/A | 0.488 | 0.549 | 0.220 | 0.000 | 0.000 | 0.000 | 0.161 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 45 | 26 | 0 | 89 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.61 | 0.93 | 0.00 | 3.18 | 1.00 |
time (sec) |
N/A | 1.183 | 2.124 | 0.367 | 0.333 | 0.104 | 4.971 | 0.000 | 0.196 | 0.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 49 | 27 | 28 | 122 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.75 | 0.96 | 1.00 | 4.36 | 1.00 |
time (sec) |
N/A | 1.068 | 1.908 | 0.365 | 0.339 | 0.088 | 3.926 | 0.376 | 0.244 | 0.198 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 49 | 27 | 0 | 93 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.75 | 0.96 | 0.00 | 3.32 | 1.00 |
time (sec) |
N/A | 0.301 | 3.834 | 0.831 | 0.322 | 0.086 | 4.076 | 0.000 | 0.229 | 0.211 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 36 | 33 | 30 | 0 | 0 | 0 | 35 | 25 | 0 |
N.S. |
1 | 0.88 | 0.80 | 0.73 | 0.00 | 0.00 | 0.00 | 0.85 | 0.61 | 0.00 |
time (sec) |
N/A | 0.373 | 0.103 | 0.418 | 0.000 | 0.000 | 0.000 | 0.145 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 25 | 22 | 23 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.93 | 0.81 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.407 | 0.091 | 0.343 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 25 | 22 | 21 | 0 | 0 | 0 | 23 | 25 | 0 |
N.S. |
1 | 0.93 | 0.81 | 0.78 | 0.00 | 0.00 | 0.00 | 0.85 | 0.93 | 0.00 |
time (sec) |
N/A | 0.352 | 0.078 | 0.209 | 0.000 | 0.000 | 0.000 | 0.132 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 25 | 22 | 21 | 0 | 0 | 0 | 23 | 25 | 0 |
N.S. |
1 | 0.93 | 0.81 | 0.78 | 0.00 | 0.00 | 0.00 | 0.85 | 0.93 | 0.00 |
time (sec) |
N/A | 0.370 | 0.010 | 0.000 | 0.000 | 0.000 | 0.000 | 0.129 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 10 | 0 | 0 | 0 | 9 | 23 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 0.00 | 0.00 | 0.00 | 1.00 | 2.56 | 0.00 |
time (sec) |
N/A | 0.291 | 0.066 | 0.191 | 0.000 | 0.000 | 0.000 | 0.136 | 0.207 | 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 | 9 | 9 | 9 | 10 | 9 | 11 | 7 | 10 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.00 | 1.22 | 0.78 | 1.11 | 1.00 | 1.00 |
time (sec) |
N/A | 0.199 | 0.014 | 0.078 | 0.141 | 0.086 | 0.190 | 0.121 | 0.225 | 0.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 24 | 35 | 24 | 24 | 25 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.46 | 1.00 | 1.00 | 1.04 | 1.00 |
time (sec) |
N/A | 0.259 | 1.334 | 0.525 | 0.222 | 0.091 | 0.442 | 0.135 | 0.214 | 0.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 24 | 37 | 26 | 24 | 25 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.54 | 1.08 | 1.00 | 1.04 | 1.00 |
time (sec) |
N/A | 0.276 | 0.654 | 0.311 | 0.214 | 0.100 | 0.455 | 0.132 | 0.197 | 0.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 154 | 136 | 139 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 0.84 | 0.74 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.597 | 0.288 | 0.224 | 0.000 | 0.000 | 0.000 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 121 | 108 | 111 | 0 | 0 | 0 | 254 | 39 | 0 |
N.S. |
1 | 0.84 | 0.75 | 0.77 | 0.00 | 0.00 | 0.00 | 1.76 | 0.27 | 0.00 |
time (sec) |
N/A | 0.511 | 0.244 | 0.189 | 0.000 | 0.000 | 0.000 | 0.155 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 104 | 92 | 93 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 0.86 | 0.76 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.502 | 0.209 | 0.184 | 0.000 | 0.000 | 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 | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 71 | 64 | 65 | 0 | 0 | 0 | 104 | 39 | 0 |
N.S. |
1 | 0.87 | 0.78 | 0.79 | 0.00 | 0.00 | 0.00 | 1.27 | 0.48 | 0.00 |
time (sec) |
N/A | 0.451 | 0.195 | 0.182 | 0.000 | 0.000 | 0.000 | 0.152 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 49 | 45 | 46 | 0 | 0 | 0 | 50 | 37 | 0 |
N.S. |
1 | 0.91 | 0.83 | 0.85 | 0.00 | 0.00 | 0.00 | 0.93 | 0.69 | 0.00 |
time (sec) |
N/A | 0.492 | 0.146 | 0.157 | 0.000 | 0.000 | 0.000 | 0.148 | 0.213 | 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 | 16 | 16 | 16 | 17 | 16 | 19 | 42 | 17 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.19 | 2.62 | 1.06 | 1.00 | 1.00 |
time (sec) |
N/A | 0.226 | 0.051 | 0.078 | 0.112 | 0.102 | 0.771 | 0.112 | 0.198 | 0.237 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 49 | 27 | 0 | 37 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.75 | 0.96 | 0.00 | 1.32 | 1.00 |
time (sec) |
N/A | 0.304 | 3.634 | 0.281 | 0.238 | 0.095 | 1.180 | 0.000 | 0.201 | 0.198 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 53 | 29 | 28 | 41 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.89 | 1.04 | 1.00 | 1.46 | 1.00 |
time (sec) |
N/A | 0.336 | 0.044 | 0.436 | 0.231 | 0.095 | 1.000 | 0.324 | 0.205 | 0.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 63 | 27 | 28 | 102 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.25 | 0.96 | 1.00 | 3.64 | 1.00 |
time (sec) |
N/A | 0.388 | 5.250 | 0.589 | 0.269 | 0.102 | 1.856 | 0.769 | 0.214 | 0.181 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 61 | 26 | 0 | 83 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 2.35 | 1.00 | 0.00 | 3.19 | 1.00 |
time (sec) |
N/A | 0.298 | 0.061 | 0.702 | 0.249 | 0.110 | 1.820 | 0.000 | 0.236 | 0.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 23 | 25 | 60 | 26 | 25 | 81 | 25 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 2.40 | 1.04 | 1.00 | 3.24 | 1.00 |
time (sec) |
N/A | 0.249 | 0.095 | 0.214 | 0.269 | 0.106 | 2.128 | 0.381 | 0.225 | 0.182 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 64 | 27 | 0 | 83 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.29 | 0.96 | 0.00 | 2.96 | 1.00 |
time (sec) |
N/A | 0.342 | 6.906 | 2.043 | 0.263 | 0.093 | 3.795 | 0.000 | 0.206 | 0.203 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 68 | 29 | 28 | 87 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.43 | 1.04 | 1.00 | 3.11 | 1.00 |
time (sec) |
N/A | 0.341 | 6.054 | 1.072 | 0.257 | 0.106 | 2.626 | 3.574 | 0.235 | 0.228 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 86 | 27 | 28 | 125 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 3.07 | 0.96 | 1.00 | 4.46 | 1.00 |
time (sec) |
N/A | 0.337 | 4.812 | 1.441 | 0.327 | 0.091 | 1.914 | 2.747 | 0.203 | 0.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 26 | 84 | 26 | 0 | 123 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 3.23 | 1.00 | 0.00 | 4.73 | 1.00 |
time (sec) |
N/A | 0.303 | 0.067 | 1.224 | 0.272 | 0.107 | 1.999 | 0.000 | 0.206 | 0.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 23 | 25 | 83 | 26 | 25 | 121 | 25 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 3.32 | 1.04 | 1.00 | 4.84 | 1.00 |
time (sec) |
N/A | 0.252 | 0.100 | 0.986 | 0.260 | 0.097 | 2.184 | 0.917 | 0.201 | 0.166 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 85 | 27 | 0 | 123 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 3.04 | 0.96 | 0.00 | 4.39 | 1.00 |
time (sec) |
N/A | 0.353 | 5.094 | 3.375 | 0.273 | 0.112 | 4.594 | 0.000 | 0.215 | 0.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 89 | 29 | 28 | 127 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 3.18 | 1.04 | 1.00 | 4.54 | 1.00 |
time (sec) |
N/A | 0.348 | 9.434 | 2.740 | 0.288 | 0.128 | 3.054 | 7.203 | 0.224 | 0.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 45 | 0 | 0 | 97 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.61 | 0.00 | 0.00 | 3.46 | 1.00 |
time (sec) |
N/A | 0.362 | 0.928 | 1.641 | 0.366 | 0.114 | 0.000 | 0.000 | 0.226 | 0.182 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 38 | 27 | 0 | 63 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.36 | 0.96 | 0.00 | 2.25 | 1.00 |
time (sec) |
N/A | 0.346 | 0.516 | 1.539 | 0.296 | 0.098 | 13.205 | 0.000 | 0.214 | 0.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 28 | 27 | 0 | 27 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.00 | 0.96 | 0.00 | 0.96 | 1.00 |
time (sec) |
N/A | 0.298 | 0.101 | 1.542 | 0.231 | 0.111 | 0.704 | 0.000 | 0.194 | 0.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 50 | 27 | 28 | 39 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 1.79 | 0.96 | 1.00 | 1.39 | 1.00 |
time (sec) |
N/A | 0.299 | 0.806 | 0.977 | 0.220 | 0.106 | 0.881 | 0.304 | 0.199 | 0.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 63 | 27 | 28 | 85 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 2.25 | 0.96 | 1.00 | 3.04 | 1.00 |
time (sec) |
N/A | 0.311 | 1.173 | 1.197 | 0.280 | 0.108 | 9.720 | 0.528 | 0.202 | 0.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 28 | 86 | 27 | 28 | 125 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.00 | 3.07 | 0.96 | 1.00 | 4.46 | 1.00 |
time (sec) |
N/A | 0.325 | 1.739 | 1.278 | 0.273 | 0.100 | 16.330 | 1.081 | 0.212 | 0.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 26 | 22 | 24 | 36 | 24 | 24 | 25 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.50 | 1.00 | 1.00 | 1.04 | 1.00 |
time (sec) |
N/A | 0.257 | 0.355 | 0.464 | 0.231 | 0.102 | 0.646 | 0.274 | 0.214 | 0.166 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 186 | 59 | 0 | 0 | 139 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 6.64 | 2.11 | 0.00 | 0.00 | 4.96 | 1.00 |
time (sec) |
N/A | 0.309 | 0.994 | 2.085 | 2.029 | 0.122 | 0.000 | 0.000 | 0.242 | 0.220 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 161 | 52 | 29 | 0 | 91 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 5.75 | 1.86 | 1.04 | 0.00 | 3.25 | 1.00 |
time (sec) |
N/A | 0.310 | 0.546 | 2.011 | 1.576 | 0.122 | 31.864 | 0.000 | 0.232 | 0.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 138 | 42 | 29 | 0 | 41 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 4.93 | 1.50 | 1.04 | 0.00 | 1.46 | 1.00 |
time (sec) |
N/A | 0.297 | 0.105 | 1.804 | 1.250 | 0.106 | 1.504 | 0.000 | 0.242 | 0.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 112 | 80 | 29 | 28 | 71 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 4.00 | 2.86 | 1.04 | 1.00 | 2.54 | 1.00 |
time (sec) |
N/A | 0.405 | 0.820 | 0.885 | 0.665 | 0.094 | 2.740 | 0.422 | 0.204 | 0.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 218 | 106 | 29 | 28 | 141 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 7.79 | 3.79 | 1.04 | 1.00 | 5.04 | 1.00 |
time (sec) |
N/A | 0.308 | 1.189 | 1.181 | 1.120 | 0.108 | 73.211 | 0.931 | 0.208 | 0.198 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 278 | 144 | 29 | 28 | 212 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 9.93 | 5.14 | 1.04 | 1.00 | 7.57 | 1.00 |
time (sec) |
N/A | 0.318 | 1.761 | 1.296 | 1.292 | 0.103 | 74.329 | 2.240 | 0.196 | 0.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 292 | 175 | 340 | 0 | 0 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.36 | 0.82 | 1.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.924 | 0.362 | 0.224 | 0.000 | 0.000 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 194 | 82 | 136 | 0 | 0 | 0 | 563 | 41 | 0 |
N.S. |
1 | 2.06 | 0.87 | 1.45 | 0.00 | 0.00 | 0.00 | 5.99 | 0.44 | 0.00 |
time (sec) |
N/A | 1.165 | 0.248 | 0.355 | 0.000 | 0.000 | 0.000 | 0.221 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 183 | 125 | 223 | 0 | 0 | 0 | 608 | 39 | 0 |
N.S. |
1 | 1.22 | 0.83 | 1.49 | 0.00 | 0.00 | 0.00 | 4.05 | 0.26 | 0.00 |
time (sec) |
N/A | 1.130 | 0.224 | 0.185 | 0.000 | 0.000 | 0.000 | 0.221 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 83 | 72 | 134 | 0 | 0 | 0 | 290 | 38 | 0 |
N.S. |
1 | 0.97 | 0.84 | 1.56 | 0.00 | 0.00 | 0.00 | 3.37 | 0.44 | 0.00 |
time (sec) |
N/A | 0.698 | 0.145 | 0.221 | 0.000 | 0.000 | 0.000 | 0.211 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 128 | 43 | 27 | 0 | 42 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 4.57 | 1.54 | 0.96 | 0.00 | 1.50 | 1.00 |
time (sec) |
N/A | 1.076 | 8.288 | 1.251 | 0.655 | 0.132 | 1.018 | 0.000 | 0.239 | 0.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 126 | 49 | 29 | 28 | 171 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 4.50 | 1.75 | 1.04 | 1.00 | 6.11 | 1.00 |
time (sec) |
N/A | 0.445 | 1.682 | 0.847 | 0.538 | 0.109 | 0.977 | 0.599 | 0.231 | 0.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 135 | 49 | 29 | 0 | 48 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 4.82 | 1.75 | 1.04 | 0.00 | 1.71 | 1.00 |
time (sec) |
N/A | 0.342 | 10.740 | 5.530 | 0.715 | 0.107 | 1.094 | 0.000 | 0.217 | 0.199 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 394 | 399 | 455 | 0 | 0 | 0 | 2065 | 88 | 0 |
N.S. |
1 | 1.42 | 1.44 | 1.64 | 0.00 | 0.00 | 0.00 | 7.43 | 0.32 | 0.00 |
time (sec) |
N/A | 1.387 | 0.722 | 0.397 | 0.000 | 0.000 | 0.000 | 0.255 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 252 | 306 | 364 | 0 | 0 | 0 | 1553 | 88 | 0 |
N.S. |
1 | 1.15 | 1.39 | 1.65 | 0.00 | 0.00 | 0.00 | 7.06 | 0.40 | 0.00 |
time (sec) |
N/A | 0.948 | 0.554 | 0.405 | 0.000 | 0.000 | 0.000 | 0.244 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 291 | 295 | 341 | 0 | 0 | 0 | 1215 | 86 | 0 |
N.S. |
1 | 1.36 | 1.38 | 1.59 | 0.00 | 0.00 | 0.00 | 5.68 | 0.40 | 0.00 |
time (sec) |
N/A | 1.298 | 0.380 | 0.401 | 0.000 | 0.000 | 0.000 | 0.238 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 140 | 122 | 250 | 0 | 0 | 0 | 747 | 85 | 0 |
N.S. |
1 | 0.93 | 0.81 | 1.67 | 0.00 | 0.00 | 0.00 | 4.98 | 0.57 | 0.00 |
time (sec) |
N/A | 0.563 | 0.414 | 0.444 | 0.000 | 0.000 | 0.000 | 0.227 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 146 | 43 | 27 | 0 | 87 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 5.21 | 1.54 | 0.96 | 0.00 | 3.11 | 1.00 |
time (sec) |
N/A | 1.013 | 7.035 | 0.906 | 0.857 | 0.086 | 2.919 | 0.000 | 0.214 | 0.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 146 | 49 | 29 | 28 | 266 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 5.21 | 1.75 | 1.04 | 1.00 | 9.50 | 1.00 |
time (sec) |
N/A | 0.539 | 2.836 | 0.918 | 0.830 | 0.102 | 2.897 | 0.612 | 0.225 | 0.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 153 | 49 | 29 | 0 | 96 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 5.46 | 1.75 | 1.04 | 0.00 | 3.43 | 1.00 |
time (sec) |
N/A | 0.307 | 10.897 | 4.954 | 0.853 | 0.084 | 3.715 | 0.000 | 0.253 | 0.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 494 | 408 | 455 | 0 | 0 | 0 | 2479 | 133 | 0 |
N.S. |
1 | 1.78 | 1.47 | 1.64 | 0.00 | 0.00 | 0.00 | 8.92 | 0.48 | 0.00 |
time (sec) |
N/A | 1.380 | 0.983 | 0.407 | 0.000 | 0.000 | 0.000 | 0.261 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 282 | 402 | 414 | 479 | 0 | 0 | 0 | 2461 | 133 | 0 |
N.S. |
1 | 1.43 | 1.47 | 1.70 | 0.00 | 0.00 | 0.00 | 8.73 | 0.47 | 0.00 |
time (sec) |
N/A | 1.339 | 0.759 | 0.403 | 0.000 | 0.000 | 0.000 | 0.251 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 276 | 391 | 404 | 455 | 0 | 0 | 0 | 2026 | 131 | 0 |
N.S. |
1 | 1.42 | 1.46 | 1.65 | 0.00 | 0.00 | 0.00 | 7.34 | 0.47 | 0.00 |
time (sec) |
N/A | 1.843 | 0.659 | 0.407 | 0.000 | 0.000 | 0.000 | 0.257 | 0.234 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 190 | 311 | 364 | 0 | 0 | 0 | 1394 | 130 | 0 |
N.S. |
1 | 0.88 | 1.43 | 1.68 | 0.00 | 0.00 | 0.00 | 6.42 | 0.60 | 0.00 |
time (sec) |
N/A | 0.742 | 0.563 | 0.449 | 0.000 | 0.000 | 0.000 | 0.232 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 161 | 60 | 27 | 0 | 132 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 5.75 | 2.14 | 0.96 | 0.00 | 4.71 | 1.00 |
time (sec) |
N/A | 1.180 | 8.616 | 0.934 | 0.934 | 0.090 | 7.363 | 0.000 | 0.228 | 0.199 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 162 | 66 | 29 | 28 | 365 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 5.79 | 2.36 | 1.04 | 1.00 | 13.04 | 1.00 |
time (sec) |
N/A | 0.556 | 2.717 | 1.045 | 1.064 | 0.085 | 6.891 | 0.672 | 0.240 | 0.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 169 | 66 | 29 | 0 | 139 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 6.04 | 2.36 | 1.04 | 0.00 | 4.96 | 1.00 |
time (sec) |
N/A | 0.295 | 10.893 | 3.721 | 1.021 | 0.091 | 7.167 | 0.000 | 0.270 | 0.195 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 177 | 157 | 340 | 0 | 0 | 0 | 0 | 64 | 0 |
N.S. |
1 | 0.87 | 0.77 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.652 | 0.233 | 0.480 | 0.000 | 0.000 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 131 | 117 | 250 | 0 | 0 | 0 | 876 | 64 | 0 |
N.S. |
1 | 0.93 | 0.83 | 1.77 | 0.00 | 0.00 | 0.00 | 6.21 | 0.45 | 0.00 |
time (sec) |
N/A | 0.605 | 0.207 | 0.470 | 0.000 | 0.000 | 0.000 | 0.231 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 127 | 113 | 227 | 0 | 0 | 0 | 0 | 64 | 0 |
N.S. |
1 | 0.89 | 0.80 | 1.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.594 | 0.182 | 0.474 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 75 | 70 | 136 | 0 | 0 | 0 | 346 | 64 | 0 |
N.S. |
1 | 0.95 | 0.89 | 1.72 | 0.00 | 0.00 | 0.00 | 4.38 | 0.81 | 0.00 |
time (sec) |
N/A | 0.691 | 0.144 | 0.467 | 0.000 | 0.000 | 0.000 | 0.230 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 68 | 59 | 108 | 0 | 0 | 0 | 200 | 62 | 0 |
N.S. |
1 | 0.94 | 0.82 | 1.50 | 0.00 | 0.00 | 0.00 | 2.78 | 0.86 | 0.00 |
time (sec) |
N/A | 0.571 | 0.104 | 0.437 | 0.000 | 0.000 | 0.000 | 0.221 | 0.242 | 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 | 18 | 18 | 18 | 19 | 18 | 18 | 53 | 18 | 21 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.00 | 2.94 | 1.00 | 1.17 | 1.00 |
time (sec) |
N/A | 0.217 | 0.007 | 0.107 | 0.114 | 0.093 | 1.145 | 0.122 | 0.212 | 0.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 111 | 80 | 29 | 0 | 63 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 3.96 | 2.86 | 1.04 | 0.00 | 2.25 | 1.00 |
time (sec) |
N/A | 0.442 | 4.899 | 0.569 | 0.690 | 0.098 | 1.744 | 0.000 | 0.216 | 0.200 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 120 | 86 | 31 | 28 | 69 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 4.29 | 3.07 | 1.11 | 1.00 | 2.46 | 1.00 |
time (sec) |
N/A | 0.433 | 1.041 | 0.371 | 0.625 | 0.086 | 1.534 | 0.640 | 0.218 | 0.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 205 | 106 | 29 | 0 | 141 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 7.32 | 3.79 | 1.04 | 0.00 | 5.04 | 1.00 |
time (sec) |
N/A | 0.373 | 41.347 | 1.442 | 0.838 | 0.088 | 3.656 | 0.000 | 0.217 | 0.198 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 193 | 106 | 29 | 28 | 309 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 6.89 | 3.79 | 1.04 | 1.00 | 11.04 | 1.00 |
time (sec) |
N/A | 0.507 | 4.712 | 1.056 | 0.617 | 0.109 | 3.454 | 1.720 | 0.225 | 0.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 24 | 198 | 104 | 27 | 0 | 139 | 26 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 7.62 | 4.00 | 1.04 | 0.00 | 5.35 | 1.00 |
time (sec) |
N/A | 0.312 | 36.722 | 0.400 | 0.712 | 0.090 | 3.610 | 0.000 | 0.232 | 0.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 23 | 192 | 103 | 27 | 25 | 137 | 25 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 7.68 | 4.12 | 1.08 | 1.00 | 5.48 | 1.00 |
time (sec) |
N/A | 0.402 | 1.872 | 0.398 | 0.621 | 0.135 | 4.039 | 0.792 | 0.206 | 0.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 209 | 108 | 29 | 0 | 140 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 7.46 | 3.86 | 1.04 | 0.00 | 5.00 | 1.00 |
time (sec) |
N/A | 0.346 | 34.177 | 5.811 | 0.924 | 0.138 | 6.368 | 0.000 | 0.211 | 0.213 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 26 | 218 | 114 | 31 | 28 | 146 | 28 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 7.79 | 4.07 | 1.11 | 1.00 | 5.21 | 1.00 |
time (sec) |
N/A | 0.353 | 22.551 | 1.496 | 0.859 | 0.087 | 5.609 | 17.741 | 0.226 | 0.203 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 0 | 38 | 22 | 0 | 73 | 15 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 2.38 | 1.38 | 0.00 | 4.56 | 0.94 | 0.00 |
time (sec) |
N/A | 0.311 | 0.199 | 0.000 | 0.476 | 0.078 | 0.000 | 0.164 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 507 | 287 | 304 | 0 | 0 | 0 | 0 | 86 | 0 |
N.S. |
1 | 2.02 | 1.14 | 1.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 1.510 | 0.354 | 0.788 | 0.000 | 0.000 | 0.000 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 591 | 585 | 514 | 447 | 0 | 0 | 0 | 0 | 86 | 0 |
N.S. |
1 | 0.99 | 0.87 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 1.533 | 0.537 | 0.947 | 0.000 | 0.000 | 0.000 | 0.000 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 241 | 285 | 276 | 303 | 0 | 0 | 0 | 0 | 84 | 0 |
N.S. |
1 | 1.18 | 1.15 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 1.638 | 0.210 | 0.792 | 0.000 | 0.000 | 0.000 | 0.000 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 256 | 348 | 304 | 0 | 0 | 0 | 0 | 1522 | 0 |
N.S. |
1 | 1.01 | 1.38 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 6.02 | 0.00 |
time (sec) |
N/A | 0.738 | 0.566 | 0.273 | 0.000 | 0.000 | 0.000 | 0.000 | 0.491 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 25 | 30 | 0 | 87 | 0 | 85 | 27 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.11 | 0.00 | 3.22 | 0.00 | 3.15 | 1.00 |
time (sec) |
N/A | 1.641 | 0.391 | 0.767 | 0.776 | 0.000 | 4.028 | 0.000 | 0.221 | 0.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 29 | 25 | 30 | 0 | 94 | 29 | 250 | 27 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.11 | 0.00 | 3.48 | 1.07 | 9.26 | 1.00 |
time (sec) |
N/A | 1.585 | 3.537 | 0.804 | 0.792 | 0.000 | 5.286 | 0.808 | 0.304 | 0.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 485 | 605 | 540 | 591 | 0 | 0 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.25 | 1.11 | 1.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 1.801 | 1.822 | 1.344 | 0.000 | 0.000 | 0.000 | 0.000 | 0.333 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 511 | 803 | 686 | 594 | 0 | 0 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.57 | 1.34 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 2.076 | 0.987 | 1.318 | 0.000 | 0.000 | 0.000 | 0.000 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 373 | 603 | 410 | 449 | 0 | 0 | 0 | 0 | 129 | 0 |
N.S. |
1 | 1.62 | 1.10 | 1.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 2.239 | 0.493 | 0.885 | 0.000 | 0.000 | 0.000 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 390 | 366 | 522 | 451 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 1.34 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.912 | 0.353 | 0.362 | 0.000 | 0.000 | 0.000 | 0.000 | 0.471 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 27 | 30 | 0 | 133 | 0 | 130 | 29 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.03 | 0.00 | 4.59 | 0.00 | 4.48 | 1.00 |
time (sec) |
N/A | 2.279 | 0.743 | 1.456 | 1.087 | 0.000 | 5.317 | 0.000 | 0.270 | 0.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 27 | 30 | 0 | 143 | 30 | 347 | 29 |
N.S. |
1 | 1.00 | 1.07 | 0.93 | 1.03 | 0.00 | 4.93 | 1.03 | 11.97 | 1.00 |
time (sec) |
N/A | 2.472 | 10.221 | 0.632 | 1.071 | 0.000 | 5.129 | 1.204 | 0.342 | 0.218 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | C | F(-2) | F(-2) | F | A | B | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 0 | 47 | 0 | 0 | 0 | 46 | 29 | 0 |
N.S. |
1 | 1.00 | 0.00 | 1.12 | 0.00 | 0.00 | 0.00 | 1.10 | 0.69 | 0.00 |
time (sec) |
N/A | 0.342 | 0.000 | 1.568 | 0.000 | 0.000 | 0.000 | 0.281 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 53 | 20 | 0 | 0 | 0 | 37 | 30 | 0 |
N.S. |
1 | 1.00 | 2.12 | 0.80 | 0.00 | 0.00 | 0.00 | 1.48 | 1.20 | 0.00 |
time (sec) |
N/A | 0.350 | 0.053 | 0.669 | 0.000 | 0.000 | 0.000 | 0.145 | 0.228 | 0.000 |