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 | F | A | B | A | B | B | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 47 | 0 | 39 | 56 | 40 | 41 | 110 | 56 |
N.S. |
1 | 1.96 | 0.00 | 1.62 | 2.33 | 1.67 | 1.71 | 4.58 | 2.33 |
time (sec) |
N/A | 2.861 | 0.000 | 0.701 | 0.491 | 0.253 | 0.299 | 0.468 | 9.614 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 0 | 16 | 15 | 0 | 14 | 15 | 14 | 15 |
N.S. |
1 | 0.00 | 1.14 | 1.07 | 0.00 | 1.00 | 1.07 | 1.00 | 1.07 |
time (sec) |
N/A | 0.000 | 0.072 | 0.534 | 0.000 | 0.260 | 0.125 | 0.262 | 9.728 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 115 | 33 | 32 | 36 | 32 | 24 | 28 | 0 |
N.S. |
1 | 3.38 | 0.97 | 0.94 | 1.06 | 0.94 | 0.71 | 0.82 | 0.00 |
time (sec) |
N/A | 1.127 | 0.066 | 0.933 | 0.235 | 0.256 | 3.510 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 73 | 54 | 39 | 39 | 55 | 36 | 43 | 37 |
N.S. |
1 | 2.15 | 1.59 | 1.15 | 1.15 | 1.62 | 1.06 | 1.26 | 1.09 |
time (sec) |
N/A | 0.466 | 0.049 | 0.256 | 0.188 | 0.265 | 3.136 | 0.257 | 9.834 |
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 | 21 | 15 | 14 | 14 | 15 | 13 | 12 | 15 | 15 |
N.S. |
1 | 0.71 | 0.67 | 0.67 | 0.71 | 0.62 | 0.57 | 0.71 | 0.71 |
time (sec) |
N/A | 0.149 | 0.005 | 0.049 | 0.187 | 0.235 | 0.043 | 0.244 | 9.573 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 70 | 33 | 27 | 26 | 26 | 29 | 26 | 30 |
N.S. |
1 | 2.33 | 1.10 | 0.90 | 0.87 | 0.87 | 0.97 | 0.87 | 1.00 |
time (sec) |
N/A | 0.227 | 1.151 | 0.121 | 0.363 | 0.262 | 0.065 | 0.273 | 9.673 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 0 | 92 | 101 | 101 | 85 | 110 | 0 |
N.S. |
1 | 0.00 | 0.00 | 2.49 | 2.73 | 2.73 | 2.30 | 2.97 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.176 | 0.281 | 0.267 | 0.429 | 0.427 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 33 | 34 | 26 | 33 | 0 | 31 | 33 |
N.S. |
1 | 0.00 | 1.06 | 1.10 | 0.84 | 1.06 | 0.00 | 1.00 | 1.06 |
time (sec) |
N/A | 0.000 | 0.198 | 7.748 | 0.242 | 0.246 | 0.000 | 0.370 | 9.941 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 25 | 21 | 0 | 26 | 17 | 0 | 20 |
N.S. |
1 | 0.00 | 1.14 | 0.95 | 0.00 | 1.18 | 0.77 | 0.00 | 0.91 |
time (sec) |
N/A | 0.000 | 0.347 | 0.281 | 0.000 | 0.243 | 0.084 | 0.000 | 10.177 |
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 | 30 | 40 | 33 | 33 | 32 | 40 | 31 | 32 | 33 |
N.S. |
1 | 1.33 | 1.10 | 1.10 | 1.07 | 1.33 | 1.03 | 1.07 | 1.10 |
time (sec) |
N/A | 0.353 | 0.041 | 0.085 | 0.187 | 0.236 | 0.449 | 0.250 | 9.859 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | F | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 45 | 31 | 40 | 0 | 18 | 0 | 35 | 37 |
N.S. |
1 | 2.14 | 1.48 | 1.90 | 0.00 | 0.86 | 0.00 | 1.67 | 1.76 |
time (sec) |
N/A | 0.502 | 0.165 | 0.185 | 0.000 | 0.271 | 0.000 | 0.255 | 10.553 |
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 | 31 | 36 | 32 | 28 | 27 | 27 | 24 | 47 | 27 |
N.S. |
1 | 1.16 | 1.03 | 0.90 | 0.87 | 0.87 | 0.77 | 1.52 | 0.87 |
time (sec) |
N/A | 0.533 | 0.142 | 0.565 | 0.220 | 0.251 | 0.107 | 0.259 | 10.346 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 21 | 66 | 30 | 53 | 53 | 121 | 109 | 19 |
N.S. |
1 | 0.75 | 2.36 | 1.07 | 1.89 | 1.89 | 4.32 | 3.89 | 0.68 |
time (sec) |
N/A | 0.206 | 0.006 | 0.394 | 0.177 | 0.241 | 0.064 | 0.259 | 10.416 |
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 | 17 | 25 | 14 | 15 | 15 | 12 | 17 | 13 |
N.S. |
1 | 0.77 | 1.14 | 0.64 | 0.68 | 0.68 | 0.55 | 0.77 | 0.59 |
time (sec) |
N/A | 0.184 | 0.009 | 0.023 | 0.263 | 0.243 | 0.054 | 0.249 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 55 | 52 | 26 | 48 | 50 | 53 | 50 | 25 |
N.S. |
1 | 2.20 | 2.08 | 1.04 | 1.92 | 2.00 | 2.12 | 2.00 | 1.00 |
time (sec) |
N/A | 0.248 | 0.028 | 0.163 | 0.189 | 0.240 | 0.383 | 0.254 | 0.095 |
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 | 18 | 17 | 27 | 14 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.94 | 1.50 | 0.78 | 0.94 | 0.94 |
time (sec) |
N/A | 0.260 | 0.018 | 1.009 | 0.182 | 0.243 | 0.155 | 0.256 | 10.234 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 37 | 23 | 34 | 56 | 29 | 32 | 33 | 41 |
N.S. |
1 | 1.42 | 0.88 | 1.31 | 2.15 | 1.12 | 1.23 | 1.27 | 1.58 |
time (sec) |
N/A | 0.254 | 0.042 | 0.106 | 0.189 | 0.244 | 0.086 | 0.261 | 9.787 |
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 | 16 | 16 | 16 | 15 | 20 | 15 | 15 | 15 |
N.S. |
1 | 0.70 | 0.70 | 0.70 | 0.65 | 0.87 | 0.65 | 0.65 | 0.65 |
time (sec) |
N/A | 0.150 | 0.003 | 0.116 | 0.200 | 0.246 | 0.053 | 0.255 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 26 | 44 | 52 | 38 | 69 | 39 | 101 | 38 |
N.S. |
1 | 1.13 | 1.91 | 2.26 | 1.65 | 3.00 | 1.70 | 4.39 | 1.65 |
time (sec) |
N/A | 0.265 | 0.034 | 0.517 | 0.183 | 0.242 | 0.255 | 0.247 | 9.740 |
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 | 19 | 15 | 15 | 17 | 15 | 22 | 24 | 16 | 15 |
N.S. |
1 | 0.79 | 0.79 | 0.89 | 0.79 | 1.16 | 1.26 | 0.84 | 0.79 |
time (sec) |
N/A | 0.145 | 0.003 | 0.072 | 0.171 | 0.256 | 0.056 | 0.249 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 42 | 36 | 33 | 63 | 45 | 29 | 37 | 41 |
N.S. |
1 | 1.40 | 1.20 | 1.10 | 2.10 | 1.50 | 0.97 | 1.23 | 1.37 |
time (sec) |
N/A | 0.243 | 0.066 | 0.143 | 0.189 | 0.252 | 0.108 | 0.244 | 9.664 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | C | A | C | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 90 | 62 | 37 | 57 | 33 | 60 | 36 | 38 |
N.S. |
1 | 3.33 | 2.30 | 1.37 | 2.11 | 1.22 | 2.22 | 1.33 | 1.41 |
time (sec) |
N/A | 0.724 | 0.096 | 0.419 | 0.314 | 0.258 | 0.400 | 0.258 | 9.512 |
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 | 29 | 42 | 25 | 26 | 25 | 26 | 29 | 37 | 27 |
N.S. |
1 | 1.45 | 0.86 | 0.90 | 0.86 | 0.90 | 1.00 | 1.28 | 0.93 |
time (sec) |
N/A | 0.303 | 0.020 | 0.117 | 0.188 | 0.245 | 0.307 | 0.254 | 0.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | B | B | B | F(-1) | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 32 | 58 | 182 | 218135 | 392 | 155 | 272 | 0 | 238 |
N.S. |
1 | 1.81 | 5.69 | 6816.72 | 12.25 | 4.84 | 8.50 | 0.00 | 7.44 |
time (sec) |
N/A | 12.227 | 0.231 | 36.632 | 0.610 | 0.265 | 13.835 | 0.000 | 11.613 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 10 | 10 | 10 | 28 | 9 | 8 | 9 | 9 |
N.S. |
1 | 0.71 | 0.71 | 0.71 | 2.00 | 0.64 | 0.57 | 0.64 | 0.64 |
time (sec) |
N/A | 0.199 | 0.008 | 0.047 | 0.183 | 0.249 | 0.040 | 0.262 | 8.011 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 27 | 36 | 117 | 47 | 31 | 38 | 55 |
N.S. |
1 | 0.00 | 1.08 | 1.44 | 4.68 | 1.88 | 1.24 | 1.52 | 2.20 |
time (sec) |
N/A | 0.000 | 0.203 | 2.249 | 0.405 | 0.263 | 0.069 | 0.266 | 8.775 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 24 | 19 | 22 | 73 | 20 | 0 | 24 |
N.S. |
1 | 0.00 | 1.14 | 0.90 | 1.05 | 3.48 | 0.95 | 0.00 | 1.14 |
time (sec) |
N/A | 0.000 | 0.459 | 0.084 | 0.319 | 0.263 | 0.095 | 0.000 | 8.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 27 | 23 | 19 | 23 | 31 | 20 | 32 | 22 |
N.S. |
1 | 1.17 | 1.00 | 0.83 | 1.00 | 1.35 | 0.87 | 1.39 | 0.96 |
time (sec) |
N/A | 0.381 | 0.061 | 0.112 | 0.204 | 0.243 | 0.071 | 0.259 | 8.427 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 25 | 25 | 24 | 92 | 22 | 17 | 27 | 25 |
N.S. |
1 | 1.09 | 1.09 | 1.04 | 4.00 | 0.96 | 0.74 | 1.17 | 1.09 |
time (sec) |
N/A | 0.215 | 0.033 | 0.245 | 0.232 | 0.255 | 0.066 | 0.266 | 8.108 |
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 | 31 | 27 | 16 | 24 | 15 | 12 | 15 | 22 |
N.S. |
1 | 1.72 | 1.50 | 0.89 | 1.33 | 0.83 | 0.67 | 0.83 | 1.22 |
time (sec) |
N/A | 0.162 | 0.061 | 0.119 | 0.176 | 0.239 | 0.046 | 0.256 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | F(-2) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 32 | 57 | 83 | 52 | 0 | 118 | 28 |
N.S. |
1 | 0.00 | 1.03 | 1.84 | 2.68 | 1.68 | 0.00 | 3.81 | 0.90 |
time (sec) |
N/A | 0.000 | 0.173 | 4.622 | 0.325 | 0.262 | 0.000 | 0.312 | 9.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 95 | 25 | 21 | 20 | 20 | 22 | 0 | 23 |
N.S. |
1 | 3.80 | 1.00 | 0.84 | 0.80 | 0.80 | 0.88 | 0.00 | 0.92 |
time (sec) |
N/A | 0.686 | 0.300 | 0.561 | 0.284 | 0.256 | 0.134 | 0.000 | 8.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 0 | 12 | 11 | 10 | 10 | 12 | 10 | 10 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 0.83 | 0.83 | 1.00 | 0.83 | 0.83 |
time (sec) |
N/A | 0.000 | 0.244 | 0.494 | 0.242 | 0.251 | 0.136 | 0.281 | 8.409 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F(-1) | A | A | A | A | A | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 0 | 32 | 28 | 28 | 24 | 33 | 101 |
N.S. |
1 | 0.00 | 0.00 | 1.03 | 0.90 | 0.90 | 0.77 | 1.06 | 3.26 |
time (sec) |
N/A | 0.000 | 0.000 | 1.477 | 0.308 | 0.271 | 0.177 | 0.294 | 8.538 |
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 | 21 | 21 | 18 | 17 | 17 | 17 | 37 | 17 |
N.S. |
1 | 0.75 | 0.75 | 0.64 | 0.61 | 0.61 | 0.61 | 1.32 | 0.61 |
time (sec) |
N/A | 0.394 | 0.082 | 0.175 | 0.223 | 0.251 | 0.097 | 0.290 | 8.417 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | B | A | B | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 27 | 1746 | 49 | 81 | 36 | 71 | 0 |
N.S. |
1 | 0.00 | 0.93 | 60.21 | 1.69 | 2.79 | 1.24 | 2.45 | 0.00 |
time (sec) |
N/A | 0.000 | 0.235 | 0.055 | 0.393 | 0.261 | 107.453 | 2.715 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 18 | 20 | 27 | 19 | 15 | 23 | 16 |
N.S. |
1 | 0.00 | 0.72 | 0.80 | 1.08 | 0.76 | 0.60 | 0.92 | 0.64 |
time (sec) |
N/A | 0.000 | 0.099 | 0.381 | 0.346 | 0.264 | 0.122 | 0.283 | 8.478 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 18 | 18 | 16 | 0 | 15 | 15 | 15 | 12 |
N.S. |
1 | 0.82 | 0.82 | 0.73 | 0.00 | 0.68 | 0.68 | 0.68 | 0.55 |
time (sec) |
N/A | 0.158 | 0.052 | 0.208 | 0.000 | 0.244 | 0.091 | 0.253 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 27 | 29 | 40 | 40 | 19 | 23 | 40 |
N.S. |
1 | 0.00 | 0.87 | 0.94 | 1.29 | 1.29 | 0.61 | 0.74 | 1.29 |
time (sec) |
N/A | 0.000 | 0.061 | 15.502 | 0.324 | 0.262 | 0.219 | 0.284 | 8.209 |
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 | 8 | 8 | 6 | 5 | 5 | 8 | 5 | 5 |
N.S. |
1 | 0.62 | 0.62 | 0.46 | 0.38 | 0.38 | 0.62 | 0.38 | 0.38 |
time (sec) |
N/A | 0.119 | 0.000 | 0.028 | 0.187 | 0.233 | 0.016 | 0.253 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 22 | 21 | 0 | 43 | 19 | 0 | 24 |
N.S. |
1 | 0.00 | 0.92 | 0.88 | 0.00 | 1.79 | 0.79 | 0.00 | 1.00 |
time (sec) |
N/A | 0.000 | 2.803 | 0.108 | 0.000 | 0.264 | 0.161 | 0.000 | 8.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 0 | 28 | 27 | 27 | 26 | 94 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.88 | 0.84 | 0.84 | 0.81 | 2.94 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.546 | 0.326 | 0.266 | 0.224 | 0.361 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | F(-1) | B | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 0 | 56 | 0 | 254 | 63 | 128 | 92 |
N.S. |
1 | 0.00 | 0.00 | 1.70 | 0.00 | 7.70 | 1.91 | 3.88 | 2.79 |
time (sec) |
N/A | 0.000 | 0.000 | 1.131 | 0.000 | 0.273 | 0.279 | 0.555 | 8.676 |
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 | 25 | 43 | 19 | 22 | 23 | 21 | 19 | 23 | 21 |
N.S. |
1 | 1.72 | 0.76 | 0.88 | 0.92 | 0.84 | 0.76 | 0.92 | 0.84 |
time (sec) |
N/A | 0.192 | 0.037 | 0.135 | 0.198 | 0.262 | 0.110 | 0.272 | 7.938 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 41 | 35 | 37 | 48 | 36 | 394 | 259 |
N.S. |
1 | 0.00 | 1.28 | 1.09 | 1.16 | 1.50 | 1.12 | 12.31 | 8.09 |
time (sec) |
N/A | 0.000 | 0.422 | 47.312 | 0.306 | 0.273 | 12.549 | 0.421 | 8.719 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 29 | 67 | 82 | 54 | 48 | 108 | 0 |
N.S. |
1 | 0.00 | 0.83 | 1.91 | 2.34 | 1.54 | 1.37 | 3.09 | 0.00 |
time (sec) |
N/A | 0.000 | 0.452 | 0.175 | 0.263 | 0.264 | 0.281 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 22 | 236 | 21 | 19 | 0 | 21 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 10.73 | 0.95 | 0.86 | 0.00 | 0.95 |
time (sec) |
N/A | 0.000 | 0.159 | 0.681 | 0.219 | 0.259 | 0.092 | 0.000 | 8.693 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 25 | 23 | 30 | 28 | 20 | 24 | 0 |
N.S. |
1 | 0.00 | 1.32 | 1.21 | 1.58 | 1.47 | 1.05 | 1.26 | 0.00 |
time (sec) |
N/A | 0.000 | 0.523 | 3.821 | 0.329 | 0.266 | 0.225 | 0.279 | 0.000 |
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 | 26 | 22 | 19 | 16 | 15 | 16 | 14 | 15 | 16 |
N.S. |
1 | 0.85 | 0.73 | 0.62 | 0.58 | 0.62 | 0.54 | 0.58 | 0.62 |
time (sec) |
N/A | 0.155 | 0.003 | 0.117 | 0.196 | 0.283 | 0.043 | 0.248 | 7.978 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 69 | 37 | 65 | 52 | 52 | 71 | 52 | 62 |
N.S. |
1 | 2.16 | 1.16 | 2.03 | 1.62 | 1.62 | 2.22 | 1.62 | 1.94 |
time (sec) |
N/A | 0.341 | 0.717 | 0.233 | 0.195 | 0.255 | 0.101 | 0.257 | 0.111 |
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 | 25 | 26 | 21 | 19 | 23 | 22 | 22 | 23 | 20 |
N.S. |
1 | 1.04 | 0.84 | 0.76 | 0.92 | 0.88 | 0.88 | 0.92 | 0.80 |
time (sec) |
N/A | 0.136 | 0.005 | 0.345 | 0.194 | 0.237 | 0.021 | 0.263 | 0.082 |
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 | 26 | 29 | 23 | 21 | 21 | 24 | 21 | 23 |
N.S. |
1 | 0.81 | 0.91 | 0.72 | 0.66 | 0.66 | 0.75 | 0.66 | 0.72 |
time (sec) |
N/A | 0.152 | 0.019 | 0.122 | 0.188 | 0.251 | 0.046 | 0.257 | 8.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | F(-1) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 26 | 30 | 0 | 28 | 0 | 51 | 64 |
N.S. |
1 | 0.00 | 0.96 | 1.11 | 0.00 | 1.04 | 0.00 | 1.89 | 2.37 |
time (sec) |
N/A | 0.000 | 5.095 | 0.208 | 0.000 | 0.259 | 0.000 | 0.362 | 8.588 |
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 | 25 | 21 | 17 | 16 | 15 | 18 | 12 | 15 | 15 |
N.S. |
1 | 0.84 | 0.68 | 0.64 | 0.60 | 0.72 | 0.48 | 0.60 | 0.60 |
time (sec) |
N/A | 0.243 | 0.004 | 0.031 | 0.193 | 0.259 | 0.057 | 0.258 | 8.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 27 | 47 | 22 | 121 | 0 | 26 | 19 | 0 | 0 |
N.S. |
1 | 1.74 | 0.81 | 4.48 | 0.00 | 0.96 | 0.70 | 0.00 | 0.00 |
time (sec) |
N/A | 0.534 | 0.058 | 9.790 | 0.000 | 0.251 | 5.181 | 0.000 | 0.000 |
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 | 9 | 9 | 8 | 7 | 7 | 8 | 8 | 7 |
N.S. |
1 | 0.69 | 0.69 | 0.62 | 0.54 | 0.54 | 0.62 | 0.62 | 0.54 |
time (sec) |
N/A | 0.125 | 0.002 | 0.278 | 0.196 | 0.263 | 0.025 | 0.243 | 0.039 |
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 | 48 | 23 | 24 | 27 | 25 | 20 | 25 | 22 |
N.S. |
1 | 1.78 | 0.85 | 0.89 | 1.00 | 0.93 | 0.74 | 0.93 | 0.81 |
time (sec) |
N/A | 0.586 | 0.236 | 0.433 | 0.324 | 0.250 | 0.156 | 0.260 | 8.528 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 19 | 23 | 53 | 20 | 27 | 26 | 18 |
N.S. |
1 | 1.00 | 0.86 | 1.05 | 2.41 | 0.91 | 1.23 | 1.18 | 0.82 |
time (sec) |
N/A | 0.188 | 0.018 | 0.081 | 0.217 | 0.242 | 0.102 | 0.257 | 7.989 |
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 | 24 | 28 | 27 | 23 | 22 | 22 | 20 | 22 | 25 |
N.S. |
1 | 1.17 | 1.12 | 0.96 | 0.92 | 0.92 | 0.83 | 0.92 | 1.04 |
time (sec) |
N/A | 0.222 | 0.065 | 0.059 | 0.187 | 0.250 | 0.081 | 0.262 | 0.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 42 | 40 | 33 | 70 | 25 | 29 | 61 | 38 |
N.S. |
1 | 1.45 | 1.38 | 1.14 | 2.41 | 0.86 | 1.00 | 2.10 | 1.31 |
time (sec) |
N/A | 0.361 | 0.052 | 0.378 | 0.208 | 0.245 | 0.144 | 0.256 | 8.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 27 | 26 | 0 | 49 | 0 | 0 | 25 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 0.00 | 1.81 | 0.00 | 0.00 | 0.93 |
time (sec) |
N/A | 0.000 | 0.503 | 0.127 | 0.000 | 0.268 | 0.000 | 0.000 | 8.388 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 21 | 14 | 14 | 49 | 14 | 17 | 14 | 13 |
N.S. |
1 | 1.50 | 1.00 | 1.00 | 3.50 | 1.00 | 1.21 | 1.00 | 0.93 |
time (sec) |
N/A | 0.234 | 0.032 | 0.126 | 0.198 | 0.244 | 0.055 | 0.250 | 0.054 |
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 | 29 | 29 | 20 | 24 | 40 | 20 | 41 | 39 | 35 |
N.S. |
1 | 1.00 | 0.69 | 0.83 | 1.38 | 0.69 | 1.41 | 1.34 | 1.21 |
time (sec) |
N/A | 0.183 | 0.048 | 0.299 | 0.280 | 0.272 | 0.151 | 0.262 | 0.137 |
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 | 17 | 17 | 17 | 14 | 17 | 19 | 15 | 20 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 1.00 | 1.12 | 0.88 | 1.18 | 0.88 |
time (sec) |
N/A | 0.215 | 0.009 | 0.046 | 0.204 | 0.241 | 0.060 | 0.259 | 0.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 31 | 26 | 28 | 28 | 24 | 29 | 29 |
N.S. |
1 | 0.00 | 1.11 | 0.93 | 1.00 | 1.00 | 0.86 | 1.04 | 1.04 |
time (sec) |
N/A | 0.000 | 4.053 | 0.088 | 0.223 | 0.255 | 0.116 | 0.251 | 8.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 72 | 52 | 55 | 0 | 71 | 56 | 83 | 49 |
N.S. |
1 | 3.79 | 2.74 | 2.89 | 0.00 | 3.74 | 2.95 | 4.37 | 2.58 |
time (sec) |
N/A | 0.613 | 4.287 | 0.100 | 0.000 | 0.252 | 0.107 | 0.264 | 7.996 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | A | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 33 | 28 | 23 | 38 | 0 | 34 | 0 | 41 |
N.S. |
1 | 1.18 | 1.00 | 0.82 | 1.36 | 0.00 | 1.21 | 0.00 | 1.46 |
time (sec) |
N/A | 9.532 | 0.296 | 97.835 | 0.451 | 0.000 | 0.452 | 0.000 | 8.660 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 31 | 31 | 31 | 19 | 26 | 31 |
N.S. |
1 | 0.00 | 1.00 | 1.19 | 1.19 | 1.19 | 0.73 | 1.00 | 1.19 |
time (sec) |
N/A | 0.000 | 0.146 | 3.398 | 0.227 | 0.260 | 0.054 | 0.271 | 0.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | F(-2) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 24 | 42 | 39 | 108 | 0 | 0 | 41 |
N.S. |
1 | 0.00 | 0.92 | 1.62 | 1.50 | 4.15 | 0.00 | 0.00 | 1.58 |
time (sec) |
N/A | 0.000 | 0.272 | 3.024 | 0.317 | 0.252 | 0.000 | 0.000 | 9.388 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | F(-2) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 31 | 31 | 0 | 31 | 0 | 65 | 62 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.00 | 1.00 | 0.00 | 2.10 | 2.00 |
time (sec) |
N/A | 0.000 | 0.076 | 58.217 | 0.000 | 0.244 | 0.000 | 0.324 | 8.339 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 2568 | 509 | 5655 | 3215 | 3501 | 3947 | 4008 | 943 |
N.S. |
1 | 107.00 | 21.21 | 235.62 | 133.96 | 145.88 | 164.46 | 167.00 | 39.29 |
time (sec) |
N/A | 34.967 | 20.375 | 0.892 | 0.294 | 0.468 | 6.650 | 0.359 | 27.751 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 37 | 23 | 30 | 30 | 26 | 22 | 22 |
N.S. |
1 | 0.00 | 1.68 | 1.05 | 1.36 | 1.36 | 1.18 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 2.366 | 0.093 | 0.223 | 0.262 | 0.155 | 0.257 | 0.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 14 | 15 | 0 | 14 | 12 | 50 | 15 |
N.S. |
1 | 0.00 | 0.88 | 0.94 | 0.00 | 0.88 | 0.75 | 3.12 | 0.94 |
time (sec) |
N/A | 0.000 | 0.096 | 0.587 | 0.000 | 0.240 | 0.074 | 0.278 | 8.171 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 35 | 85 | 115 | 47 | 44 | 71 | 216 |
N.S. |
1 | 0.00 | 1.13 | 2.74 | 3.71 | 1.52 | 1.42 | 2.29 | 6.97 |
time (sec) |
N/A | 0.000 | 0.472 | 0.579 | 0.285 | 0.251 | 0.132 | 0.470 | 8.210 |
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 | 18 | 17 | 18 | 17 | 18 | 17 | 17 | 39 | 15 |
N.S. |
1 | 0.94 | 1.00 | 0.94 | 1.00 | 0.94 | 0.94 | 2.17 | 0.83 |
time (sec) |
N/A | 0.446 | 0.095 | 0.648 | 0.203 | 0.247 | 0.285 | 0.317 | 8.707 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 396 | 316 | 78 | 295 | 86 | 94 | 262 | 0 |
N.S. |
1 | 13.66 | 10.90 | 2.69 | 10.17 | 2.97 | 3.24 | 9.03 | 0.00 |
time (sec) |
N/A | 1.553 | 0.260 | 1.100 | 0.349 | 0.266 | 0.337 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 24 | 24 | 23 | 23 | 20 | 23 | 23 |
N.S. |
1 | 0.00 | 0.96 | 0.96 | 0.92 | 0.92 | 0.80 | 0.92 | 0.92 |
time (sec) |
N/A | 0.000 | 0.065 | 2.030 | 0.230 | 0.255 | 0.866 | 0.281 | 8.080 |
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 | 36 | 40 | 27 | 27 | 35 | 32 | 26 | 29 |
N.S. |
1 | 1.57 | 1.74 | 1.17 | 1.17 | 1.52 | 1.39 | 1.13 | 1.26 |
time (sec) |
N/A | 0.250 | 0.023 | 0.523 | 0.203 | 0.244 | 0.088 | 0.251 | 8.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 37 | 19 | 76 | 25 | 25 | 20 | 25 | 24 |
N.S. |
1 | 1.28 | 0.66 | 2.62 | 0.86 | 0.86 | 0.69 | 0.86 | 0.83 |
time (sec) |
N/A | 1.060 | 0.404 | 0.379 | 0.224 | 0.254 | 0.162 | 0.290 | 8.234 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | F | B | A | F(-1) | F | B |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 0 | 0 | 191 | 54 | 0 | 0 | 54 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 5.79 | 1.64 | 0.00 | 0.00 | 1.64 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.631 | 0.271 | 0.000 | 0.000 | 9.535 |
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 | 26 | 25 | 16 | 25 | 15 | 17 | 15 | 15 |
N.S. |
1 | 1.44 | 1.39 | 0.89 | 1.39 | 0.83 | 0.94 | 0.83 | 0.83 |
time (sec) |
N/A | 0.180 | 0.012 | 0.107 | 0.186 | 0.257 | 0.071 | 0.264 | 8.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 23 | 21 | 19 | 20 | 20 | 44 | 21 |
N.S. |
1 | 0.00 | 0.82 | 0.75 | 0.68 | 0.71 | 0.71 | 1.57 | 0.75 |
time (sec) |
N/A | 0.000 | 0.122 | 0.325 | 0.241 | 0.274 | 0.154 | 0.270 | 7.951 |
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 | 26 | 27 | 21 | 33 | 30 | 31 | 49 | 30 | 28 |
N.S. |
1 | 1.04 | 0.81 | 1.27 | 1.15 | 1.19 | 1.88 | 1.15 | 1.08 |
time (sec) |
N/A | 0.144 | 0.003 | 0.423 | 0.184 | 0.253 | 0.041 | 0.265 | 8.206 |
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 | 26 | 45 | 19 | 18 | 17 | 17 | 17 | 17 | 17 |
N.S. |
1 | 1.73 | 0.73 | 0.69 | 0.65 | 0.65 | 0.65 | 0.65 | 0.65 |
time (sec) |
N/A | 0.184 | 0.030 | 0.222 | 0.254 | 0.271 | 0.107 | 0.263 | 7.964 |
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 | 25 | 11 | 9 | 9 | 9 | 9 | 7 | 9 | 8 |
N.S. |
1 | 0.44 | 0.36 | 0.36 | 0.36 | 0.36 | 0.28 | 0.36 | 0.32 |
time (sec) |
N/A | 0.120 | 0.000 | 0.037 | 0.192 | 0.264 | 0.023 | 0.262 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 633 | 35 | 37 | 65 | 61 | 44 | 67 | 39 |
N.S. |
1 | 16.66 | 0.92 | 0.97 | 1.71 | 1.61 | 1.16 | 1.76 | 1.03 |
time (sec) |
N/A | 16.132 | 5.116 | 0.289 | 0.323 | 0.265 | 0.140 | 0.275 | 8.598 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 21 | 29 | 28 | 48 | 29 | 0 | 28 |
N.S. |
1 | 0.00 | 0.95 | 1.32 | 1.27 | 2.18 | 1.32 | 0.00 | 1.27 |
time (sec) |
N/A | 0.000 | 0.216 | 0.763 | 0.250 | 0.278 | 1.751 | 0.000 | 0.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 45 | 267 | 41 | 41 | 42 | 42 |
N.S. |
1 | 0.00 | 1.00 | 1.88 | 11.12 | 1.71 | 1.71 | 1.75 | 1.75 |
time (sec) |
N/A | 0.000 | 0.397 | 3.226 | 0.423 | 0.264 | 0.707 | 2.597 | 8.841 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 205 | 78 | 58 | 314 | 56 | 56 | 56 | 25 |
N.S. |
1 | 9.32 | 3.55 | 2.64 | 14.27 | 2.55 | 2.55 | 2.55 | 1.14 |
time (sec) |
N/A | 0.757 | 0.189 | 0.365 | 0.211 | 0.260 | 0.111 | 0.320 | 8.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 36 | 271 | 301 | 341 | 632 | 739 | 6440 |
N.S. |
1 | 0.00 | 1.03 | 7.74 | 8.60 | 9.74 | 18.06 | 21.11 | 184.00 |
time (sec) |
N/A | 0.000 | 0.227 | 6.810 | 0.349 | 0.276 | 0.752 | 0.316 | 10.392 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 112 | 30 | 25 | 0 | 24 | 20 | 0 | 25 |
N.S. |
1 | 3.73 | 1.00 | 0.83 | 0.00 | 0.80 | 0.67 | 0.00 | 0.83 |
time (sec) |
N/A | 1.759 | 3.260 | 0.187 | 0.000 | 0.260 | 0.150 | 0.000 | 0.519 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-1) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 22 | 20 | 19 | 19 | 22 | 0 | 170 |
N.S. |
1 | 0.00 | 0.92 | 0.83 | 0.79 | 0.79 | 0.92 | 0.00 | 7.08 |
time (sec) |
N/A | 0.000 | 0.099 | 3.098 | 0.248 | 0.263 | 0.255 | 0.000 | 8.419 |
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 | 26 | 28 | 22 | 20 | 26 | 19 | 23 | 27 |
N.S. |
1 | 1.13 | 1.22 | 0.96 | 0.87 | 1.13 | 0.83 | 1.00 | 1.17 |
time (sec) |
N/A | 0.564 | 0.263 | 0.092 | 0.311 | 0.253 | 0.184 | 0.288 | 8.162 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 17 | 14 | 14 | 0 | 17 | 10 | 19 | 13 |
N.S. |
1 | 0.61 | 0.50 | 0.50 | 0.00 | 0.61 | 0.36 | 0.68 | 0.46 |
time (sec) |
N/A | 0.600 | 0.407 | 0.193 | 0.000 | 0.259 | 0.059 | 0.281 | 0.092 |
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 | 30 | 34 | 34 | 33 | 37 | 32 | 32 | 32 | 32 |
N.S. |
1 | 1.13 | 1.13 | 1.10 | 1.23 | 1.07 | 1.07 | 1.07 | 1.07 |
time (sec) |
N/A | 0.939 | 0.063 | 5.341 | 0.315 | 0.262 | 0.443 | 0.415 | 8.450 |
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 | 8 | 7 | 7 | 7 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.70 | 0.70 | 0.70 | 0.70 | 0.70 |
time (sec) |
N/A | 0.123 | 0.001 | 0.361 | 0.191 | 0.266 | 0.032 | 0.264 | 7.852 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 30 | 20 | 23 | 84 | 25 | 17 | 24 | 20 |
N.S. |
1 | 1.67 | 1.11 | 1.28 | 4.67 | 1.39 | 0.94 | 1.33 | 1.11 |
time (sec) |
N/A | 0.545 | 0.206 | 0.125 | 0.199 | 0.257 | 0.064 | 0.261 | 8.077 |
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 | 16 | 16 | 15 | 16 | 16 | 15 | 18 | 14 |
N.S. |
1 | 0.89 | 0.89 | 0.83 | 0.89 | 0.89 | 0.83 | 1.00 | 0.78 |
time (sec) |
N/A | 0.297 | 0.008 | 0.021 | 0.186 | 0.268 | 0.062 | 0.265 | 7.893 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 42 | 35 | 0 | 39 | 26 | 48 | 41 |
N.S. |
1 | 0.00 | 1.35 | 1.13 | 0.00 | 1.26 | 0.84 | 1.55 | 1.32 |
time (sec) |
N/A | 0.000 | 0.923 | 0.319 | 0.000 | 0.276 | 0.119 | 0.282 | 8.392 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 34 | 40 | 34 | 41 | 37 | 41 | 37 |
N.S. |
1 | 0.00 | 1.31 | 1.54 | 1.31 | 1.58 | 1.42 | 1.58 | 1.42 |
time (sec) |
N/A | 0.000 | 1.852 | 0.334 | 0.257 | 0.261 | 0.139 | 0.272 | 8.277 |