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 | 8 | 8 | 8 | 9 | 8 | 8 | 7 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.12 | 1.00 | 1.00 | 0.88 | 1.00 | 1.00 |
time (sec) |
N/A | 0.122 | 0.000 | 0.267 | 0.208 | 0.217 | 0.131 | 0.273 | 0.013 |
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 | 13 | 13 | 13 | 14 | 13 | 13 | 19 | 14 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.00 | 1.46 | 1.08 | 1.00 |
time (sec) |
N/A | 0.124 | 0.001 | 0.153 | 0.208 | 0.222 | 0.049 | 0.316 | 0.200 |
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 | 16 | 19 | 19 | 19 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.27 | 1.27 | 1.27 | 1.00 | 1.00 |
time (sec) |
N/A | 0.128 | 0.002 | 0.150 | 0.208 | 0.218 | 0.103 | 0.289 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 16 | 47 | 47 | 53 | 15 | 49 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 2.76 | 2.76 | 3.12 | 0.88 | 2.88 |
time (sec) |
N/A | 0.133 | 0.004 | 0.294 | 0.197 | 0.216 | 0.257 | 0.283 | 0.181 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 16 | 61 | 61 | 68 | 15 | 63 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 3.59 | 3.59 | 4.00 | 0.88 | 3.71 |
time (sec) |
N/A | 0.123 | 0.004 | 0.172 | 0.218 | 0.215 | 0.284 | 0.281 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 16 | 75 | 75 | 83 | 15 | 77 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 4.41 | 4.41 | 4.88 | 0.88 | 4.53 |
time (sec) |
N/A | 0.126 | 0.004 | 0.298 | 0.202 | 0.229 | 0.338 | 0.287 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 16 | 35 | 35 | 34 | 35 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 2.06 | 2.06 | 2.00 | 2.06 | 1.59 |
time (sec) |
N/A | 0.128 | 0.002 | 0.155 | 0.204 | 0.210 | 0.101 | 0.299 | 0.060 |
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 | 23 | 17 | 19 | 17 | 21 | 21 | 20 | 21 | 16 |
N.S. |
1 | 0.74 | 0.83 | 0.74 | 0.91 | 0.91 | 0.87 | 0.91 | 0.70 |
time (sec) |
N/A | 0.127 | 0.001 | 0.276 | 0.208 | 0.214 | 0.078 | 0.282 | 0.036 |
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 | 8 | 8 | 8 | 9 | 8 | 8 | 7 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.12 | 1.00 | 1.00 | 0.88 | 1.00 | 1.00 |
time (sec) |
N/A | 0.119 | 0.000 | 0.146 | 0.212 | 0.211 | 0.078 | 0.299 | 0.011 |
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 | 13 | 13 | 13 | 14 | 13 | 13 | 17 | 14 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.00 | 1.31 | 1.08 | 1.00 |
time (sec) |
N/A | 0.125 | 0.001 | 0.153 | 0.227 | 0.222 | 0.094 | 0.315 | 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 | 13 | 13 | 13 | 14 | 16 | 16 | 12 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.23 | 1.23 | 0.92 | 1.00 | 1.00 |
time (sec) |
N/A | 0.123 | 0.002 | 0.291 | 0.222 | 0.212 | 0.146 | 0.293 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 36 | 36 | 44 | 12 | 38 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 2.57 | 2.57 | 3.14 | 0.86 | 2.71 |
time (sec) |
N/A | 0.125 | 0.003 | 0.164 | 0.203 | 0.212 | 0.395 | 0.293 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 59 | 59 | 68 | 20 | 61 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 3.93 | 3.93 | 4.53 | 1.33 | 4.07 |
time (sec) |
N/A | 0.126 | 0.003 | 0.299 | 0.209 | 0.218 | 0.225 | 0.299 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 16 | 75 | 75 | 83 | 15 | 77 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 4.41 | 4.41 | 4.88 | 0.88 | 4.53 |
time (sec) |
N/A | 0.125 | 0.004 | 0.171 | 0.198 | 0.227 | 0.322 | 0.287 | 0.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 25 | 27 | 649 | 80 | 212 | 141 | 107 |
N.S. |
1 | 1.00 | 1.04 | 1.12 | 27.04 | 3.33 | 8.83 | 5.88 | 4.46 |
time (sec) |
N/A | 0.132 | 0.007 | 0.346 | 0.241 | 0.221 | 1.482 | 0.297 | 0.393 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 91 | 113 | 113 | 124 | 113 | 113 |
N.S. |
1 | 1.00 | 1.00 | 5.35 | 6.65 | 6.65 | 7.29 | 6.65 | 6.65 |
time (sec) |
N/A | 0.128 | 0.002 | 0.267 | 0.221 | 0.215 | 0.081 | 0.280 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 80 | 99 | 99 | 110 | 99 | 99 |
N.S. |
1 | 1.00 | 1.00 | 4.71 | 5.82 | 5.82 | 6.47 | 5.82 | 5.82 |
time (sec) |
N/A | 0.127 | 0.002 | 0.139 | 0.200 | 0.215 | 0.081 | 0.284 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 67 | 71 | 71 | 78 | 71 | 71 |
N.S. |
1 | 1.00 | 1.00 | 4.47 | 4.73 | 4.73 | 5.20 | 4.73 | 4.73 |
time (sec) |
N/A | 0.126 | 0.001 | 0.261 | 0.205 | 0.218 | 0.047 | 0.280 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 16 | 48 | 48 | 51 | 48 | 57 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 2.82 | 2.82 | 3.00 | 2.82 | 3.35 |
time (sec) |
N/A | 0.126 | 0.001 | 0.151 | 0.206 | 0.216 | 0.093 | 0.295 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 16 | 37 | 37 | 46 | 18 | 43 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 2.18 | 2.18 | 2.71 | 1.06 | 2.53 |
time (sec) |
N/A | 0.126 | 0.001 | 0.147 | 0.216 | 0.214 | 0.063 | 0.282 | 0.059 |
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 | 17 | 17 | 17 | 16 | 26 | 26 | 29 | 26 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 1.53 | 1.53 | 1.71 | 1.53 | 1.41 |
time (sec) |
N/A | 0.127 | 0.001 | 0.278 | 0.225 | 0.217 | 0.092 | 0.297 | 0.053 |
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 | 18 | 17 | 16 | 14 | 15 | 15 | 15 | 15 | 13 |
N.S. |
1 | 0.94 | 0.89 | 0.78 | 0.83 | 0.83 | 0.83 | 0.83 | 0.72 |
time (sec) |
N/A | 0.126 | 0.001 | 0.149 | 0.219 | 0.228 | 0.109 | 0.292 | 0.027 |
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 | 5 | 5 | 5 | 6 | 5 | 5 | 3 | 15 | 5 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 1.00 | 1.00 | 0.60 | 3.00 | 1.00 |
time (sec) |
N/A | 0.117 | 0.000 | 0.150 | 0.212 | 0.219 | 0.087 | 0.284 | 0.009 |
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 | 13 | 13 | 13 | 14 | 13 | 13 | 17 | 14 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.00 | 1.31 | 1.08 | 1.00 |
time (sec) |
N/A | 0.133 | 0.001 | 0.284 | 0.198 | 0.226 | 0.161 | 0.284 | 0.048 |
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 | 16 | 19 | 19 | 17 | 15 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.27 | 1.27 | 1.13 | 1.00 | 1.27 |
time (sec) |
N/A | 0.129 | 0.001 | 0.152 | 0.202 | 0.215 | 0.281 | 0.277 | 0.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 16 | 33 | 33 | 36 | 15 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 1.94 | 1.94 | 2.12 | 0.88 | 2.06 |
time (sec) |
N/A | 0.131 | 0.002 | 0.163 | 0.206 | 0.211 | 0.312 | 0.276 | 0.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | C | C | C | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 10 | 6 | 8 | 66 | 11 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.36 | 0.21 | 0.29 | 2.36 | 0.39 | 1.25 |
time (sec) |
N/A | 0.136 | 0.004 | 0.278 | 0.289 | 0.229 | 1.652 | 0.324 | 0.206 |
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 | 38 | 38 | 40 | 37 | 44 | 44 | 44 | 44 | 44 |
N.S. |
1 | 1.00 | 1.05 | 0.97 | 1.16 | 1.16 | 1.16 | 1.16 | 1.16 |
time (sec) |
N/A | 0.168 | 0.003 | 0.135 | 0.207 | 0.217 | 0.061 | 0.334 | 0.178 |
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 | 38 | 38 | 42 | 37 | 44 | 44 | 46 | 44 | 44 |
N.S. |
1 | 1.00 | 1.11 | 0.97 | 1.16 | 1.16 | 1.21 | 1.16 | 1.16 |
time (sec) |
N/A | 0.167 | 0.002 | 0.135 | 0.203 | 0.214 | 0.050 | 0.306 | 0.053 |
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 | 18 | 18 | 18 | 17 | 16 | 16 | 15 | 16 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.89 | 0.89 | 0.83 | 0.89 | 1.00 |
time (sec) |
N/A | 0.145 | 0.001 | 0.011 | 0.209 | 0.215 | 0.021 | 0.335 | 0.025 |
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 | 12 | 14 | 12 | 11 | 10 | 10 | 8 | 10 | 10 |
N.S. |
1 | 1.17 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.83 | 0.83 |
time (sec) |
N/A | 0.126 | 0.000 | 0.001 | 0.211 | 0.188 | 0.020 | 0.305 | 0.019 |
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 | 23 | 23 | 23 | 22 | 24 | 23 | 17 | 25 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 1.04 | 1.00 | 0.74 | 1.09 | 1.00 |
time (sec) |
N/A | 0.153 | 0.004 | 0.287 | 0.220 | 0.228 | 0.067 | 0.305 | 0.049 |
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 | 32 | 32 | 28 | 31 | 37 | 39 | 29 | 81 | 37 |
N.S. |
1 | 1.00 | 0.88 | 0.97 | 1.16 | 1.22 | 0.91 | 2.53 | 1.16 |
time (sec) |
N/A | 0.162 | 0.012 | 0.154 | 0.215 | 0.217 | 0.094 | 0.314 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 14 | 30 | 30 | 27 | 14 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 2.31 | 2.31 | 2.08 | 1.08 | 1.00 |
time (sec) |
N/A | 0.126 | 0.007 | 0.156 | 0.233 | 0.214 | 0.244 | 0.319 | 0.156 |
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 | 38 | 38 | 25 | 23 | 54 | 54 | 56 | 23 | 54 |
N.S. |
1 | 1.00 | 0.66 | 0.61 | 1.42 | 1.42 | 1.47 | 0.61 | 1.42 |
time (sec) |
N/A | 0.163 | 0.010 | 0.302 | 0.199 | 0.218 | 0.383 | 0.319 | 0.052 |
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 | 38 | 24 | 23 | 67 | 67 | 73 | 40 | 67 |
N.S. |
1 | 1.00 | 0.63 | 0.61 | 1.76 | 1.76 | 1.92 | 1.05 | 1.76 |
time (sec) |
N/A | 0.165 | 0.009 | 0.159 | 0.200 | 0.218 | 0.265 | 0.304 | 0.177 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 27 | 23 | 84 | 84 | 88 | 25 | 82 |
N.S. |
1 | 1.00 | 0.71 | 0.61 | 2.21 | 2.21 | 2.32 | 0.66 | 2.16 |
time (sec) |
N/A | 0.164 | 0.010 | 0.301 | 0.213 | 0.213 | 0.251 | 0.306 | 0.088 |
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 | 57 | 57 | 68 | 59 | 72 | 72 | 78 | 72 | 72 |
N.S. |
1 | 1.00 | 1.19 | 1.04 | 1.26 | 1.26 | 1.37 | 1.26 | 1.26 |
time (sec) |
N/A | 0.189 | 0.003 | 0.145 | 0.197 | 0.210 | 0.036 | 0.345 | 0.042 |
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 | 38 | 38 | 38 | 32 | 34 | 34 | 36 | 34 | 31 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.89 | 0.89 | 0.95 | 0.89 | 0.82 |
time (sec) |
N/A | 0.166 | 0.001 | 0.142 | 0.204 | 0.221 | 0.045 | 0.296 | 0.069 |
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 | 32 | 32 | 40 | 35 | 36 | 36 | 39 | 36 | 36 |
N.S. |
1 | 1.00 | 1.25 | 1.09 | 1.12 | 1.12 | 1.22 | 1.12 | 1.12 |
time (sec) |
N/A | 0.161 | 0.002 | 0.275 | 0.196 | 0.218 | 0.112 | 0.309 | 0.061 |
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 | 14 | 14 | 14 | 13 | 20 | 20 | 19 | 12 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 1.43 | 1.43 | 1.36 | 0.86 | 1.43 |
time (sec) |
N/A | 0.125 | 0.000 | 0.137 | 0.215 | 0.211 | 0.040 | 0.290 | 0.034 |
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 | 43 | 43 | 37 | 31 | 35 | 34 | 31 | 46 | 34 |
N.S. |
1 | 1.00 | 0.86 | 0.72 | 0.81 | 0.79 | 0.72 | 1.07 | 0.79 |
time (sec) |
N/A | 0.163 | 0.006 | 0.161 | 0.234 | 0.217 | 0.107 | 0.299 | 0.056 |
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 | 41 | 41 | 35 | 36 | 46 | 57 | 39 | 79 | 46 |
N.S. |
1 | 1.00 | 0.85 | 0.88 | 1.12 | 1.39 | 0.95 | 1.93 | 1.12 |
time (sec) |
N/A | 0.169 | 0.021 | 0.305 | 0.199 | 0.218 | 0.154 | 0.301 | 0.344 |
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 | 52 | 52 | 33 | 42 | 61 | 69 | 54 | 46 | 59 |
N.S. |
1 | 1.00 | 0.63 | 0.81 | 1.17 | 1.33 | 1.04 | 0.88 | 1.13 |
time (sec) |
N/A | 0.181 | 0.016 | 0.168 | 0.210 | 0.215 | 0.399 | 0.306 | 0.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 31 | 27 | 60 | 60 | 61 | 29 | 58 |
N.S. |
1 | 1.00 | 1.11 | 0.96 | 2.14 | 2.14 | 2.18 | 1.04 | 2.07 |
time (sec) |
N/A | 0.136 | 0.012 | 0.306 | 0.202 | 0.214 | 0.236 | 0.304 | 0.047 |
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 | 56 | 56 | 35 | 32 | 78 | 78 | 85 | 64 | 76 |
N.S. |
1 | 1.00 | 0.62 | 0.57 | 1.39 | 1.39 | 1.52 | 1.14 | 1.36 |
time (sec) |
N/A | 0.178 | 0.008 | 0.165 | 0.190 | 0.218 | 0.233 | 0.292 | 0.056 |
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 | 57 | 57 | 38 | 32 | 95 | 95 | 100 | 36 | 91 |
N.S. |
1 | 1.00 | 0.67 | 0.56 | 1.67 | 1.67 | 1.75 | 0.63 | 1.60 |
time (sec) |
N/A | 0.181 | 0.013 | 0.309 | 0.207 | 0.217 | 0.653 | 0.316 | 0.201 |
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 | 59 | 59 | 37 | 32 | 108 | 108 | 117 | 36 | 104 |
N.S. |
1 | 1.00 | 0.63 | 0.54 | 1.83 | 1.83 | 1.98 | 0.61 | 1.76 |
time (sec) |
N/A | 0.183 | 0.011 | 0.172 | 0.209 | 0.218 | 0.385 | 0.287 | 0.234 |
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 | 61 | 61 | 42 | 41 | 48 | 52 | 49 | 59 | 48 |
N.S. |
1 | 1.00 | 0.69 | 0.67 | 0.79 | 0.85 | 0.80 | 0.97 | 0.79 |
time (sec) |
N/A | 0.181 | 0.005 | 0.306 | 0.201 | 0.215 | 0.075 | 0.329 | 0.053 |
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 | 43 | 43 | 31 | 30 | 34 | 38 | 34 | 45 | 32 |
N.S. |
1 | 1.00 | 0.72 | 0.70 | 0.79 | 0.88 | 0.79 | 1.05 | 0.74 |
time (sec) |
N/A | 0.165 | 0.004 | 0.162 | 0.220 | 0.219 | 0.063 | 0.307 | 0.170 |
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 | 18 | 18 | 18 | 19 | 18 | 20 | 15 | 19 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.11 | 0.83 | 1.06 | 1.00 |
time (sec) |
N/A | 0.146 | 0.003 | 0.299 | 0.205 | 0.217 | 0.051 | 0.291 | 0.041 |
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 | 10 | 10 | 10 | 11 | 10 | 10 | 7 | 11 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.00 | 1.00 | 0.70 | 1.10 | 1.00 |
time (sec) |
N/A | 0.125 | 0.000 | 0.153 | 0.212 | 0.211 | 0.023 | 0.299 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 29 | 37 | 28 | 22 | 39 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.71 | 2.18 | 1.65 | 1.29 | 2.29 | 1.00 |
time (sec) |
N/A | 0.133 | 0.005 | 0.180 | 0.206 | 0.224 | 0.096 | 0.283 | 0.069 |
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 | 42 | 42 | 53 | 51 | 60 | 60 | 48 | 53 | 42 |
N.S. |
1 | 1.00 | 1.26 | 1.21 | 1.43 | 1.43 | 1.14 | 1.26 | 1.00 |
time (sec) |
N/A | 0.173 | 0.011 | 0.330 | 0.218 | 0.216 | 0.157 | 0.291 | 0.076 |
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 | 63 | 63 | 65 | 64 | 82 | 98 | 71 | 69 | 64 |
N.S. |
1 | 1.00 | 1.03 | 1.02 | 1.30 | 1.56 | 1.13 | 1.10 | 1.02 |
time (sec) |
N/A | 0.191 | 0.013 | 0.188 | 0.205 | 0.221 | 0.192 | 0.319 | 0.087 |
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 | 54 | 54 | 46 | 45 | 53 | 79 | 51 | 80 | 52 |
N.S. |
1 | 1.00 | 0.85 | 0.83 | 0.98 | 1.46 | 0.94 | 1.48 | 0.96 |
time (sec) |
N/A | 0.183 | 0.014 | 0.311 | 0.200 | 0.218 | 0.132 | 0.290 | 0.056 |
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 | 39 | 39 | 33 | 34 | 40 | 61 | 36 | 59 | 39 |
N.S. |
1 | 1.00 | 0.85 | 0.87 | 1.03 | 1.56 | 0.92 | 1.51 | 1.00 |
time (sec) |
N/A | 0.170 | 0.013 | 0.165 | 0.198 | 0.221 | 0.101 | 0.296 | 0.226 |
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 | 27 | 27 | 23 | 25 | 28 | 33 | 24 | 54 | 27 |
N.S. |
1 | 1.00 | 0.85 | 0.93 | 1.04 | 1.22 | 0.89 | 2.00 | 1.00 |
time (sec) |
N/A | 0.156 | 0.007 | 0.315 | 0.196 | 0.222 | 0.098 | 0.286 | 0.062 |
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 | 12 | 12 | 12 | 13 | 12 | 13 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.08 | 0.83 | 1.00 | 1.00 |
time (sec) |
N/A | 0.125 | 0.000 | 0.153 | 0.209 | 0.218 | 0.069 | 0.296 | 0.028 |
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 | 41 | 41 | 50 | 50 | 55 | 51 | 44 | 44 | 37 |
N.S. |
1 | 1.00 | 1.22 | 1.22 | 1.34 | 1.24 | 1.07 | 1.07 | 0.90 |
time (sec) |
N/A | 0.169 | 0.010 | 0.186 | 0.196 | 0.225 | 0.294 | 0.304 | 0.213 |
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 | 46 | 74 | 61 | 64 | 76 | 49 | 83 | 46 |
N.S. |
1 | 1.00 | 1.61 | 1.33 | 1.39 | 1.65 | 1.07 | 1.80 | 1.00 |
time (sec) |
N/A | 0.151 | 0.017 | 0.331 | 0.209 | 0.226 | 0.533 | 0.297 | 0.332 |
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 | 83 | 83 | 68 | 80 | 108 | 146 | 104 | 81 | 86 |
N.S. |
1 | 1.00 | 0.82 | 0.96 | 1.30 | 1.76 | 1.25 | 0.98 | 1.04 |
time (sec) |
N/A | 0.203 | 0.025 | 0.194 | 0.248 | 0.221 | 0.258 | 0.307 | 0.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 113 | 63 | 92 | 68 | 62 | 287 | 185 | 0 |
N.S. |
1 | 1.05 | 0.58 | 0.85 | 0.63 | 0.57 | 2.66 | 1.71 | 0.00 |
time (sec) |
N/A | 0.185 | 0.147 | 0.476 | 0.285 | 0.230 | 125.260 | 0.367 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 58 | 87 | 54 | 57 | 252 | 115 | 0 |
N.S. |
1 | 1.00 | 0.66 | 0.99 | 0.61 | 0.65 | 2.86 | 1.31 | 0.00 |
time (sec) |
N/A | 0.172 | 0.128 | 0.168 | 0.301 | 0.227 | 40.032 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 63 | 53 | 82 | 40 | 52 | 216 | 101 | 0 |
N.S. |
1 | 0.93 | 0.78 | 1.21 | 0.59 | 0.76 | 3.18 | 1.49 | 0.00 |
time (sec) |
N/A | 0.150 | 0.103 | 0.309 | 0.292 | 0.221 | 13.858 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 38 | 46 | 71 | 28 | 47 | 167 | 50 | 0 |
N.S. |
1 | 0.79 | 0.96 | 1.48 | 0.58 | 0.98 | 3.48 | 1.04 | 0.00 |
time (sec) |
N/A | 0.137 | 0.089 | 0.164 | 0.298 | 0.238 | 6.115 | 0.293 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 23 | 37 | 57 | 17 | 38 | 131 | 42 | 37 |
N.S. |
1 | 0.82 | 1.32 | 2.04 | 0.61 | 1.36 | 4.68 | 1.50 | 1.32 |
time (sec) |
N/A | 0.130 | 0.003 | 0.309 | 0.305 | 0.219 | 2.737 | 0.302 | 0.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 16 | 34 | 42 | 14 | 37 | 99 | 28 | 14 |
N.S. |
1 | 0.76 | 1.62 | 2.00 | 0.67 | 1.76 | 4.71 | 1.33 | 0.67 |
time (sec) |
N/A | 0.126 | 0.004 | 0.163 | 0.313 | 0.223 | 1.883 | 0.312 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 39 | 64 | 21 | 48 | 70 | 33 | 0 |
N.S. |
1 | 1.00 | 1.70 | 2.78 | 0.91 | 2.09 | 3.04 | 1.43 | 0.00 |
time (sec) |
N/A | 0.129 | 0.052 | 0.166 | 0.284 | 0.221 | 1.239 | 0.311 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 15 | 38 | 33 | 60 | 19 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 1.90 | 1.65 | 3.00 | 0.95 | 1.70 |
time (sec) |
N/A | 0.122 | 0.017 | 0.312 | 0.203 | 0.221 | 1.776 | 0.298 | 0.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 25 | 18 | 64 | 53 | 172 | 22 | 50 |
N.S. |
1 | 1.00 | 0.61 | 0.44 | 1.56 | 1.29 | 4.20 | 0.54 | 1.22 |
time (sec) |
N/A | 0.140 | 0.026 | 0.165 | 0.215 | 0.222 | 6.408 | 0.337 | 0.314 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 66 | 30 | 25 | 95 | 70 | 566 | 29 | 64 |
N.S. |
1 | 1.08 | 0.49 | 0.41 | 1.56 | 1.15 | 9.28 | 0.48 | 1.05 |
time (sec) |
N/A | 0.152 | 0.029 | 0.318 | 0.200 | 0.226 | 20.654 | 0.297 | 0.328 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 91 | 35 | 30 | 131 | 85 | 1561 | 35 | 80 |
N.S. |
1 | 1.12 | 0.43 | 0.37 | 1.62 | 1.05 | 19.27 | 0.43 | 0.99 |
time (sec) |
N/A | 0.157 | 0.036 | 0.173 | 0.207 | 0.225 | 70.616 | 0.306 | 0.465 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 116 | 40 | 35 | 172 | 100 | 0 | 42 | 94 |
N.S. |
1 | 1.15 | 0.40 | 0.35 | 1.70 | 0.99 | 0.00 | 0.42 | 0.93 |
time (sec) |
N/A | 0.169 | 0.041 | 0.323 | 0.207 | 0.236 | 0.000 | 0.324 | 0.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 109 | 109 | 68 | 97 | 66 | 67 | 0 | 237 | 0 |
N.S. |
1 | 1.00 | 0.62 | 0.89 | 0.61 | 0.61 | 0.00 | 2.17 | 0.00 |
time (sec) |
N/A | 0.175 | 0.165 | 0.167 | 0.302 | 0.224 | 0.000 | 0.358 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 84 | 63 | 92 | 52 | 62 | 287 | 185 | 0 |
N.S. |
1 | 0.94 | 0.71 | 1.03 | 0.58 | 0.70 | 3.22 | 2.08 | 0.00 |
time (sec) |
N/A | 0.166 | 0.152 | 0.315 | 0.297 | 0.220 | 164.060 | 0.336 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 59 | 58 | 87 | 40 | 57 | 248 | 91 | 0 |
N.S. |
1 | 0.86 | 0.84 | 1.26 | 0.58 | 0.83 | 3.59 | 1.32 | 0.00 |
time (sec) |
N/A | 0.147 | 0.124 | 0.166 | 0.308 | 0.227 | 54.462 | 0.315 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 44 | 46 | 75 | 29 | 46 | 212 | 101 | 0 |
N.S. |
1 | 0.90 | 0.94 | 1.53 | 0.59 | 0.94 | 4.33 | 2.06 | 0.00 |
time (sec) |
N/A | 0.140 | 0.067 | 0.330 | 0.295 | 0.221 | 17.472 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 38 | 46 | 71 | 28 | 47 | 163 | 66 | 0 |
N.S. |
1 | 0.79 | 0.96 | 1.48 | 0.58 | 0.98 | 3.40 | 1.38 | 0.00 |
time (sec) |
N/A | 0.141 | 0.082 | 0.162 | 0.286 | 0.223 | 9.953 | 0.319 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 41 | 39 | 57 | 28 | 40 | 134 | 31 | 0 |
N.S. |
1 | 0.87 | 0.83 | 1.21 | 0.60 | 0.85 | 2.85 | 0.66 | 0.00 |
time (sec) |
N/A | 0.139 | 0.059 | 0.312 | 0.289 | 0.223 | 3.619 | 0.302 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 37 | 41 | 72 | 42 | 52 | 99 | 35 | 0 |
N.S. |
1 | 0.90 | 1.00 | 1.76 | 1.02 | 1.27 | 2.41 | 0.85 | 0.00 |
time (sec) |
N/A | 0.140 | 0.071 | 0.167 | 0.282 | 0.222 | 1.966 | 0.287 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 46 | 76 | 66 | 71 | 498 | 38 | 0 |
N.S. |
1 | 1.00 | 1.12 | 1.85 | 1.61 | 1.73 | 12.15 | 0.93 | 0.00 |
time (sec) |
N/A | 0.147 | 0.062 | 0.317 | 0.293 | 0.229 | 3.966 | 0.300 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 15 | 94 | 52 | 87 | 19 | 50 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 4.70 | 2.60 | 4.35 | 0.95 | 2.50 |
time (sec) |
N/A | 0.121 | 0.022 | 0.168 | 0.219 | 0.227 | 6.072 | 0.311 | 0.298 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 25 | 18 | 131 | 69 | 226 | 22 | 64 |
N.S. |
1 | 1.00 | 0.61 | 0.44 | 3.20 | 1.68 | 5.51 | 0.54 | 1.56 |
time (sec) |
N/A | 0.130 | 0.029 | 0.170 | 0.203 | 0.226 | 20.204 | 0.513 | 0.448 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 66 | 30 | 25 | 172 | 86 | 675 | 29 | 80 |
N.S. |
1 | 1.08 | 0.49 | 0.41 | 2.82 | 1.41 | 11.07 | 0.48 | 1.31 |
time (sec) |
N/A | 0.145 | 0.035 | 0.320 | 0.211 | 0.217 | 67.397 | 0.394 | 0.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 91 | 35 | 30 | 218 | 101 | 1751 | 35 | 94 |
N.S. |
1 | 1.12 | 0.43 | 0.37 | 2.69 | 1.25 | 21.62 | 0.43 | 1.16 |
time (sec) |
N/A | 0.165 | 0.041 | 0.172 | 0.226 | 0.240 | 169.071 | 0.317 | 0.337 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 116 | 40 | 35 | 269 | 116 | 0 | 42 | 110 |
N.S. |
1 | 1.15 | 0.40 | 0.35 | 2.66 | 1.15 | 0.00 | 0.42 | 1.09 |
time (sec) |
N/A | 0.170 | 0.047 | 0.323 | 0.222 | 0.227 | 0.000 | 0.331 | 0.345 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 130 | 78 | 107 | 78 | 77 | 0 | 323 | 0 |
N.S. |
1 | 1.00 | 0.60 | 0.82 | 0.60 | 0.59 | 0.00 | 2.48 | 0.00 |
time (sec) |
N/A | 0.188 | 0.203 | 0.173 | 0.308 | 0.227 | 0.000 | 0.381 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 105 | 72 | 102 | 64 | 72 | 0 | 296 | 0 |
N.S. |
1 | 0.95 | 0.65 | 0.93 | 0.58 | 0.65 | 0.00 | 2.69 | 0.00 |
time (sec) |
N/A | 0.172 | 0.191 | 0.323 | 0.288 | 0.222 | 0.000 | 0.369 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 90 | 80 | 68 | 97 | 52 | 67 | 0 | 143 | 0 |
N.S. |
1 | 0.89 | 0.76 | 1.08 | 0.58 | 0.74 | 0.00 | 1.59 | 0.00 |
time (sec) |
N/A | 0.154 | 0.163 | 0.170 | 0.287 | 0.223 | 0.000 | 0.332 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 70 | 65 | 51 | 80 | 41 | 51 | 0 | 185 | 0 |
N.S. |
1 | 0.93 | 0.73 | 1.14 | 0.59 | 0.73 | 0.00 | 2.64 | 0.00 |
time (sec) |
N/A | 0.148 | 0.082 | 0.320 | 0.299 | 0.224 | 0.000 | 0.348 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 59 | 58 | 87 | 40 | 57 | 245 | 114 | 0 |
N.S. |
1 | 0.86 | 0.84 | 1.26 | 0.58 | 0.83 | 3.55 | 1.65 | 0.00 |
time (sec) |
N/A | 0.143 | 0.114 | 0.168 | 0.298 | 0.223 | 84.967 | 0.320 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 63 | 53 | 82 | 40 | 52 | 212 | 101 | 0 |
N.S. |
1 | 0.93 | 0.78 | 1.21 | 0.59 | 0.76 | 3.12 | 1.49 | 0.00 |
time (sec) |
N/A | 0.150 | 0.088 | 0.319 | 0.299 | 0.217 | 33.346 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 66 | 46 | 71 | 42 | 47 | 170 | 39 | 0 |
N.S. |
1 | 0.99 | 0.69 | 1.06 | 0.63 | 0.70 | 2.54 | 0.58 | 0.00 |
time (sec) |
N/A | 0.150 | 0.070 | 0.167 | 0.294 | 0.220 | 11.190 | 0.326 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 62 | 49 | 77 | 56 | 58 | 138 | 42 | 0 |
N.S. |
1 | 0.95 | 0.75 | 1.18 | 0.86 | 0.89 | 2.12 | 0.65 | 0.00 |
time (sec) |
N/A | 0.148 | 0.091 | 0.321 | 0.291 | 0.222 | 6.992 | 0.319 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 62 | 51 | 84 | 99 | 75 | 575 | 44 | 0 |
N.S. |
1 | 0.98 | 0.81 | 1.33 | 1.57 | 1.19 | 9.13 | 0.70 | 0.00 |
time (sec) |
N/A | 0.149 | 0.092 | 0.172 | 0.314 | 0.222 | 5.618 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | C | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 51 | 84 | 160 | 91 | 1606 | 44 | 0 |
N.S. |
1 | 1.00 | 0.81 | 1.33 | 2.54 | 1.44 | 25.49 | 0.70 | 0.00 |
time (sec) |
N/A | 0.147 | 0.074 | 0.324 | 0.325 | 0.222 | 11.086 | 0.340 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 15 | 171 | 66 | 114 | 19 | 64 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 8.55 | 3.30 | 5.70 | 0.95 | 3.20 |
time (sec) |
N/A | 0.124 | 0.023 | 0.175 | 0.215 | 0.223 | 20.232 | 0.311 | 0.309 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 25 | 18 | 218 | 83 | 280 | 22 | 80 |
N.S. |
1 | 1.00 | 0.61 | 0.44 | 5.32 | 2.02 | 6.83 | 0.54 | 1.95 |
time (sec) |
N/A | 0.134 | 0.035 | 0.335 | 0.214 | 0.236 | 71.904 | 0.302 | 0.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 66 | 30 | 25 | 269 | 100 | 784 | 29 | 94 |
N.S. |
1 | 1.08 | 0.49 | 0.41 | 4.41 | 1.64 | 12.85 | 0.48 | 1.54 |
time (sec) |
N/A | 0.145 | 0.037 | 0.176 | 0.242 | 0.225 | 178.852 | 0.332 | 0.329 |