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 | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 42 | 37 | 37 | 36 | 36 | 68 | 68 | 36 |
N.S. |
1 | 0.91 | 0.80 | 0.80 | 0.78 | 0.78 | 1.48 | 1.48 | 0.78 |
time (sec) |
N/A | 0.206 | 0.091 | 0.201 | 0.187 | 0.298 | 0.909 | 0.326 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 29 | 48 | 26 | 26 | 36 | 65 | 26 | 26 |
N.S. |
1 | 0.94 | 1.55 | 0.84 | 0.84 | 1.16 | 2.10 | 0.84 | 0.84 |
time (sec) |
N/A | 0.201 | 0.071 | 0.158 | 0.214 | 0.286 | 0.635 | 0.352 | 0.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 42 | 37 | 37 | 36 | 36 | 68 | 54 | 36 |
N.S. |
1 | 0.91 | 0.80 | 0.80 | 0.78 | 0.78 | 1.48 | 1.17 | 0.78 |
time (sec) |
N/A | 0.204 | 0.057 | 0.119 | 0.201 | 0.313 | 0.442 | 0.315 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 34 | 20 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 2.27 | 1.33 | 0.87 | 0.87 |
time (sec) |
N/A | 0.173 | 0.003 | 0.091 | 0.197 | 0.302 | 0.307 | 0.304 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 39 | 35 | 35 | 37 | 35 | 0 | 226 | 53 |
N.S. |
1 | 0.98 | 0.88 | 0.88 | 0.92 | 0.88 | 0.00 | 5.65 | 1.32 |
time (sec) |
N/A | 0.200 | 0.025 | 0.160 | 0.186 | 0.324 | 0.000 | 0.345 | 0.279 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 34 | 39 | 46 | 32 | 33 | 0 | 99 | 31 |
N.S. |
1 | 0.92 | 1.05 | 1.24 | 0.86 | 0.89 | 0.00 | 2.68 | 0.84 |
time (sec) |
N/A | 0.206 | 0.092 | 0.121 | 0.195 | 0.302 | 0.000 | 0.319 | 0.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 35 | 33 | 51 | 41 | 54 | 0 | 182 | 37 |
N.S. |
1 | 0.81 | 0.77 | 1.19 | 0.95 | 1.26 | 0.00 | 4.23 | 0.86 |
time (sec) |
N/A | 0.212 | 0.031 | 0.178 | 0.193 | 0.346 | 0.000 | 0.336 | 0.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 32 | 38 | 54 | 35 | 35 | 0 | 100 | 35 |
N.S. |
1 | 0.84 | 1.00 | 1.42 | 0.92 | 0.92 | 0.00 | 2.63 | 0.92 |
time (sec) |
N/A | 0.195 | 0.080 | 0.158 | 0.190 | 0.304 | 0.000 | 0.340 | 0.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 37 | 35 | 54 | 44 | 0 | 226 | 38 |
N.S. |
1 | 1.00 | 0.86 | 0.81 | 1.26 | 1.02 | 0.00 | 5.26 | 0.88 |
time (sec) |
N/A | 0.275 | 0.039 | 0.182 | 0.194 | 0.312 | 0.000 | 0.347 | 0.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 35 | 41 | 32 | 35 | 35 | 0 | 72 | 35 |
N.S. |
1 | 0.85 | 1.00 | 0.78 | 0.85 | 0.85 | 0.00 | 1.76 | 0.85 |
time (sec) |
N/A | 0.199 | 0.082 | 0.132 | 0.191 | 0.302 | 0.000 | 0.359 | 0.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 32 | 59 | 35 | 0 | 48 | 13 |
N.S. |
1 | 1.00 | 1.00 | 2.13 | 3.93 | 2.33 | 0.00 | 3.20 | 0.87 |
time (sec) |
N/A | 0.184 | 0.006 | 0.143 | 0.193 | 0.294 | 0.000 | 0.420 | 0.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 41 | 46 | 36 | 35 | 35 | 0 | 116 | 35 |
N.S. |
1 | 0.89 | 1.00 | 0.78 | 0.76 | 0.76 | 0.00 | 2.52 | 0.76 |
time (sec) |
N/A | 0.225 | 0.089 | 0.200 | 0.191 | 0.291 | 0.000 | 0.342 | 0.328 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 29 | 46 | 36 | 69 | 35 | 0 | 93 | 25 |
N.S. |
1 | 0.94 | 1.48 | 1.16 | 2.23 | 1.13 | 0.00 | 3.00 | 0.81 |
time (sec) |
N/A | 0.202 | 0.021 | 0.239 | 0.188 | 0.289 | 0.000 | 0.366 | 0.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 41 | 46 | 36 | 35 | 35 | 0 | 160 | 35 |
N.S. |
1 | 0.89 | 1.00 | 0.78 | 0.76 | 0.76 | 0.00 | 3.48 | 0.76 |
time (sec) |
N/A | 0.214 | 0.087 | 0.263 | 0.186 | 0.318 | 0.000 | 0.364 | 0.525 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 44 | 46 | 36 | 79 | 35 | 0 | 139 | 35 |
N.S. |
1 | 0.96 | 1.00 | 0.78 | 1.72 | 0.76 | 0.00 | 3.02 | 0.76 |
time (sec) |
N/A | 0.216 | 0.020 | 0.381 | 0.204 | 0.270 | 0.000 | 0.395 | 0.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 41 | 46 | 36 | 35 | 35 | 0 | 204 | 35 |
N.S. |
1 | 0.89 | 1.00 | 0.78 | 0.76 | 0.76 | 0.00 | 4.43 | 0.76 |
time (sec) |
N/A | 0.207 | 0.091 | 0.489 | 0.198 | 0.337 | 0.000 | 0.359 | 0.771 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 46 | 44 | 46 | 36 | 89 | 35 | 0 | 183 | 45 |
N.S. |
1 | 0.96 | 1.00 | 0.78 | 1.93 | 0.76 | 0.00 | 3.98 | 0.98 |
time (sec) |
N/A | 0.214 | 0.021 | 0.575 | 0.185 | 0.290 | 0.000 | 0.360 | 0.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 63 | 78 | 68 | 66 | 84 | 0 | 68 | 147 |
N.S. |
1 | 0.95 | 1.18 | 1.03 | 1.00 | 1.27 | 0.00 | 1.03 | 2.23 |
time (sec) |
N/A | 0.222 | 0.019 | 0.241 | 0.185 | 0.329 | 0.000 | 0.334 | 7.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 42 | 50 | 70 | 45 | 45 | 0 | 144 | 50 |
N.S. |
1 | 0.84 | 1.00 | 1.40 | 0.90 | 0.90 | 0.00 | 2.88 | 1.00 |
time (sec) |
N/A | 0.203 | 0.094 | 0.296 | 0.186 | 0.301 | 0.000 | 0.332 | 0.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 45 | 75 | 48 | 56 | 60 | 1085 | 145 | 88 |
N.S. |
1 | 0.85 | 1.42 | 0.91 | 1.06 | 1.13 | 20.47 | 2.74 | 1.66 |
time (sec) |
N/A | 0.212 | 0.080 | 0.144 | 0.194 | 0.336 | 2.060 | 0.335 | 5.266 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 37 | 40 | 33 | 35 | 35 | 1086 | 170 | 66 |
N.S. |
1 | 0.92 | 1.00 | 0.82 | 0.88 | 0.88 | 27.15 | 4.25 | 1.65 |
time (sec) |
N/A | 0.211 | 0.012 | 0.129 | 0.185 | 0.312 | 1.332 | 0.326 | 0.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 33 | 60 | 37 | 46 | 50 | 473 | 101 | 62 |
N.S. |
1 | 0.87 | 1.58 | 0.97 | 1.21 | 1.32 | 12.45 | 2.66 | 1.63 |
time (sec) |
N/A | 0.210 | 0.065 | 0.103 | 0.192 | 0.305 | 0.881 | 0.306 | 1.471 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 26 | 27 | 23 | 25 | 25 | 369 | 25 | 35 |
N.S. |
1 | 0.96 | 1.00 | 0.85 | 0.93 | 0.93 | 13.67 | 0.93 | 1.30 |
time (sec) |
N/A | 0.204 | 0.012 | 0.082 | 0.183 | 0.303 | 0.609 | 0.298 | 0.153 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 21 | 42 | 23 | 34 | 38 | 92 | 57 | 35 |
N.S. |
1 | 0.91 | 1.83 | 1.00 | 1.48 | 1.65 | 4.00 | 2.48 | 1.52 |
time (sec) |
N/A | 0.182 | 0.030 | 0.066 | 0.191 | 0.312 | 0.434 | 0.320 | 0.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 13 | 23 | 12 | 11 | 13 | 17 | 12 | 26 |
N.S. |
1 | 1.18 | 2.09 | 1.09 | 1.00 | 1.18 | 1.55 | 1.09 | 2.36 |
time (sec) |
N/A | 0.165 | 0.008 | 0.029 | 0.181 | 0.295 | 0.207 | 0.310 | 0.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 31 | 12 | 28 | 30 | 0 | 56 | 11 |
N.S. |
1 | 1.00 | 2.82 | 1.09 | 2.55 | 2.73 | 0.00 | 5.09 | 1.00 |
time (sec) |
N/A | 0.166 | 0.019 | 0.080 | 0.190 | 0.290 | 0.000 | 0.422 | 0.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 20 | 42 | 30 | 36 | 52 | 0 | 55 | 23 |
N.S. |
1 | 0.87 | 1.83 | 1.30 | 1.57 | 2.26 | 0.00 | 2.39 | 1.00 |
time (sec) |
N/A | 0.186 | 0.084 | 0.092 | 0.184 | 0.293 | 0.000 | 0.327 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 24 | 39 | 23 | 40 | 56 | 0 | 124 | 35 |
N.S. |
1 | 0.89 | 1.44 | 0.85 | 1.48 | 2.07 | 0.00 | 4.59 | 1.30 |
time (sec) |
N/A | 0.191 | 0.016 | 0.160 | 0.184 | 0.301 | 0.000 | 0.316 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 32 | 57 | 40 | 50 | 67 | 0 | 101 | 33 |
N.S. |
1 | 0.84 | 1.50 | 1.05 | 1.32 | 1.76 | 0.00 | 2.66 | 0.87 |
time (sec) |
N/A | 0.201 | 0.055 | 0.156 | 0.190 | 0.317 | 0.000 | 0.321 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 54 | 33 | 65 | 67 | 0 | 170 | 46 |
N.S. |
1 | 1.00 | 1.38 | 0.85 | 1.67 | 1.72 | 0.00 | 4.36 | 1.18 |
time (sec) |
N/A | 0.198 | 0.015 | 0.221 | 0.185 | 0.316 | 0.000 | 0.366 | 0.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 44 | 72 | 50 | 60 | 77 | 0 | 145 | 45 |
N.S. |
1 | 0.83 | 1.36 | 0.94 | 1.13 | 1.45 | 0.00 | 2.74 | 0.85 |
time (sec) |
N/A | 0.204 | 0.065 | 0.239 | 0.185 | 0.298 | 0.000 | 0.336 | 0.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 51 | 69 | 43 | 85 | 77 | 0 | 214 | 56 |
N.S. |
1 | 0.89 | 1.21 | 0.75 | 1.49 | 1.35 | 0.00 | 3.75 | 0.98 |
time (sec) |
N/A | 0.203 | 0.025 | 0.348 | 0.190 | 0.308 | 0.000 | 0.339 | 0.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 42 | 50 | 62 | 42 | 43 | 82 | 42 | 43 |
N.S. |
1 | 0.84 | 1.00 | 1.24 | 0.84 | 0.86 | 1.64 | 0.84 | 0.86 |
time (sec) |
N/A | 0.215 | 0.019 | 0.248 | 0.181 | 0.281 | 0.818 | 0.325 | 0.225 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 79 | 41 | 63 | 63 | 52 | 119 | 55 | 47 |
N.S. |
1 | 1.30 | 0.67 | 1.03 | 1.03 | 0.85 | 1.95 | 0.90 | 0.77 |
time (sec) |
N/A | 0.221 | 0.198 | 0.145 | 0.272 | 0.287 | 0.647 | 0.315 | 0.333 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 32 | 38 | 52 | 32 | 33 | 61 | 32 | 35 |
N.S. |
1 | 0.84 | 1.00 | 1.37 | 0.84 | 0.87 | 1.61 | 0.84 | 0.92 |
time (sec) |
N/A | 0.208 | 0.014 | 0.214 | 0.187 | 0.282 | 0.527 | 0.312 | 0.182 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 50 | 31 | 54 | 43 | 40 | 75 | 43 | 43 |
N.S. |
1 | 1.25 | 0.78 | 1.35 | 1.08 | 1.00 | 1.88 | 1.08 | 1.08 |
time (sec) |
N/A | 0.206 | 0.180 | 0.099 | 0.268 | 0.330 | 0.427 | 0.327 | 0.320 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 18 | 23 | 35 | 20 | 22 | 39 | 20 | 23 |
N.S. |
1 | 0.78 | 1.00 | 1.52 | 0.87 | 0.96 | 1.70 | 0.87 | 1.00 |
time (sec) |
N/A | 0.197 | 0.013 | 0.173 | 0.202 | 0.291 | 0.361 | 0.316 | 0.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 29 | 21 | 18 | 29 | 29 | 35 | 15 |
N.S. |
1 | 1.00 | 1.93 | 1.40 | 1.20 | 1.93 | 1.93 | 2.33 | 1.00 |
time (sec) |
N/A | 0.169 | 0.012 | 0.051 | 0.276 | 0.283 | 0.330 | 0.426 | 0.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 14 | 13 | 13 | 20 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.27 | 1.18 | 1.18 | 1.82 | 1.18 | 1.18 |
time (sec) |
N/A | 0.174 | 0.008 | 0.032 | 0.191 | 0.286 | 0.308 | 0.353 | 0.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-1) | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 21 | 27 | 30 | 0 | 50 | 0 | 38 | 22 |
N.S. |
1 | 0.91 | 1.17 | 1.30 | 0.00 | 2.17 | 0.00 | 1.65 | 0.96 |
time (sec) |
N/A | 0.189 | 0.012 | 0.084 | 0.000 | 0.303 | 0.000 | 0.383 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 19 | 13 | 31 | 22 | 33 | 0 | 16 | 14 |
N.S. |
1 | 0.86 | 0.59 | 1.41 | 1.00 | 1.50 | 0.00 | 0.73 | 0.64 |
time (sec) |
N/A | 0.200 | 0.038 | 0.262 | 0.181 | 0.275 | 0.000 | 0.390 | 0.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 52 | 27 | 50 | 61 | 85 | 0 | 63 | 48 |
N.S. |
1 | 1.06 | 0.55 | 1.02 | 1.24 | 1.73 | 0.00 | 1.29 | 0.98 |
time (sec) |
N/A | 0.210 | 0.011 | 0.165 | 0.190 | 0.297 | 0.000 | 0.362 | 0.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 33 | 46 | 46 | 32 | 43 | 0 | 32 | 33 |
N.S. |
1 | 0.87 | 1.21 | 1.21 | 0.84 | 1.13 | 0.00 | 0.84 | 0.87 |
time (sec) |
N/A | 0.208 | 0.113 | 0.157 | 0.184 | 0.294 | 0.000 | 0.361 | 0.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 83 | 27 | 68 | 79 | 95 | 0 | 73 | 67 |
N.S. |
1 | 1.19 | 0.39 | 0.97 | 1.13 | 1.36 | 0.00 | 1.04 | 0.96 |
time (sec) |
N/A | 0.225 | 0.012 | 0.266 | 0.192 | 0.319 | 0.000 | 0.336 | 0.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 45 | 58 | 63 | 45 | 71 | 1484 | 231 | 85 |
N.S. |
1 | 0.78 | 1.00 | 1.09 | 0.78 | 1.22 | 25.59 | 3.98 | 1.47 |
time (sec) |
N/A | 0.229 | 0.019 | 0.204 | 0.186 | 0.320 | 3.460 | 0.371 | 0.460 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 64 | 103 | 70 | 66 | 93 | 719 | 163 | 129 |
N.S. |
1 | 0.97 | 1.56 | 1.06 | 1.00 | 1.41 | 10.89 | 2.47 | 1.95 |
time (sec) |
N/A | 0.238 | 0.117 | 0.170 | 0.189 | 0.324 | 2.250 | 0.331 | 1.161 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 33 | 35 | 53 | 35 | 61 | 614 | 187 | 62 |
N.S. |
1 | 0.77 | 0.81 | 1.23 | 0.81 | 1.42 | 14.28 | 4.35 | 1.44 |
time (sec) |
N/A | 0.226 | 0.046 | 0.141 | 0.187 | 0.322 | 1.325 | 0.355 | 0.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 52 | 86 | 60 | 56 | 83 | 241 | 140 | 77 |
N.S. |
1 | 1.06 | 1.76 | 1.22 | 1.14 | 1.69 | 4.92 | 2.86 | 1.57 |
time (sec) |
N/A | 0.209 | 0.065 | 0.104 | 0.196 | 0.324 | 0.866 | 0.362 | 0.303 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 30 | 34 | 25 | 23 | 41 | 42 | 36 | 36 |
N.S. |
1 | 1.07 | 1.21 | 0.89 | 0.82 | 1.46 | 1.50 | 1.29 | 1.29 |
time (sec) |
N/A | 0.231 | 0.060 | 0.083 | 0.194 | 0.298 | 0.389 | 0.318 | 0.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 75 | 43 | 46 | 72 | 58 | 93 | 48 |
N.S. |
1 | 1.00 | 2.21 | 1.26 | 1.35 | 2.12 | 1.71 | 2.74 | 1.41 |
time (sec) |
N/A | 0.235 | 0.064 | 0.079 | 0.201 | 0.320 | 0.506 | 0.329 | 0.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 18 | 24 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 1.20 | 1.60 | 0.87 | 0.87 |
time (sec) |
N/A | 0.185 | 0.010 | 0.035 | 0.191 | 0.321 | 0.371 | 0.333 | 0.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 24 | 39 | 23 | 36 | 65 | 0 | 119 | 34 |
N.S. |
1 | 0.89 | 1.44 | 0.85 | 1.33 | 2.41 | 0.00 | 4.41 | 1.26 |
time (sec) |
N/A | 0.197 | 0.016 | 0.109 | 0.200 | 0.288 | 0.000 | 0.333 | 0.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 51 | 143 | 52 | 61 | 96 | 0 | 140 | 49 |
N.S. |
1 | 1.04 | 2.92 | 1.06 | 1.24 | 1.96 | 0.00 | 2.86 | 1.00 |
time (sec) |
N/A | 0.206 | 0.279 | 0.138 | 0.209 | 0.279 | 0.000 | 0.352 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 35 | 61 | 43 | 64 | 102 | 0 | 188 | 39 |
N.S. |
1 | 0.81 | 1.42 | 1.00 | 1.49 | 2.37 | 0.00 | 4.37 | 0.91 |
time (sec) |
N/A | 0.215 | 0.046 | 0.212 | 0.200 | 0.296 | 0.000 | 0.369 | 0.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 63 | 205 | 70 | 73 | 112 | 0 | 163 | 60 |
N.S. |
1 | 0.95 | 3.11 | 1.06 | 1.11 | 1.70 | 0.00 | 2.47 | 0.91 |
time (sec) |
N/A | 0.225 | 0.378 | 0.231 | 0.203 | 0.291 | 0.000 | 0.341 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 49 | 67 | 61 | 82 | 112 | 0 | 232 | 74 |
N.S. |
1 | 0.84 | 1.16 | 1.05 | 1.41 | 1.93 | 0.00 | 4.00 | 1.28 |
time (sec) |
N/A | 0.219 | 0.020 | 0.338 | 0.204 | 0.355 | 0.000 | 0.357 | 0.179 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 58 | 68 | 90 | 56 | 68 | 105 | 56 | 55 |
N.S. |
1 | 0.85 | 1.00 | 1.32 | 0.82 | 1.00 | 1.54 | 0.82 | 0.81 |
time (sec) |
N/A | 0.220 | 0.024 | 0.309 | 0.187 | 0.309 | 1.480 | 0.377 | 0.286 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 91 | 53 | 93 | 75 | 89 | 141 | 68 | 56 |
N.S. |
1 | 1.14 | 0.66 | 1.16 | 0.94 | 1.11 | 1.76 | 0.85 | 0.70 |
time (sec) |
N/A | 0.242 | 0.288 | 0.311 | 0.285 | 0.290 | 1.154 | 0.502 | 1.463 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 46 | 53 | 61 | 44 | 56 | 82 | 41 | 45 |
N.S. |
1 | 0.87 | 1.00 | 1.15 | 0.83 | 1.06 | 1.55 | 0.77 | 0.85 |
time (sec) |
N/A | 0.214 | 0.020 | 0.138 | 0.194 | 0.329 | 0.888 | 0.329 | 0.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 62 | 43 | 78 | 55 | 79 | 97 | 55 | 46 |
N.S. |
1 | 1.09 | 0.75 | 1.37 | 0.96 | 1.39 | 1.70 | 0.96 | 0.81 |
time (sec) |
N/A | 0.231 | 0.200 | 0.148 | 0.285 | 0.286 | 0.725 | 0.320 | 0.508 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 34 | 37 | 52 | 35 | 48 | 63 | 35 | 32 |
N.S. |
1 | 0.92 | 1.00 | 1.41 | 0.95 | 1.30 | 1.70 | 0.95 | 0.86 |
time (sec) |
N/A | 0.204 | 0.015 | 0.098 | 0.195 | 0.301 | 0.582 | 0.342 | 0.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 33 | 26 | 34 | 69 | 48 | 62 | 24 |
N.S. |
1 | 1.00 | 1.22 | 0.96 | 1.26 | 2.56 | 1.78 | 2.30 | 0.89 |
time (sec) |
N/A | 0.227 | 0.009 | 0.095 | 0.279 | 0.307 | 0.507 | 0.387 | 0.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 54 | 25 | 38 | 42 | 25 | 22 |
N.S. |
1 | 1.00 | 1.00 | 2.08 | 0.96 | 1.46 | 1.62 | 0.96 | 0.85 |
time (sec) |
N/A | 0.202 | 0.012 | 0.083 | 0.193 | 0.274 | 0.512 | 0.309 | 0.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 22 | 13 | 34 | 71 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.47 | 0.87 | 2.27 | 4.73 | 0.87 | 0.87 |
time (sec) |
N/A | 0.184 | 0.007 | 0.062 | 0.203 | 0.266 | 0.731 | 0.313 | 0.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 26 | 24 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 1.73 | 1.60 | 0.87 | 0.87 |
time (sec) |
N/A | 0.180 | 0.009 | 0.049 | 0.188 | 0.272 | 0.415 | 0.296 | 0.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 33 | 31 | 40 | 50 | 94 | 0 | 52 | 32 |
N.S. |
1 | 0.87 | 0.82 | 1.05 | 1.32 | 2.47 | 0.00 | 1.37 | 0.84 |
time (sec) |
N/A | 0.199 | 0.011 | 0.132 | 0.209 | 0.281 | 0.000 | 0.308 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 31 | 45 | 46 | 35 | 54 | 0 | 35 | 36 |
N.S. |
1 | 0.84 | 1.22 | 1.24 | 0.95 | 1.46 | 0.00 | 0.95 | 0.97 |
time (sec) |
N/A | 0.202 | 0.116 | 0.145 | 0.186 | 0.308 | 0.000 | 0.326 | 0.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 64 | 31 | 68 | 73 | 130 | 0 | 72 | 61 |
N.S. |
1 | 0.97 | 0.47 | 1.03 | 1.11 | 1.97 | 0.00 | 1.09 | 0.92 |
time (sec) |
N/A | 0.221 | 0.012 | 0.260 | 0.184 | 0.305 | 0.000 | 0.314 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 45 | 43 | 46 | 44 | 66 | 0 | 31 | 45 |
N.S. |
1 | 0.85 | 0.81 | 0.87 | 0.83 | 1.25 | 0.00 | 0.58 | 0.85 |
time (sec) |
N/A | 0.210 | 0.040 | 0.234 | 0.181 | 0.284 | 0.000 | 0.315 | 0.218 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 95 | 31 | 86 | 91 | 140 | 0 | 85 | 79 |
N.S. |
1 | 1.07 | 0.35 | 0.97 | 1.02 | 1.57 | 0.00 | 0.96 | 0.89 |
time (sec) |
N/A | 0.243 | 0.013 | 0.415 | 0.186 | 0.286 | 0.000 | 0.448 | 0.237 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 59 | 69 | 89 | 56 | 100 | 1664 | 277 | 92 |
N.S. |
1 | 0.86 | 1.00 | 1.29 | 0.81 | 1.45 | 24.12 | 4.01 | 1.33 |
time (sec) |
N/A | 0.235 | 0.027 | 0.263 | 0.254 | 0.325 | 7.676 | 0.316 | 1.287 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 95 | 141 | 98 | 89 | 132 | 869 | 209 | 157 |
N.S. |
1 | 1.07 | 1.58 | 1.10 | 1.00 | 1.48 | 9.76 | 2.35 | 1.76 |
time (sec) |
N/A | 0.255 | 0.128 | 0.213 | 0.242 | 0.302 | 4.654 | 0.350 | 0.315 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 45 | 58 | 81 | 49 | 90 | 733 | 232 | 74 |
N.S. |
1 | 0.78 | 1.00 | 1.40 | 0.84 | 1.55 | 12.64 | 4.00 | 1.28 |
time (sec) |
N/A | 0.224 | 0.020 | 0.181 | 0.187 | 0.328 | 3.218 | 0.344 | 0.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 83 | 123 | 88 | 79 | 122 | 330 | 164 | 105 |
N.S. |
1 | 1.19 | 1.76 | 1.26 | 1.13 | 1.74 | 4.71 | 2.34 | 1.50 |
time (sec) |
N/A | 0.228 | 0.079 | 0.143 | 0.187 | 0.292 | 1.713 | 0.313 | 0.350 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 44 | 53 | 33 | 38 | 70 | 61 | 164 | 52 |
N.S. |
1 | 1.05 | 1.26 | 0.79 | 0.90 | 1.67 | 1.45 | 3.90 | 1.24 |
time (sec) |
N/A | 0.302 | 0.017 | 0.116 | 0.204 | 0.364 | 0.574 | 0.357 | 0.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 60 | 113 | 69 | 71 | 112 | 92 | 139 | 78 |
N.S. |
1 | 1.09 | 2.05 | 1.25 | 1.29 | 2.04 | 1.67 | 2.53 | 1.42 |
time (sec) |
N/A | 0.330 | 0.072 | 0.108 | 0.183 | 0.292 | 0.988 | 0.335 | 0.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 22 | 25 | 39 | 44 | 25 | 25 |
N.S. |
1 | 1.00 | 1.00 | 1.47 | 1.67 | 2.60 | 2.93 | 1.67 | 1.67 |
time (sec) |
N/A | 0.195 | 0.005 | 0.085 | 0.198 | 0.429 | 0.550 | 0.327 | 0.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 60 | 113 | 51 | 65 | 111 | 58 | 98 | 48 |
N.S. |
1 | 1.09 | 2.05 | 0.93 | 1.18 | 2.02 | 1.05 | 1.78 | 0.87 |
time (sec) |
N/A | 0.324 | 0.084 | 0.094 | 0.189 | 0.505 | 0.929 | 0.323 | 0.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 27 | 24 | 13 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 1.80 | 1.60 | 0.87 | 1.53 |
time (sec) |
N/A | 0.181 | 0.008 | 0.059 | 0.181 | 0.292 | 0.480 | 0.309 | 0.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 37 | 54 | 33 | 51 | 105 | 0 | 165 | 79 |
N.S. |
1 | 0.92 | 1.35 | 0.82 | 1.28 | 2.62 | 0.00 | 4.12 | 1.98 |
time (sec) |
N/A | 0.205 | 0.016 | 0.145 | 0.181 | 0.371 | 0.000 | 0.311 | 0.196 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 82 | 129 | 70 | 79 | 132 | 0 | 163 | 66 |
N.S. |
1 | 1.17 | 1.84 | 1.00 | 1.13 | 1.89 | 0.00 | 2.33 | 0.94 |
time (sec) |
N/A | 0.222 | 2.884 | 0.211 | 0.183 | 0.291 | 0.000 | 0.302 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 47 | 54 | 61 | 74 | 138 | 0 | 232 | 82 |
N.S. |
1 | 0.81 | 0.93 | 1.05 | 1.28 | 2.38 | 0.00 | 4.00 | 1.41 |
time (sec) |
N/A | 0.213 | 0.223 | 0.314 | 0.192 | 0.307 | 0.000 | 0.505 | 0.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 94 | 268 | 88 | 91 | 148 | 0 | 209 | 78 |
N.S. |
1 | 1.06 | 3.01 | 0.99 | 1.02 | 1.66 | 0.00 | 2.35 | 0.88 |
time (sec) |
N/A | 0.246 | 0.454 | 0.329 | 0.186 | 0.348 | 0.000 | 0.318 | 0.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 61 | 91 | 79 | 92 | 148 | 0 | 278 | 64 |
N.S. |
1 | 0.88 | 1.32 | 1.14 | 1.33 | 2.14 | 0.00 | 4.03 | 0.93 |
time (sec) |
N/A | 0.224 | 0.048 | 0.469 | 0.180 | 0.334 | 0.000 | 0.317 | 0.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 27 | 18 | 14 | 33 | 29 | 14 | 19 |
N.S. |
1 | 1.00 | 1.59 | 1.06 | 0.82 | 1.94 | 1.71 | 0.82 | 1.12 |
time (sec) |
N/A | 0.191 | 0.025 | 0.082 | 0.182 | 0.296 | 0.020 | 0.293 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 22 | 14 | 30 | 15 | 14 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.29 | 0.82 | 1.76 | 0.88 | 0.82 | 0.76 |
time (sec) |
N/A | 0.201 | 0.007 | 0.074 | 0.184 | 0.304 | 0.042 | 0.303 | 0.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 18 | 24 | 37 | 0 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 1.09 | 1.68 | 0.00 | 0.82 |
time (sec) |
N/A | 0.182 | 0.023 | 0.086 | 0.192 | 0.314 | 2.885 | 0.000 | 0.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 18 | 21 | 37 | 21 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 0.95 | 1.68 | 0.95 | 0.82 |
time (sec) |
N/A | 0.181 | 0.013 | 0.027 | 0.188 | 0.300 | 0.254 | 0.280 | 0.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 19 | 18 | 18 | 36 | 18 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 0.90 | 1.80 | 0.90 | 0.90 |
time (sec) |
N/A | 0.181 | 0.011 | 0.033 | 0.190 | 0.334 | 0.426 | 0.306 | 0.200 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 19 | 18 | 26 | 34 | 0 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 1.30 | 1.70 | 0.00 | 1.85 |
time (sec) |
N/A | 0.184 | 0.017 | 0.029 | 0.183 | 0.310 | 0.771 | 0.000 | 0.271 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 18 | 26 | 36 | 0 | 53 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 1.18 | 1.64 | 0.00 | 2.41 |
time (sec) |
N/A | 0.185 | 0.020 | 0.030 | 0.198 | 0.306 | 3.456 | 0.000 | 0.581 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 18 | 26 | 36 | 0 | 65 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 1.18 | 1.64 | 0.00 | 2.95 |
time (sec) |
N/A | 0.186 | 0.027 | 0.027 | 0.192 | 0.292 | 29.620 | 0.000 | 6.663 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 18 | 26 | 0 | 0 | 65 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 1.18 | 0.00 | 0.00 | 2.95 |
time (sec) |
N/A | 0.182 | 0.041 | 0.032 | 0.187 | 0.315 | 0.000 | 0.000 | 3.909 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 137 | 60 | 249 | 0 | 119 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.48 | 1.98 | 0.00 | 0.94 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.540 | 0.099 | 4.692 | 0.000 | 0.133 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 137 | 60 | 236 | 0 | 107 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.48 | 1.87 | 0.00 | 0.85 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.527 | 0.095 | 1.938 | 0.000 | 0.133 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 103 | 57 | 223 | 0 | 106 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.58 | 2.28 | 0.00 | 1.08 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.419 | 0.037 | 1.552 | 0.000 | 0.120 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 103 | 57 | 208 | 0 | 90 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.58 | 2.12 | 0.00 | 0.92 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.424 | 0.046 | 0.660 | 0.000 | 0.124 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 58 | 194 | 0 | 87 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.84 | 2.81 | 0.00 | 1.26 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.316 | 0.061 | 0.503 | 0.000 | 0.108 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 58 | 188 | 0 | 78 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.84 | 2.72 | 0.00 | 1.13 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.318 | 0.071 | 0.362 | 0.000 | 0.091 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 60 | 198 | 0 | 105 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.88 | 2.91 | 0.00 | 1.54 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.332 | 0.064 | 0.584 | 0.000 | 0.093 | 0.000 | 0.000 | 0.000 |