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 | F | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 194 | 143 | 0 | 0 | 1215 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.16 | 0.86 | 0.00 | 0.00 | 7.28 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.269 | 0.331 | 0.000 | 0.000 | 0.107 | 0.000 | 0.000 | 0.367 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 153 | 127 | 0 | 0 | 691 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.20 | 1.00 | 0.00 | 0.00 | 5.44 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.234 | 0.229 | 0.000 | 0.000 | 0.115 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 119 | 73 | 0 | 0 | 222 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.40 | 0.86 | 0.00 | 0.00 | 2.61 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.202 | 0.094 | 0.000 | 0.000 | 0.110 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 27 | 0 | 42 | 0 | 0 | 38 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.00 | 1.40 | 0.00 | 0.00 | 1.27 | 0.87 |
time (sec) |
N/A | 0.135 | 0.022 | 0.164 | 0.000 | 0.076 | 0.000 | 0.000 | 0.244 | 0.402 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 45 | 54 | 0 | 118 | 0 | 0 | 63 | 71 |
N.S. |
1 | 1.00 | 0.68 | 0.82 | 0.00 | 1.79 | 0.00 | 0.00 | 0.95 | 1.08 |
time (sec) |
N/A | 0.155 | 0.128 | 0.312 | 0.000 | 0.077 | 0.000 | 0.000 | 0.355 | 0.484 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 114 | 75 | 105 | 0 | 251 | 0 | 0 | 88 | 133 |
N.S. |
1 | 1.13 | 0.74 | 1.04 | 0.00 | 2.49 | 0.00 | 0.00 | 0.87 | 1.32 |
time (sec) |
N/A | 0.180 | 0.299 | 0.316 | 0.000 | 0.096 | 0.000 | 0.000 | 0.603 | 0.584 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 162 | 116 | 171 | 0 | 419 | 0 | 0 | 113 | 209 |
N.S. |
1 | 1.19 | 0.85 | 1.26 | 0.00 | 3.08 | 0.00 | 0.00 | 0.83 | 1.54 |
time (sec) |
N/A | 0.203 | 0.743 | 0.166 | 0.000 | 0.089 | 0.000 | 0.000 | 1.148 | 0.698 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 178 | 73 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.14 | 0.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.303 | 0.025 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.342 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 137 | 73 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.15 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.279 | 0.021 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 113 | 71 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.19 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.245 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 148 | 73 | 0 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.14 | 0.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.275 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 196 | 73 | 0 | 0 | 0 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.20 | 0.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.322 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 186 | 140 | 0 | 0 | 754 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.22 | 0.92 | 0.00 | 0.00 | 4.96 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.254 | 0.309 | 0.000 | 0.000 | 0.105 | 0.000 | 0.000 | 0.351 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 146 | 108 | 0 | 0 | 276 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.35 | 1.00 | 0.00 | 0.00 | 2.56 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.217 | 0.143 | 0.000 | 0.000 | 0.086 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 27 | 0 | 42 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.00 | 1.40 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.138 | 0.019 | 0.160 | 0.000 | 0.069 | 0.000 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 66 | 45 | 53 | 0 | 126 | 0 | 0 | 78 | 0 |
N.S. |
1 | 1.03 | 0.70 | 0.83 | 0.00 | 1.97 | 0.00 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 0.159 | 0.141 | 0.158 | 0.000 | 0.079 | 0.000 | 0.000 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 114 | 76 | 105 | 0 | 273 | 0 | 0 | 130 | 0 |
N.S. |
1 | 1.16 | 0.78 | 1.07 | 0.00 | 2.79 | 0.00 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.179 | 0.296 | 0.168 | 0.000 | 0.178 | 0.000 | 0.000 | 0.347 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 162 | 116 | 171 | 0 | 457 | 0 | 0 | 182 | 0 |
N.S. |
1 | 1.21 | 0.87 | 1.28 | 0.00 | 3.41 | 0.00 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.207 | 0.679 | 0.165 | 0.000 | 0.389 | 0.000 | 0.000 | 0.461 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 272 | 73 | 0 | 0 | 0 | 0 | 0 | 113 | 0 |
N.S. |
1 | 1.42 | 0.38 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.385 | 0.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.688 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 231 | 73 | 0 | 0 | 0 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.50 | 0.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.352 | 0.036 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.416 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 188 | 73 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.59 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.322 | 0.032 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 202 | 73 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 2.20 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.324 | 0.027 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 246 | 71 | 0 | 0 | 0 | 0 | 0 | 42 | 0 |
N.S. |
1 | 2.00 | 0.58 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.369 | 0.027 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 294 | 73 | 0 | 0 | 0 | 0 | 0 | 98 | 0 |
N.S. |
1 | 1.85 | 0.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.403 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 113 | 71 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.19 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.248 | 0.002 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 117 | 75 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.17 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.238 | 0.034 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 111 | 71 | 0 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.16 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.267 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 115 | 71 | 0 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.20 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.242 | 0.030 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | C | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 348 | 156 | 0 | 0 | 232 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.78 | 0.80 | 0.00 | 0.00 | 1.18 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.435 | 0.284 | 0.000 | 0.000 | 0.082 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 181 | 98 | 0 | 0 | 194 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.33 | 0.72 | 0.00 | 0.00 | 1.43 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.299 | 0.144 | 0.000 | 0.000 | 0.113 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 109 | 39 | 0 | 0 | 0 | 37 | 0 | 17 | 0 |
N.S. |
1 | 3.30 | 1.18 | 0.00 | 0.00 | 0.00 | 1.12 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.228 | 0.012 | 0.000 | 0.000 | 0.000 | 0.915 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 78 | 37 | 0 | 0 | 0 | 34 | 0 | 17 | 0 |
N.S. |
1 | 2.60 | 1.23 | 0.00 | 0.00 | 0.00 | 1.13 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.213 | 0.013 | 0.000 | 0.000 | 0.000 | 1.206 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 51 | 28 | 0 | 0 | 0 | 42 | 0 | 17 | 0 |
N.S. |
1 | 2.55 | 1.40 | 0.00 | 0.00 | 0.00 | 2.10 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.181 | 0.007 | 0.000 | 0.000 | 0.000 | 1.132 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 51 | 28 | 0 | 0 | 0 | 44 | 0 | 17 | 0 |
N.S. |
1 | 2.55 | 1.40 | 0.00 | 0.00 | 0.00 | 2.20 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.178 | 0.007 | 0.000 | 0.000 | 0.000 | 1.126 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 52 | 30 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 2.48 | 1.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.81 | 0.00 |
time (sec) |
N/A | 0.177 | 0.009 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 56 | 30 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 2.55 | 1.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.175 | 0.010 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 78 | 61 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.04 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.210 | 0.022 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 82 | 62 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.02 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.203 | 0.025 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 78 | 64 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.04 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.222 | 0.027 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 82 | 68 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.02 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.211 | 0.026 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 101 | 28 | 0 | 0 | 0 | 42 | 0 | 38 | 0 |
N.S. |
1 | 5.05 | 1.40 | 0.00 | 0.00 | 0.00 | 2.10 | 0.00 | 1.90 | 0.00 |
time (sec) |
N/A | 0.219 | 0.007 | 0.000 | 0.000 | 0.000 | 1.413 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 101 | 28 | 0 | 0 | 0 | 44 | 0 | 40 | 0 |
N.S. |
1 | 5.05 | 1.40 | 0.00 | 0.00 | 0.00 | 2.20 | 0.00 | 2.00 | 0.00 |
time (sec) |
N/A | 0.213 | 0.008 | 0.000 | 0.000 | 0.000 | 1.404 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 103 | 32 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 4.90 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.81 | 0.00 |
time (sec) |
N/A | 0.218 | 0.008 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 111 | 32 | 0 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 5.05 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.00 | 0.00 |
time (sec) |
N/A | 0.223 | 0.009 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 101 | 28 | 0 | 0 | 0 | 34 | 0 | 38 | 0 |
N.S. |
1 | 2.35 | 0.65 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.216 | 0.007 | 0.000 | 0.000 | 0.000 | 1.408 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | F | F | F | C | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 101 | 28 | 0 | 0 | 0 | 44 | 0 | 40 | 0 |
N.S. |
1 | 2.35 | 0.65 | 0.00 | 0.00 | 0.00 | 1.02 | 0.00 | 0.93 | 0.00 |
time (sec) |
N/A | 0.219 | 0.007 | 0.000 | 0.000 | 0.000 | 1.323 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 103 | 30 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 2.29 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.217 | 0.009 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 111 | 30 | 0 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 2.31 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.223 | 0.009 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 143 | 61 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.91 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.273 | 0.017 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 151 | 62 | 0 | 0 | 0 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.89 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.268 | 0.018 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 143 | 63 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 2.01 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.273 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 151 | 64 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.99 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.274 | 0.032 | 0.000 | 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 | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 143 | 73 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.91 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.287 | 0.021 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 151 | 76 | 0 | 0 | 0 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.89 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.284 | 0.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 100 | 102 | 78 | 118 | 165 | 167 | 326 | 169 | 87 |
N.S. |
1 | 1.00 | 1.02 | 0.78 | 1.18 | 1.65 | 1.67 | 3.26 | 1.69 | 0.87 |
time (sec) |
N/A | 0.226 | 0.066 | 0.224 | 0.030 | 0.064 | 0.822 | 0.130 | 0.165 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 61 | 54 | 68 | 100 | 105 | 204 | 99 | 68 |
N.S. |
1 | 1.00 | 0.86 | 0.76 | 0.96 | 1.41 | 1.48 | 2.87 | 1.39 | 0.96 |
time (sec) |
N/A | 0.197 | 0.047 | 0.188 | 0.047 | 0.078 | 0.756 | 0.128 | 0.160 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 30 | 27 | 33 | 48 | 51 | 104 | 46 | 29 |
N.S. |
1 | 1.00 | 0.71 | 0.64 | 0.79 | 1.14 | 1.21 | 2.48 | 1.10 | 0.69 |
time (sec) |
N/A | 0.169 | 0.026 | 0.190 | 0.048 | 0.069 | 0.607 | 0.127 | 0.152 | 0.024 |
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 | 13 | 12 | 12 | 12 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.75 | 0.75 | 0.75 | 0.75 | 0.75 |
time (sec) |
N/A | 0.129 | 0.002 | 0.116 | 0.026 | 0.066 | 0.017 | 0.126 | 0.159 | 0.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | C | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 498 | 48 | 421 | 429 | 523 | 93460 | 0 | 461 | 0 | 424 |
N.S. |
1 | 0.10 | 0.85 | 0.86 | 1.05 | 187.67 | 0.00 | 0.93 | 0.00 | 0.85 |
time (sec) |
N/A | 0.151 | 1.143 | 3.189 | 0.132 | 2.531 | 0.000 | 0.331 | 0.221 | 0.659 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | F(-1) | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 512 | 72 | 422 | 428 | 536 | 0 | 0 | 510 | 0 | 457 |
N.S. |
1 | 0.14 | 0.82 | 0.84 | 1.05 | 0.00 | 0.00 | 1.00 | 0.00 | 0.89 |
time (sec) |
N/A | 0.165 | 1.604 | 1.408 | 0.169 | 0.000 | 0.000 | 0.403 | 0.258 | 0.589 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | F(-1) | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 558 | 110 | 458 | 471 | 644 | 0 | 0 | 637 | 0 | 591 |
N.S. |
1 | 0.20 | 0.82 | 0.84 | 1.15 | 0.00 | 0.00 | 1.14 | 0.00 | 1.06 |
time (sec) |
N/A | 0.182 | 3.844 | 1.444 | 0.154 | 0.000 | 0.000 | 0.449 | 0.304 | 0.650 |
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 | 100 | 100 | 102 | 78 | 118 | 116 | 167 | 139 | 115 | 87 |
N.S. |
1 | 1.00 | 1.02 | 0.78 | 1.18 | 1.16 | 1.67 | 1.39 | 1.15 | 0.87 |
time (sec) |
N/A | 0.204 | 0.061 | 0.213 | 0.037 | 0.082 | 0.697 | 0.129 | 0.164 | 0.045 |
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 | 71 | 71 | 61 | 54 | 68 | 64 | 105 | 84 | 62 | 68 |
N.S. |
1 | 1.00 | 0.86 | 0.76 | 0.96 | 0.90 | 1.48 | 1.18 | 0.87 | 0.96 |
time (sec) |
N/A | 0.179 | 0.038 | 0.185 | 0.037 | 0.089 | 0.648 | 0.124 | 0.159 | 0.042 |
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 | 42 | 42 | 30 | 27 | 33 | 26 | 51 | 41 | 26 | 29 |
N.S. |
1 | 1.00 | 0.71 | 0.64 | 0.79 | 0.62 | 1.21 | 0.98 | 0.62 | 0.69 |
time (sec) |
N/A | 0.158 | 0.022 | 0.129 | 0.052 | 0.094 | 0.509 | 0.130 | 0.156 | 0.170 |
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 | 13 | 12 | 12 | 12 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.75 | 0.75 | 0.75 | 0.75 | 0.75 |
time (sec) |
N/A | 0.124 | 0.002 | 0.112 | 0.026 | 0.065 | 0.015 | 0.124 | 0.158 | 0.010 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | F(-1) | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 483 | 48 | 488 | 362 | 469 | 0 | 0 | 495 | 0 | 527 |
N.S. |
1 | 0.10 | 1.01 | 0.75 | 0.97 | 0.00 | 0.00 | 1.02 | 0.00 | 1.09 |
time (sec) |
N/A | 0.141 | 1.037 | 1.036 | 0.148 | 0.000 | 0.000 | 0.358 | 0.202 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | F(-1) | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 519 | 78 | 458 | 578 | 543 | 0 | 0 | 577 | 0 | 493 |
N.S. |
1 | 0.15 | 0.88 | 1.11 | 1.05 | 0.00 | 0.00 | 1.11 | 0.00 | 0.95 |
time (sec) |
N/A | 0.160 | 1.779 | 3.960 | 0.133 | 0.000 | 0.000 | 0.349 | 0.243 | 0.794 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | F(-1) | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 566 | 124 | 474 | 601 | 672 | 0 | 0 | 714 | 0 | 567 |
N.S. |
1 | 0.22 | 0.84 | 1.06 | 1.19 | 0.00 | 0.00 | 1.26 | 0.00 | 1.00 |
time (sec) |
N/A | 0.189 | 2.672 | 6.476 | 0.139 | 0.000 | 0.000 | 0.404 | 0.271 | 1.192 |
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 | 98 | 98 | 102 | 95 | 127 | 126 | 136 | 153 | 115 | 114 |
N.S. |
1 | 1.00 | 1.04 | 0.97 | 1.30 | 1.29 | 1.39 | 1.56 | 1.17 | 1.16 |
time (sec) |
N/A | 0.200 | 0.069 | 0.205 | 0.026 | 0.099 | 1.724 | 0.126 | 0.156 | 0.200 |
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 | 69 | 69 | 61 | 56 | 76 | 74 | 90 | 84 | 62 | 68 |
N.S. |
1 | 1.00 | 0.88 | 0.81 | 1.10 | 1.07 | 1.30 | 1.22 | 0.90 | 0.99 |
time (sec) |
N/A | 0.187 | 0.042 | 0.173 | 0.033 | 0.086 | 1.173 | 0.120 | 0.164 | 0.040 |
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 | 40 | 32 | 26 | 38 | 36 | 63 | 34 | 26 | 29 |
N.S. |
1 | 1.00 | 0.80 | 0.65 | 0.95 | 0.90 | 1.58 | 0.85 | 0.65 | 0.72 |
time (sec) |
N/A | 0.157 | 0.027 | 0.148 | 0.026 | 0.091 | 0.365 | 0.126 | 0.157 | 0.179 |
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 | 13 | 12 | 20 | 14 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 1.25 | 0.88 | 0.75 | 0.75 | 0.75 |
time (sec) |
N/A | 0.123 | 0.001 | 0.130 | 0.036 | 0.093 | 0.020 | 0.123 | 0.157 | 0.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | C | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 505 | 48 | 446 | 431 | 534 | 216715 | 0 | 535 | 54 | 1059 |
N.S. |
1 | 0.10 | 0.88 | 0.85 | 1.06 | 429.14 | 0.00 | 1.06 | 0.11 | 2.10 |
time (sec) |
N/A | 0.155 | 1.198 | 1.309 | 0.154 | 5.649 | 0.000 | 0.355 | 0.186 | 0.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | F(-1) | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 547 | 78 | 472 | 487 | 644 | 0 | 0 | 692 | 95 | 1799 |
N.S. |
1 | 0.14 | 0.86 | 0.89 | 1.18 | 0.00 | 0.00 | 1.27 | 0.17 | 3.29 |
time (sec) |
N/A | 0.160 | 3.093 | 1.858 | 0.144 | 0.000 | 0.000 | 0.452 | 0.227 | 0.368 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | F(-1) | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 592 | 124 | 505 | 497 | 805 | 0 | 0 | 846 | 136 | 2510 |
N.S. |
1 | 0.21 | 0.85 | 0.84 | 1.36 | 0.00 | 0.00 | 1.43 | 0.23 | 4.24 |
time (sec) |
N/A | 0.179 | 4.808 | 1.624 | 0.141 | 0.000 | 0.000 | 0.565 | 0.257 | 0.506 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 84 | 73 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.45 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.17 | 0.00 |
time (sec) |
N/A | 0.177 | 0.058 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.984 | 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 | 58 | 82 | 73 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.41 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.170 | 0.038 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.626 | 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 | 58 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.161 | 0.022 | 0.000 | 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 | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.167 | 0.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.354 | 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 | 58 | 81 | 73 | 0 | 0 | 0 | 0 | 0 | 816 | 0 |
N.S. |
1 | 1.40 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 14.07 | 0.00 |
time (sec) |
N/A | 0.169 | 0.035 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 3.329 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 82 | 81 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.41 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.169 | 0.026 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 4.659 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F(-1) | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 346 | 437 | 316 | 0 | 0 | 2599 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.26 | 0.91 | 0.00 | 0.00 | 7.51 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.479 | 0.938 | 0.000 | 0.000 | 0.156 | 0.000 | 0.000 | 6.583 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 396 | 294 | 0 | 0 | 1443 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.32 | 0.98 | 0.00 | 0.00 | 4.83 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.440 | 0.797 | 0.000 | 0.000 | 0.129 | 0.000 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 386 | 268 | 0 | 0 | 504 | 0 | 0 | 133 | 0 |
N.S. |
1 | 1.50 | 1.04 | 0.00 | 0.00 | 1.95 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.426 | 0.535 | 0.000 | 0.000 | 0.102 | 0.000 | 0.000 | 6.016 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 27 | 0 | 65 | 0 | 0 | 494 | 130 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.00 | 2.03 | 0.00 | 0.00 | 15.44 | 4.06 |
time (sec) |
N/A | 0.137 | 0.023 | 0.171 | 0.000 | 0.078 | 0.000 | 0.000 | 6.311 | 0.338 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 46 | 54 | 0 | 175 | 0 | 0 | 919 | 137 |
N.S. |
1 | 1.00 | 0.70 | 0.82 | 0.00 | 2.65 | 0.00 | 0.00 | 13.92 | 2.08 |
time (sec) |
N/A | 0.162 | 0.211 | 0.171 | 0.000 | 0.077 | 0.000 | 0.000 | 6.587 | 0.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 114 | 77 | 105 | 0 | 338 | 0 | 0 | 1430 | 213 |
N.S. |
1 | 1.13 | 0.76 | 1.04 | 0.00 | 3.35 | 0.00 | 0.00 | 14.16 | 2.11 |
time (sec) |
N/A | 0.186 | 0.321 | 0.173 | 0.000 | 0.125 | 0.000 | 0.000 | 6.976 | 0.512 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 162 | 118 | 171 | 0 | 533 | 0 | 0 | 2011 | 302 |
N.S. |
1 | 1.19 | 0.87 | 1.26 | 0.00 | 3.92 | 0.00 | 0.00 | 14.79 | 2.22 |
time (sec) |
N/A | 0.209 | 0.997 | 0.183 | 0.000 | 0.116 | 0.000 | 0.000 | 8.024 | 0.620 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 346 | 444 | 316 | 0 | 0 | 2599 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.28 | 0.91 | 0.00 | 0.00 | 7.51 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.499 | 0.954 | 0.000 | 0.000 | 0.139 | 0.000 | 0.000 | 6.760 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 299 | 403 | 295 | 0 | 0 | 1455 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.35 | 0.99 | 0.00 | 0.00 | 4.87 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.465 | 0.778 | 0.000 | 0.000 | 0.117 | 0.000 | 0.000 | 14.869 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 260 | 399 | 274 | 0 | 0 | 565 | 0 | 0 | 132 | 0 |
N.S. |
1 | 1.53 | 1.05 | 0.00 | 0.00 | 2.17 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.455 | 0.589 | 0.000 | 0.000 | 0.087 | 0.000 | 0.000 | 0.493 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 27 | 0 | 65 | 0 | 0 | 481 | 130 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.00 | 2.03 | 0.00 | 0.00 | 15.03 | 4.06 |
time (sec) |
N/A | 0.139 | 0.025 | 0.171 | 0.000 | 0.101 | 0.000 | 0.000 | 0.741 | 0.329 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 46 | 54 | 0 | 175 | 0 | 0 | 816 | 137 |
N.S. |
1 | 1.00 | 0.70 | 0.82 | 0.00 | 2.65 | 0.00 | 0.00 | 12.36 | 2.08 |
time (sec) |
N/A | 0.167 | 0.287 | 0.175 | 0.000 | 0.085 | 0.000 | 0.000 | 1.043 | 0.403 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 114 | 77 | 105 | 0 | 338 | 0 | 0 | 1236 | 214 |
N.S. |
1 | 1.13 | 0.76 | 1.04 | 0.00 | 3.35 | 0.00 | 0.00 | 12.24 | 2.12 |
time (sec) |
N/A | 0.183 | 0.440 | 0.191 | 0.000 | 0.163 | 0.000 | 0.000 | 1.441 | 0.521 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 162 | 118 | 171 | 0 | 533 | 0 | 0 | 1733 | 303 |
N.S. |
1 | 1.19 | 0.87 | 1.26 | 0.00 | 3.92 | 0.00 | 0.00 | 12.74 | 2.23 |
time (sec) |
N/A | 0.206 | 1.636 | 0.184 | 0.000 | 0.137 | 0.000 | 0.000 | 2.134 | 0.647 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 82 | 73 | 0 | 0 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.41 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.176 | 0.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.781 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.167 | 0.023 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.778 | 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 | 58 | 74 | 73 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.28 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.166 | 0.022 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.317 | 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 | 58 | 81 | 73 | 0 | 0 | 0 | 0 | 0 | 268 | 0 |
N.S. |
1 | 1.40 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 4.62 | 0.00 |
time (sec) |
N/A | 0.167 | 0.036 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 3.112 | 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 | 58 | 82 | 73 | 0 | 0 | 0 | 0 | 0 | 973 | 0 |
N.S. |
1 | 1.41 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 16.78 | 0.00 |
time (sec) |
N/A | 0.175 | 0.046 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 4.858 | 0.000 |