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 | A | A | B | B |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 63 | 65 | 60 | 62 | 61 | 88 | 74 | 61 | 75 |
N.S. |
1 | 0.94 | 0.97 | 0.90 | 0.93 | 0.91 | 1.31 | 1.10 | 0.91 | 1.12 |
time (sec) |
N/A | 0.343 | 0.196 | 0.150 | 0.038 | 0.071 | 0.376 | 0.120 | 0.178 | 23.216 |
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 | 30 | 30 | 30 | 31 | 29 | 37 | 41 | 31 | 37 | 31 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 0.97 | 1.23 | 1.37 | 1.03 | 1.23 | 1.03 |
time (sec) |
N/A | 0.273 | 0.049 | 0.034 | 0.034 | 0.077 | 0.189 | 0.116 | 0.184 | 23.330 |
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 | 40 | 52 | 55 | 44 | 59 | 44 | 51 | 72 | 44 | 44 |
N.S. |
1 | 1.30 | 1.38 | 1.10 | 1.48 | 1.10 | 1.28 | 1.80 | 1.10 | 1.10 |
time (sec) |
N/A | 0.328 | 0.196 | 0.042 | 0.043 | 0.071 | 2.031 | 0.117 | 0.155 | 22.671 |
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 | 74 | 73 | 107 | 74 | 94 | 100 | 0 | 108 | 131 | 80 |
N.S. |
1 | 0.99 | 1.45 | 1.00 | 1.27 | 1.35 | 0.00 | 1.46 | 1.77 | 1.08 |
time (sec) |
N/A | 0.380 | 0.276 | 0.092 | 0.043 | 0.078 | 0.000 | 0.116 | 0.181 | 22.731 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 95 | 89 | 82 | 123 | 203 | 0 | 90 | 95 | 0 |
N.S. |
1 | 0.81 | 0.75 | 0.69 | 1.04 | 1.72 | 0.00 | 0.76 | 0.81 | 0.00 |
time (sec) |
N/A | 0.385 | 0.308 | 0.086 | 0.131 | 0.082 | 0.000 | 0.124 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 69 | 68 | 62 | 101 | 162 | 0 | 66 | 19 | 0 |
N.S. |
1 | 0.85 | 0.84 | 0.77 | 1.25 | 2.00 | 0.00 | 0.81 | 0.23 | 0.00 |
time (sec) |
N/A | 0.354 | 0.247 | 0.066 | 0.142 | 0.077 | 0.000 | 0.116 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 46 | 41 | 67 | 123 | 0 | 45 | 21 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 1.46 | 2.67 | 0.00 | 0.98 | 0.46 | 0.00 |
time (sec) |
N/A | 0.337 | 0.229 | 0.065 | 0.141 | 0.083 | 0.000 | 0.122 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 72 | 72 | 65 | 104 | 247 | 0 | 87 | 60 | 0 |
N.S. |
1 | 0.86 | 0.86 | 0.77 | 1.24 | 2.94 | 0.00 | 1.04 | 0.71 | 0.00 |
time (sec) |
N/A | 0.356 | 0.324 | 0.016 | 0.160 | 0.085 | 0.000 | 0.133 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 103 | 94 | 87 | 123 | 395 | 0 | 107 | 82 | 0 |
N.S. |
1 | 0.84 | 0.76 | 0.71 | 1.00 | 3.21 | 0.00 | 0.87 | 0.67 | 0.00 |
time (sec) |
N/A | 0.385 | 0.443 | 0.016 | 0.140 | 0.087 | 0.000 | 0.164 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 170 | 213 | 176 | 215 | 180 | 0 | 185 | 100 | 0 |
N.S. |
1 | 0.87 | 1.09 | 0.90 | 1.10 | 0.92 | 0.00 | 0.94 | 0.51 | 0.00 |
time (sec) |
N/A | 0.463 | 0.522 | 0.102 | 0.134 | 0.083 | 0.000 | 0.161 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 145 | 179 | 154 | 192 | 182 | 0 | 158 | 20 | 0 |
N.S. |
1 | 0.91 | 1.12 | 0.96 | 1.20 | 1.14 | 0.00 | 0.99 | 0.12 | 0.00 |
time (sec) |
N/A | 0.444 | 0.532 | 0.074 | 0.128 | 0.075 | 0.000 | 0.132 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 144 | 179 | 154 | 193 | 161 | 0 | 157 | 20 | 0 |
N.S. |
1 | 0.91 | 1.13 | 0.97 | 1.21 | 1.01 | 0.00 | 0.99 | 0.13 | 0.00 |
time (sec) |
N/A | 0.436 | 0.406 | 0.053 | 0.130 | 0.088 | 0.000 | 0.130 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 119 | 148 | 129 | 159 | 373 | 0 | 138 | 20 | 0 |
N.S. |
1 | 0.96 | 1.19 | 1.04 | 1.28 | 3.01 | 0.00 | 1.11 | 0.16 | 0.00 |
time (sec) |
N/A | 0.414 | 0.491 | 0.067 | 0.135 | 0.091 | 0.000 | 0.140 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 120 | 146 | 130 | 160 | 170 | 0 | 137 | 20 | 0 |
N.S. |
1 | 0.96 | 1.17 | 1.04 | 1.28 | 1.36 | 0.00 | 1.10 | 0.16 | 0.00 |
time (sec) |
N/A | 0.413 | 0.391 | 0.050 | 0.143 | 0.081 | 0.000 | 0.168 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 148 | 174 | 159 | 195 | 560 | 0 | 278 | 57 | 0 |
N.S. |
1 | 0.92 | 1.08 | 0.99 | 1.21 | 3.48 | 0.00 | 1.73 | 0.35 | 0.00 |
time (sec) |
N/A | 0.438 | 0.511 | 0.017 | 0.149 | 0.086 | 0.000 | 0.155 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 151 | 174 | 159 | 196 | 273 | 0 | 278 | 57 | 0 |
N.S. |
1 | 0.92 | 1.06 | 0.97 | 1.20 | 1.66 | 0.00 | 1.70 | 0.35 | 0.00 |
time (sec) |
N/A | 0.448 | 0.567 | 0.017 | 0.152 | 0.081 | 0.000 | 0.144 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 179 | 192 | 181 | 214 | 789 | 0 | 298 | 97 | 0 |
N.S. |
1 | 0.90 | 0.96 | 0.90 | 1.07 | 3.94 | 0.00 | 1.49 | 0.48 | 0.00 |
time (sec) |
N/A | 0.458 | 0.782 | 0.019 | 0.133 | 0.095 | 0.000 | 0.195 | 0.180 | 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 | 69 | 68 | 68 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.99 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.341 | 0.232 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | B | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 130 | 392 | 282 | 267 | 496 | 5716 | 401 | 225 |
N.S. |
1 | 1.00 | 0.85 | 2.56 | 1.84 | 1.75 | 3.24 | 37.36 | 2.62 | 1.47 |
time (sec) |
N/A | 0.695 | 0.618 | 0.456 | 0.056 | 0.077 | 1.686 | 0.200 | 0.174 | 23.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 91 | 163 | 171 | 166 | 294 | 2716 | 238 | 135 |
N.S. |
1 | 1.00 | 0.79 | 1.42 | 1.49 | 1.44 | 2.56 | 23.62 | 2.07 | 1.17 |
time (sec) |
N/A | 0.559 | 0.505 | 0.191 | 0.085 | 0.076 | 0.714 | 0.163 | 0.195 | 22.954 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 73 | 84 | 85 | 87 | 144 | 1101 | 112 | 72 |
N.S. |
1 | 1.00 | 0.95 | 1.09 | 1.10 | 1.13 | 1.87 | 14.30 | 1.45 | 0.94 |
time (sec) |
N/A | 0.415 | 0.371 | 0.089 | 0.053 | 0.083 | 0.378 | 0.159 | 0.166 | 22.852 |
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 | 30 | 30 | 30 | 31 | 29 | 37 | 41 | 31 | 37 | 31 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 0.97 | 1.23 | 1.37 | 1.03 | 1.23 | 1.03 |
time (sec) |
N/A | 0.261 | 0.023 | 0.000 | 0.036 | 0.069 | 0.198 | 0.115 | 0.178 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 56 | 0 | 0 | 53 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.78 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.499 | 0.474 | 0.000 | 0.000 | 0.072 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 78 | 0 | 0 | 90 | 0 | 0 | 93 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.90 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.571 | 0.594 | 0.000 | 0.000 | 0.074 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 111 | 0 | 0 | 162 | 0 | 0 | 186 | 0 |
N.S. |
1 | 1.00 | 0.76 | 0.00 | 0.00 | 1.10 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.686 | 0.636 | 0.000 | 0.000 | 0.100 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | B | C | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 322 | 322 | 239 | 739 | 568 | 482 | 913 | 12013 | 758 | 438 |
N.S. |
1 | 1.00 | 0.74 | 2.30 | 1.76 | 1.50 | 2.84 | 37.31 | 2.35 | 1.36 |
time (sec) |
N/A | 1.170 | 1.292 | 1.158 | 0.074 | 0.078 | 4.359 | 0.238 | 0.170 | 23.231 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | C | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 239 | 171 | 424 | 347 | 287 | 527 | 5675 | 435 | 267 |
N.S. |
1 | 1.00 | 0.72 | 1.77 | 1.45 | 1.20 | 2.21 | 23.74 | 1.82 | 1.12 |
time (sec) |
N/A | 0.893 | 0.778 | 0.463 | 0.092 | 0.080 | 1.710 | 0.195 | 0.211 | 23.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 117 | 174 | 178 | 139 | 258 | 2284 | 191 | 146 |
N.S. |
1 | 1.00 | 0.75 | 1.12 | 1.14 | 0.89 | 1.65 | 14.64 | 1.22 | 0.94 |
time (sec) |
N/A | 0.600 | 0.595 | 0.215 | 0.061 | 0.074 | 0.813 | 0.159 | 0.165 | 23.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 63 | 65 | 60 | 62 | 61 | 88 | 74 | 61 | 75 |
N.S. |
1 | 0.94 | 0.97 | 0.90 | 0.93 | 0.91 | 1.31 | 1.10 | 0.91 | 1.12 |
time (sec) |
N/A | 0.346 | 0.018 | 0.000 | 0.053 | 0.075 | 0.305 | 0.122 | 0.170 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 134 | 108 | 0 | 0 | 101 | 0 | 0 | 73 | 0 |
N.S. |
1 | 1.00 | 0.81 | 0.00 | 0.00 | 0.75 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.728 | 0.733 | 0.000 | 0.000 | 0.082 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 202 | 136 | 0 | 0 | 177 | 0 | 0 | 713 | 0 |
N.S. |
1 | 1.00 | 0.67 | 0.00 | 0.00 | 0.88 | 0.00 | 0.00 | 3.53 | 0.00 |
time (sec) |
N/A | 0.911 | 1.056 | 0.000 | 0.000 | 0.073 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 286 | 286 | 217 | 0 | 0 | 318 | 0 | 0 | 1407 | 0 |
N.S. |
1 | 1.00 | 0.76 | 0.00 | 0.00 | 1.11 | 0.00 | 0.00 | 4.92 | 0.00 |
time (sec) |
N/A | 1.139 | 0.979 | 0.000 | 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 | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 219 | 166 | 3075 | 480 | 429 | 0 | 0 | 154 | 0 |
N.S. |
1 | 1.14 | 0.86 | 16.02 | 2.50 | 2.23 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 1.516 | 1.136 | 0.318 | 0.194 | 0.076 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 161 | 121 | 1124 | 303 | 280 | 0 | 0 | 116 | 0 |
N.S. |
1 | 1.11 | 0.83 | 7.75 | 2.09 | 1.93 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 1.144 | 0.817 | 0.146 | 0.111 | 0.083 | 0.000 | 0.000 | 0.214 | 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 | 98 | 103 | 74 | 456 | 0 | 149 | 0 | 0 | 76 | 0 |
N.S. |
1 | 1.05 | 0.76 | 4.65 | 0.00 | 1.52 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.715 | 0.410 | 0.075 | 0.000 | 0.072 | 0.000 | 0.000 | 0.203 | 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 | 40 | 52 | 55 | 44 | 59 | 44 | 51 | 72 | 44 | 44 |
N.S. |
1 | 1.30 | 1.38 | 1.10 | 1.48 | 1.10 | 1.28 | 1.80 | 1.10 | 1.10 |
time (sec) |
N/A | 0.321 | 0.013 | 0.000 | 0.056 | 0.081 | 1.897 | 0.111 | 0.196 | 0.002 |
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 | 25 | 26 | 33 | 22 | 27 | 43 | 27 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.04 | 1.32 | 0.88 | 1.08 | 1.72 | 1.08 |
time (sec) |
N/A | 0.458 | 2.811 | 0.043 | 0.097 | 0.073 | 1.837 | 0.122 | 0.194 | 22.683 |
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 | 25 | 26 | 57 | 24 | 27 | 79 | 27 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.04 | 2.28 | 0.96 | 1.08 | 3.16 | 1.08 |
time (sec) |
N/A | 0.451 | 0.622 | 0.060 | 0.134 | 0.072 | 4.092 | 0.159 | 0.196 | 22.647 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | B | A | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 388 | 453 | 0 | 3319 | 699 | 1469 | 0 | 0 | 537 | 0 |
N.S. |
1 | 1.17 | 0.00 | 8.55 | 1.80 | 3.79 | 0.00 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 4.283 | 0.000 | 0.342 | 0.153 | 0.119 | 0.000 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | B | A | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 294 | 337 | 0 | 1650 | 468 | 875 | 0 | 0 | 400 | 0 |
N.S. |
1 | 1.15 | 0.00 | 5.61 | 1.59 | 2.98 | 0.00 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 3.024 | 0.000 | 0.135 | 0.159 | 0.088 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 211 | 0 | 591 | 0 | 409 | 0 | 0 | 257 | 0 |
N.S. |
1 | 1.10 | 0.00 | 3.09 | 0.00 | 2.14 | 0.00 | 0.00 | 1.35 | 0.00 |
time (sec) |
N/A | 1.614 | 0.000 | 0.156 | 0.000 | 0.080 | 0.000 | 0.000 | 0.190 | 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 | 74 | 73 | 107 | 74 | 94 | 100 | 0 | 108 | 131 | 80 |
N.S. |
1 | 0.99 | 1.45 | 1.00 | 1.27 | 1.35 | 0.00 | 1.46 | 1.77 | 1.08 |
time (sec) |
N/A | 0.373 | 0.045 | 0.000 | 0.048 | 0.077 | 0.000 | 0.123 | 0.163 | 0.002 |
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 | 25 | 192 | 67 | 24 | 27 | 90 | 27 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 7.68 | 2.68 | 0.96 | 1.08 | 3.60 | 1.08 |
time (sec) |
N/A | 0.457 | 1.328 | 0.063 | 0.139 | 0.073 | 4.199 | 0.131 | 0.198 | 23.861 |
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 | 25 | 280 | 108 | 26 | 27 | 157 | 27 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 11.20 | 4.32 | 1.04 | 1.08 | 6.28 | 1.08 |
time (sec) |
N/A | 0.438 | 1.254 | 0.004 | 0.235 | 0.069 | 25.442 | 0.182 | 0.197 | 23.605 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | F | F | F(-2) | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 535 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 495 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | F | F | F(-2) | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 451 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 364 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.251 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 367 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 335 | 335 | 0 | 0 | 0 | 0 | 0 | 0 | 126 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 1.362 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-2) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 421 | 420 | 0 | 0 | 0 | 0 | 0 | 0 | 170 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 1.652 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-2) | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 505 | 503 | 0 | 0 | 0 | 0 | 0 | 0 | 214 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 1.961 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.238 | 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 | F(-1) | 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 | 25 | 26 | 28 | 0 | 27 | 28 | 27 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.04 | 1.12 | 0.00 | 1.08 | 1.12 | 1.08 |
time (sec) |
N/A | 0.323 | 0.501 | 0.029 | 0.131 | 0.082 | 0.000 | 0.379 | 0.182 | 23.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 228 | 0 | 0 | 0 | 193 | 0 | 0 | 325 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.905 | 0.000 | 0.000 | 0.000 | 0.081 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 112 | 0 | 0 | 112 | 0 | 0 | 175 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.97 | 0.00 | 0.00 | 1.51 | 0.00 |
time (sec) |
N/A | 0.543 | 2.086 | 0.000 | 0.000 | 0.072 | 0.000 | 0.000 | 0.190 | 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 | 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 | 25 | 26 | 28 | 22 | 27 | 28 | 27 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.04 | 1.12 | 0.88 | 1.08 | 1.12 | 1.08 |
time (sec) |
N/A | 0.326 | 0.707 | 0.013 | 0.080 | 0.067 | 3.123 | 0.125 | 0.169 | 22.831 |
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 | 25 | 26 | 50 | 24 | 27 | 50 | 27 |
N.S. |
1 | 1.00 | 1.08 | 1.00 | 1.04 | 2.00 | 0.96 | 1.08 | 2.00 | 1.08 |
time (sec) |
N/A | 0.324 | 0.851 | 0.008 | 0.106 | 0.070 | 37.454 | 0.137 | 0.214 | 22.934 |
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 | 12 | 12 | 12 | 8 | 9 | 9 | 8 | 9 | 10 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.75 | 0.75 | 0.67 | 0.75 | 0.83 | 0.75 |
time (sec) |
N/A | 0.257 | 0.024 | 0.023 | 0.030 | 0.066 | 0.036 | 0.116 | 0.176 | 0.051 |
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 | 12 | 12 | 12 | 12 | 11 | 11 | 8 | 12 | 12 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.92 | 0.92 | 0.67 | 1.00 | 1.00 | 0.92 |
time (sec) |
N/A | 0.263 | 0.023 | 0.018 | 0.045 | 0.065 | 0.047 | 0.125 | 0.170 | 22.900 |
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 | 24 | 24 | 24 | 23 | 22 | 22 | 19 | 23 | 24 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.92 | 0.92 | 0.79 | 0.96 | 1.00 | 0.92 |
time (sec) |
N/A | 0.369 | 0.039 | 0.035 | 0.030 | 0.071 | 0.073 | 0.110 | 0.188 | 23.077 |
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 | 19 | 19 | 19 | 19 | 18 | 18 | 14 | 19 | 19 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.95 | 0.95 | 0.74 | 1.00 | 1.00 | 0.95 |
time (sec) |
N/A | 0.290 | 0.033 | 0.019 | 0.045 | 0.086 | 0.053 | 0.115 | 0.169 | 0.052 |
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 | 20 | 20 | 19 | 20 | 19 | 22 | 56 | 19 | 25 | 19 |
N.S. |
1 | 1.00 | 0.95 | 1.00 | 0.95 | 1.10 | 2.80 | 0.95 | 1.25 | 0.95 |
time (sec) |
N/A | 0.265 | 0.053 | 0.058 | 0.030 | 0.078 | 0.350 | 0.119 | 0.199 | 23.289 |
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 | 32 | 32 | 31 | 31 | 30 | 36 | 114 | 30 | 41 | 44 |
N.S. |
1 | 1.00 | 0.97 | 0.97 | 0.94 | 1.12 | 3.56 | 0.94 | 1.28 | 1.38 |
time (sec) |
N/A | 0.372 | 0.104 | 0.198 | 0.030 | 0.076 | 2.392 | 0.117 | 0.179 | 23.343 |
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 | 27 | 27 | 26 | 27 | 26 | 33 | 107 | 26 | 36 | 26 |
N.S. |
1 | 1.00 | 0.96 | 1.00 | 0.96 | 1.22 | 3.96 | 0.96 | 1.33 | 0.96 |
time (sec) |
N/A | 0.299 | 0.070 | 0.049 | 0.030 | 0.077 | 5.333 | 0.110 | 0.176 | 23.066 |
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 | 16 | 16 | 16 | 17 | 16 | 16 | 12 | 17 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.00 | 0.75 | 1.06 | 1.00 | 1.00 |
time (sec) |
N/A | 0.272 | 0.043 | 0.026 | 0.031 | 0.073 | 0.052 | 0.107 | 0.185 | 22.983 |
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 | 28 | 28 | 28 | 33 | 28 | 28 | 24 | 30 | 28 | 28 |
N.S. |
1 | 1.00 | 1.00 | 1.18 | 1.00 | 1.00 | 0.86 | 1.07 | 1.00 | 1.00 |
time (sec) |
N/A | 0.381 | 0.081 | 0.047 | 0.027 | 0.072 | 0.178 | 0.115 | 0.175 | 23.007 |
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 | 23 | 23 | 23 | 24 | 23 | 23 | 17 | 24 | 23 | 23 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.00 | 1.00 | 0.74 | 1.04 | 1.00 | 1.00 |
time (sec) |
N/A | 0.300 | 0.058 | 0.025 | 0.027 | 0.064 | 0.055 | 0.116 | 0.184 | 23.010 |
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 | 24 | 24 | 24 | 25 | 24 | 28 | 82 | 24 | 29 | 24 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.00 | 1.17 | 3.42 | 1.00 | 1.21 | 1.00 |
time (sec) |
N/A | 0.275 | 0.076 | 0.084 | 0.032 | 0.076 | 0.412 | 0.111 | 0.175 | 23.067 |
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 | 36 | 36 | 35 | 48 | 36 | 50 | 71 | 36 | 45 | 55 |
N.S. |
1 | 1.00 | 0.97 | 1.33 | 1.00 | 1.39 | 1.97 | 1.00 | 1.25 | 1.53 |
time (sec) |
N/A | 0.368 | 0.147 | 0.385 | 0.026 | 0.083 | 0.996 | 0.122 | 0.178 | 22.986 |
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 | 31 | 31 | 30 | 32 | 31 | 39 | 299 | 31 | 40 | 52 |
N.S. |
1 | 1.00 | 0.97 | 1.03 | 1.00 | 1.26 | 9.65 | 1.00 | 1.29 | 1.68 |
time (sec) |
N/A | 0.299 | 0.103 | 0.075 | 0.031 | 0.074 | 1.028 | 0.125 | 0.187 | 23.599 |
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 | 25 | 25 | 25 | 25 | 24 | 29 | 80 | 24 | 32 | 24 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.96 | 1.16 | 3.20 | 0.96 | 1.28 | 0.96 |
time (sec) |
N/A | 0.291 | 0.197 | 0.135 | 0.027 | 0.072 | 0.675 | 0.114 | 0.165 | 23.806 |
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 | 37 | 37 | 36 | 31 | 24 | 29 | 0 | 24 | 32 | 24 |
N.S. |
1 | 1.00 | 0.97 | 0.84 | 0.65 | 0.78 | 0.00 | 0.65 | 0.86 | 0.65 |
time (sec) |
N/A | 0.368 | 0.065 | 0.570 | 0.027 | 0.088 | 0.000 | 0.120 | 0.199 | 24.002 |
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 | 41 | 41 | 41 | 42 | 40 | 53 | 90 | 42 | 56 | 74 |
N.S. |
1 | 1.00 | 1.00 | 1.02 | 0.98 | 1.29 | 2.20 | 1.02 | 1.37 | 1.80 |
time (sec) |
N/A | 0.333 | 0.421 | 0.281 | 0.028 | 0.094 | 23.000 | 0.115 | 0.186 | 24.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 0 | 0 | 86 | 88 | 0 | 143 | 47 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 1.08 | 1.10 | 0.00 | 1.79 | 0.59 | 0.00 |
time (sec) |
N/A | 0.534 | 0.000 | 0.000 | 0.068 | 0.083 | 0.000 | 0.252 | 0.171 | 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 | 22 | 22 | 22 | 21 | 20 | 19 | 20 | 21 | 21 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.91 | 0.86 | 0.91 | 0.95 | 0.95 | 0.91 |
time (sec) |
N/A | 0.314 | 0.036 | 0.030 | 0.027 | 0.068 | 0.056 | 0.106 | 0.178 | 23.386 |
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 | 27 | 27 | 26 | 26 | 28 | 31 | 24 | 26 | 43 | 27 |
N.S. |
1 | 1.00 | 0.96 | 0.96 | 1.04 | 1.15 | 0.89 | 0.96 | 1.59 | 1.00 |
time (sec) |
N/A | 0.321 | 0.062 | 0.062 | 0.032 | 0.073 | 0.057 | 0.123 | 0.161 | 0.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 26 | 18 | 61 | 35 | 37 | 20 | 32 | 29 |
N.S. |
1 | 1.00 | 1.24 | 0.86 | 2.90 | 1.67 | 1.76 | 0.95 | 1.52 | 1.38 |
time (sec) |
N/A | 0.274 | 0.049 | 0.096 | 0.028 | 0.064 | 0.068 | 0.110 | 0.181 | 0.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 26 | 21 | 85 | 47 | 51 | 20 | 50 | 53 |
N.S. |
1 | 1.00 | 0.76 | 0.62 | 2.50 | 1.38 | 1.50 | 0.59 | 1.47 | 1.56 |
time (sec) |
N/A | 0.321 | 0.050 | 0.224 | 0.031 | 0.064 | 0.072 | 0.110 | 0.184 | 0.181 |
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 | 31 | 30 | 28 | 26 | 25 | 24 | 27 | 26 | 26 | 24 |
N.S. |
1 | 0.97 | 0.90 | 0.84 | 0.81 | 0.77 | 0.87 | 0.84 | 0.84 | 0.77 |
time (sec) |
N/A | 0.315 | 0.041 | 0.030 | 0.033 | 0.066 | 0.066 | 0.113 | 0.160 | 23.182 |
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 | 37 | 35 | 33 | 32 | 34 | 38 | 32 | 32 | 54 | 34 |
N.S. |
1 | 0.95 | 0.89 | 0.86 | 0.92 | 1.03 | 0.86 | 0.86 | 1.46 | 0.92 |
time (sec) |
N/A | 0.318 | 0.068 | 0.059 | 0.028 | 0.067 | 0.062 | 0.133 | 0.183 | 23.279 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 30 | 20 | 67 | 39 | 41 | 24 | 34 | 31 |
N.S. |
1 | 1.00 | 1.30 | 0.87 | 2.91 | 1.70 | 1.78 | 1.04 | 1.48 | 1.35 |
time (sec) |
N/A | 0.280 | 0.055 | 0.090 | 0.028 | 0.068 | 0.058 | 0.126 | 0.165 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 42 | 30 | 25 | 91 | 51 | 54 | 24 | 54 | 55 |
N.S. |
1 | 1.11 | 0.79 | 0.66 | 2.39 | 1.34 | 1.42 | 0.63 | 1.42 | 1.45 |
time (sec) |
N/A | 0.316 | 0.057 | 0.217 | 0.034 | 0.067 | 0.068 | 0.123 | 0.189 | 23.237 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 44 | 31 | 27 | 32 | 25 | 46 | 32 | 19 | 26 |
N.S. |
1 | 1.05 | 0.74 | 0.64 | 0.76 | 0.60 | 1.10 | 0.76 | 0.45 | 0.62 |
time (sec) |
N/A | 0.329 | 0.066 | 0.020 | 0.027 | 0.070 | 0.441 | 0.115 | 0.182 | 23.174 |
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 | 16 | 22 | 16 | 16 | 15 | 21 | 15 | 17 | 24 | 15 |
N.S. |
1 | 1.38 | 1.00 | 1.00 | 0.94 | 1.31 | 0.94 | 1.06 | 1.50 | 0.94 |
time (sec) |
N/A | 0.288 | 0.019 | 0.036 | 0.033 | 0.065 | 0.039 | 0.107 | 0.174 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 35 | 36 | 32 | 30 | 34 | 39 | 29 | 38 | 30 |
N.S. |
1 | 1.09 | 1.12 | 1.00 | 0.94 | 1.06 | 1.22 | 0.91 | 1.19 | 0.94 |
time (sec) |
N/A | 0.315 | 0.050 | 0.056 | 0.027 | 0.069 | 0.076 | 0.129 | 0.184 | 23.755 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 53 | 49 | 47 | 48 | 71 | 43 | 53 | 44 |
N.S. |
1 | 1.00 | 1.02 | 0.94 | 0.90 | 0.92 | 1.37 | 0.83 | 1.02 | 0.85 |
time (sec) |
N/A | 0.334 | 0.062 | 0.102 | 0.028 | 0.089 | 0.086 | 0.117 | 0.160 | 24.362 |
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 | 40 | 43 | 40 | 42 | 32 | 39 | 34 | 39 | 45 | 38 |
N.S. |
1 | 1.08 | 1.00 | 1.05 | 0.80 | 0.98 | 0.85 | 0.98 | 1.12 | 0.95 |
time (sec) |
N/A | 0.343 | 0.053 | 0.027 | 0.029 | 0.082 | 0.066 | 0.121 | 0.164 | 0.115 |
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 | 61 | 61 | 59 | 59 | 57 | 84 | 61 | 60 | 106 | 86 |
N.S. |
1 | 1.00 | 0.97 | 0.97 | 0.93 | 1.38 | 1.00 | 0.98 | 1.74 | 1.41 |
time (sec) |
N/A | 0.371 | 0.116 | 0.042 | 0.032 | 0.074 | 0.078 | 0.117 | 0.173 | 24.278 |
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 | 83 | 80 | 79 | 73 | 85 | 140 | 95 | 77 | 172 | 104 |
N.S. |
1 | 0.96 | 0.95 | 0.88 | 1.02 | 1.69 | 1.14 | 0.93 | 2.07 | 1.25 |
time (sec) |
N/A | 0.396 | 0.120 | 0.054 | 0.027 | 0.074 | 0.097 | 0.122 | 0.154 | 23.749 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 55 | 50 | 91 | 37 | 179 | 51 | 45 | 55 | 64 |
N.S. |
1 | 1.10 | 1.00 | 1.82 | 0.74 | 3.58 | 1.02 | 0.90 | 1.10 | 1.28 |
time (sec) |
N/A | 0.368 | 0.129 | 0.093 | 0.108 | 0.080 | 0.340 | 0.115 | 0.180 | 23.531 |
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 | 34 | 34 | 34 | 47 | 32 | 32 | 42 | 35 | 33 | 37 |
N.S. |
1 | 1.00 | 1.00 | 1.38 | 0.94 | 0.94 | 1.24 | 1.03 | 0.97 | 1.09 |
time (sec) |
N/A | 0.405 | 0.056 | 0.050 | 0.028 | 0.073 | 0.441 | 0.129 | 0.170 | 23.484 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 70 | 67 | 171 | 68 | 166 | 110 | 69 | 67 | 66 |
N.S. |
1 | 0.80 | 0.76 | 1.94 | 0.77 | 1.89 | 1.25 | 0.78 | 0.76 | 0.75 |
time (sec) |
N/A | 0.356 | 0.173 | 0.086 | 0.111 | 0.083 | 0.626 | 0.130 | 0.158 | 23.583 |
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 | 61 | 50 | 73 | 76 | 65 | 53 | 92 | 58 | 49 | 47 |
N.S. |
1 | 0.82 | 1.20 | 1.25 | 1.07 | 0.87 | 1.51 | 0.95 | 0.80 | 0.77 |
time (sec) |
N/A | 0.371 | 0.635 | 0.059 | 0.035 | 0.072 | 0.528 | 0.115 | 0.198 | 23.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 90 | 85 | 212 | 89 | 211 | 185 | 106 | 85 | 102 |
N.S. |
1 | 0.71 | 0.67 | 1.67 | 0.70 | 1.66 | 1.46 | 0.83 | 0.67 | 0.80 |
time (sec) |
N/A | 0.407 | 0.334 | 0.085 | 0.115 | 0.082 | 0.709 | 0.122 | 0.158 | 23.859 |
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 | 4 | 4 | 4 | 4 | 3 | 3 | 15 | 3 | 4 | 3 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.75 | 0.75 | 3.75 | 0.75 | 1.00 | 0.75 |
time (sec) |
N/A | 0.247 | 0.002 | 0.025 | 0.108 | 0.067 | 0.044 | 0.135 | 0.165 | 0.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 4 | 4 | 4 | 4 | 15 | 15 | 15 | 16 | 17 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 3.75 | 3.75 | 3.75 | 4.00 | 4.25 | 3.75 |
time (sec) |
N/A | 0.253 | 0.003 | 0.023 | 0.030 | 0.067 | 0.046 | 0.115 | 0.177 | 24.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 45 | 34 | 31 | 31 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 1.67 | 1.26 | 1.15 | 1.15 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.423 | 0.132 | 0.023 | 0.033 | 0.067 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 53 | 60 | 51 | 48 | 48 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.32 | 1.50 | 1.28 | 1.20 | 1.20 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.673 | 0.145 | 0.029 | 0.034 | 0.065 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 81 | 89 | 74 | 71 | 71 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.17 | 1.29 | 1.07 | 1.03 | 1.03 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.870 | 0.192 | 0.033 | 0.035 | 0.064 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 53 | 21 | 86 | 24 | 21 | 29 | 21 |
N.S. |
1 | 1.00 | 1.00 | 1.77 | 0.70 | 2.87 | 0.80 | 0.70 | 0.97 | 0.70 |
time (sec) |
N/A | 0.289 | 0.054 | 0.055 | 0.104 | 0.078 | 0.081 | 0.111 | 0.165 | 23.377 |
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 | 110 | 99 | 108 | 134 | 0 | 112 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.90 | 0.98 | 1.22 | 0.00 | 1.02 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.609 | 0.122 | 0.057 | 0.000 | 0.075 | 0.000 | 0.000 | 0.170 | 0.000 |