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 | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 57 | 34 | 44 | 54 | 38 | 34 | 50 | 51 |
N.S. |
1 | 2.11 | 1.26 | 1.63 | 2.00 | 1.41 | 1.26 | 1.85 | 1.89 |
time (sec) |
N/A | 0.204 | 0.135 | 0.170 | 0.268 | 0.240 | 0.087 | 0.294 | 0.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | A | F(-1) | A | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 33 | 216 | 36 | 34 | 0 | 36 | 0 |
N.S. |
1 | 0.00 | 1.32 | 8.64 | 1.44 | 1.36 | 0.00 | 1.44 | 0.00 |
time (sec) |
N/A | 0.000 | 0.233 | 0.421 | 0.417 | 0.258 | 0.000 | 20.290 | 0.000 |
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 | 19 | 16 | 13 | 13 | 51 | 15 | 15 | 15 | 17 |
N.S. |
1 | 0.84 | 0.68 | 0.68 | 2.68 | 0.79 | 0.79 | 0.79 | 0.89 |
time (sec) |
N/A | 0.184 | 0.024 | 0.076 | 0.216 | 0.267 | 0.054 | 0.274 | 0.093 |
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 | 36 | 28 | 31 | 36 | 30 | 29 | 32 | 25 |
N.S. |
1 | 1.20 | 0.93 | 1.03 | 1.20 | 1.00 | 0.97 | 1.07 | 0.83 |
time (sec) |
N/A | 0.217 | 0.050 | 0.101 | 0.180 | 0.234 | 0.104 | 0.277 | 12.944 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 105 | 19 | 38 | 116 | 48 | 53 | 89 | 18 |
N.S. |
1 | 5.00 | 0.90 | 1.81 | 5.52 | 2.29 | 2.52 | 4.24 | 0.86 |
time (sec) |
N/A | 0.253 | 0.053 | 0.309 | 0.188 | 0.247 | 0.100 | 0.293 | 11.554 |
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 | 21 | 35 | 19 | 19 | 63 | 18 | 17 | 18 | 18 |
N.S. |
1 | 1.67 | 0.90 | 0.90 | 3.00 | 0.86 | 0.81 | 0.86 | 0.86 |
time (sec) |
N/A | 0.233 | 0.060 | 0.118 | 0.201 | 0.256 | 0.045 | 0.266 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 23 | 23 | 46 | 46 | 49 | 46 | 46 |
N.S. |
1 | 0.00 | 0.92 | 0.92 | 1.84 | 1.84 | 1.96 | 1.84 | 1.84 |
time (sec) |
N/A | 0.000 | 0.415 | 79.140 | 0.281 | 0.245 | 0.132 | 0.283 | 11.420 |
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 | 24 | 0 | 25 | 21 | 33 | 20 | 17 | 20 | 20 |
N.S. |
1 | 0.00 | 1.04 | 0.88 | 1.38 | 0.83 | 0.71 | 0.83 | 0.83 |
time (sec) |
N/A | 0.000 | 0.273 | 1.996 | 0.309 | 0.265 | 0.064 | 0.295 | 12.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 21 | 18 | 20 | 17 | 0 | 20 | 17 |
N.S. |
1 | 0.00 | 0.91 | 0.78 | 0.87 | 0.74 | 0.00 | 0.87 | 0.74 |
time (sec) |
N/A | 0.000 | 5.102 | 0.962 | 0.344 | 0.232 | 0.000 | 0.301 | 0.291 |
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 | 23 | 0 | 26 | 33 | 32 | 33 | 31 | 33 | 0 |
N.S. |
1 | 0.00 | 1.13 | 1.43 | 1.39 | 1.43 | 1.35 | 1.43 | 0.00 |
time (sec) |
N/A | 0.000 | 0.136 | 1.475 | 0.254 | 0.241 | 0.339 | 0.386 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 77 | 55 | 88 | 64 | 61 | 71 | 0 |
N.S. |
1 | 0.00 | 2.48 | 1.77 | 2.84 | 2.06 | 1.97 | 2.29 | 0.00 |
time (sec) |
N/A | 0.000 | 0.231 | 0.297 | 0.326 | 0.267 | 0.637 | 0.377 | 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 | 28 | 79 | 31 | 23 | 21 | 22 | 19 | 21 | 23 |
N.S. |
1 | 2.82 | 1.11 | 0.82 | 0.75 | 0.79 | 0.68 | 0.75 | 0.82 |
time (sec) |
N/A | 0.267 | 0.662 | 0.151 | 0.277 | 0.239 | 0.199 | 0.278 | 12.401 |
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 | 27 | 51 | 37 | 33 | 0 | 50 | 37 | 40 | 122 |
N.S. |
1 | 1.89 | 1.37 | 1.22 | 0.00 | 1.85 | 1.37 | 1.48 | 4.52 |
time (sec) |
N/A | 0.831 | 0.321 | 1.096 | 0.000 | 0.238 | 0.276 | 0.540 | 12.864 |
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 | 20 | 20 | 12 | 11 | 17 | 14 | 16 | 15 |
N.S. |
1 | 1.18 | 1.18 | 0.71 | 0.65 | 1.00 | 0.82 | 0.94 | 0.88 |
time (sec) |
N/A | 0.330 | 0.074 | 0.110 | 0.187 | 0.271 | 0.080 | 0.287 | 0.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 22 | 26 | 28 | 21 | 24 | 0 | 19 |
N.S. |
1 | 0.00 | 0.81 | 0.96 | 1.04 | 0.78 | 0.89 | 0.00 | 0.70 |
time (sec) |
N/A | 0.000 | 0.743 | 0.732 | 0.243 | 0.248 | 0.391 | 0.000 | 13.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 66 | 55 | 26 | 53 | 25 | 29 | 32 | 23 |
N.S. |
1 | 2.28 | 1.90 | 0.90 | 1.83 | 0.86 | 1.00 | 1.10 | 0.79 |
time (sec) |
N/A | 0.259 | 0.188 | 0.129 | 0.188 | 0.246 | 0.081 | 0.276 | 12.558 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 36 | 36 | 59 | 64 | 87 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 1.16 | 1.90 | 2.06 | 2.81 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.622 | 0.275 | 0.763 | 0.440 | 0.255 | 0.000 | 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 | 27 | 29 | 27 | 28 | 42 | 25 | 27 | 27 | 28 |
N.S. |
1 | 1.07 | 1.00 | 1.04 | 1.56 | 0.93 | 1.00 | 1.00 | 1.04 |
time (sec) |
N/A | 0.262 | 0.033 | 0.508 | 0.185 | 0.230 | 0.059 | 0.266 | 0.134 |
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 | 14 | 11 | 11 | 10 | 11 | 18 | 7 | 11 | 9 |
N.S. |
1 | 0.79 | 0.79 | 0.71 | 0.79 | 1.29 | 0.50 | 0.79 | 0.64 |
time (sec) |
N/A | 0.160 | 0.009 | 0.820 | 0.183 | 0.249 | 0.033 | 0.271 | 11.740 |
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 | 23 | 30 | 24 | 26 | 0 | 30 | 24 | 30 | 27 |
N.S. |
1 | 1.30 | 1.04 | 1.13 | 0.00 | 1.30 | 1.04 | 1.30 | 1.17 |
time (sec) |
N/A | 0.584 | 0.285 | 0.189 | 0.000 | 0.262 | 0.115 | 0.288 | 12.391 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 27 | 32 | 49 | 34 | 0 | 0 | 32 |
N.S. |
1 | 0.00 | 0.96 | 1.14 | 1.75 | 1.21 | 0.00 | 0.00 | 1.14 |
time (sec) |
N/A | 0.000 | 0.135 | 0.954 | 0.275 | 0.249 | 0.000 | 0.000 | 12.120 |
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 | 29 | 37 | 39 | 24 | 42 | 31 | 19 | 100 | 33 |
N.S. |
1 | 1.28 | 1.34 | 0.83 | 1.45 | 1.07 | 0.66 | 3.45 | 1.14 |
time (sec) |
N/A | 0.202 | 0.023 | 0.606 | 0.186 | 0.264 | 0.089 | 0.278 | 11.723 |
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 | 14 | 11 | 11 | 13 | 13 | 14 | 13 | 14 |
N.S. |
1 | 0.64 | 0.50 | 0.50 | 0.59 | 0.59 | 0.64 | 0.59 | 0.64 |
time (sec) |
N/A | 0.152 | 0.017 | 0.226 | 0.190 | 0.237 | 0.047 | 0.294 | 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 | 17 | 20 | 20 | 17 | 16 | 16 | 17 | 16 | 16 |
N.S. |
1 | 1.18 | 1.18 | 1.00 | 0.94 | 0.94 | 1.00 | 0.94 | 0.94 |
time (sec) |
N/A | 0.476 | 0.050 | 0.440 | 0.214 | 0.238 | 0.079 | 0.268 | 11.720 |
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 | 16 | 30 | 16 | 16 | 38 | 26 | 10 | 15 | 15 |
N.S. |
1 | 1.88 | 1.00 | 1.00 | 2.38 | 1.62 | 0.62 | 0.94 | 0.94 |
time (sec) |
N/A | 0.584 | 0.168 | 0.893 | 0.212 | 0.247 | 0.068 | 0.272 | 11.493 |
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 | 5 | 7 | 7 | 6 | 8 | 5 | 6 | 6 |
N.S. |
1 | 0.28 | 0.39 | 0.39 | 0.33 | 0.44 | 0.28 | 0.33 | 0.33 |
time (sec) |
N/A | 0.118 | 0.000 | 0.025 | 0.179 | 0.225 | 0.020 | 0.264 | 0.002 |
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 | 29 | 0 | 21 | 27 | 53 | 37 | 24 | 29 | 35 |
N.S. |
1 | 0.00 | 0.72 | 0.93 | 1.83 | 1.28 | 0.83 | 1.00 | 1.21 |
time (sec) |
N/A | 0.000 | 0.246 | 0.695 | 0.309 | 0.238 | 0.072 | 0.282 | 11.354 |
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 | 21 | 0 | 19 | 28 | 24 | 22 | 19 | 24 | 22 |
N.S. |
1 | 0.00 | 0.90 | 1.33 | 1.14 | 1.05 | 0.90 | 1.14 | 1.05 |
time (sec) |
N/A | 0.000 | 0.110 | 9.478 | 0.324 | 0.255 | 0.489 | 0.347 | 11.360 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 38 | 78 | 69 | 34 | 264 | 2546 |
N.S. |
1 | 0.00 | 1.00 | 1.36 | 2.79 | 2.46 | 1.21 | 9.43 | 90.93 |
time (sec) |
N/A | 0.000 | 0.509 | 45.077 | 0.344 | 0.235 | 0.140 | 2.969 | 14.459 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | C | A | B | A | F | F(-1) |
verified |
N/A | N/A | N/A | No | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 81 | 30 | 63 | 26 | 0 | 0 |
N.S. |
1 | 0.00 | 0.00 | 2.70 | 1.00 | 2.10 | 0.87 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.580 | 0.730 | 0.242 | 0.977 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 55 | 27 | 28 | 45 | 25 | 29 | 46 | 22 |
N.S. |
1 | 2.50 | 1.23 | 1.27 | 2.05 | 1.14 | 1.32 | 2.09 | 1.00 |
time (sec) |
N/A | 0.182 | 0.006 | 0.077 | 0.191 | 0.244 | 0.071 | 0.277 | 12.799 |
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 | 13 | 13 | 13 | 12 | 12 | 10 | 12 | 12 |
N.S. |
1 | 0.50 | 0.50 | 0.50 | 0.46 | 0.46 | 0.38 | 0.46 | 0.46 |
time (sec) |
N/A | 0.163 | 0.006 | 0.060 | 0.187 | 0.230 | 0.049 | 0.275 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 18 | 20 | 14 | 71 | 22 | 14 | 16 |
N.S. |
1 | 0.00 | 0.95 | 1.05 | 0.74 | 3.74 | 1.16 | 0.74 | 0.84 |
time (sec) |
N/A | 0.000 | 0.183 | 0.220 | 0.466 | 0.237 | 0.173 | 0.294 | 12.622 |
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 | 27 | 20 | 21 | 28 | 28 | 19 | 28 | 21 |
N.S. |
1 | 1.12 | 0.83 | 0.88 | 1.17 | 1.17 | 0.79 | 1.17 | 0.88 |
time (sec) |
N/A | 0.197 | 0.035 | 0.133 | 0.192 | 0.238 | 0.065 | 0.284 | 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 | 10 | 10 | 10 | 11 | 23 | 10 | 8 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 2.30 | 1.00 | 0.80 | 1.00 | 1.00 |
time (sec) |
N/A | 0.176 | 0.005 | 0.707 | 0.203 | 0.232 | 0.043 | 0.267 | 12.816 |
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 | 24 | 30 | 27 | 26 | 29 | 27 | 24 | 456 | 24 |
N.S. |
1 | 1.25 | 1.12 | 1.08 | 1.21 | 1.12 | 1.00 | 19.00 | 1.00 |
time (sec) |
N/A | 0.399 | 0.036 | 0.446 | 0.319 | 0.232 | 0.111 | 0.345 | 13.169 |
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 | 15 | 21 | 16 | 15 | 19 | 12 | 15 | 15 |
N.S. |
1 | 0.68 | 0.95 | 0.73 | 0.68 | 0.86 | 0.55 | 0.68 | 0.68 |
time (sec) |
N/A | 0.215 | 0.009 | 0.478 | 0.290 | 0.236 | 0.043 | 0.272 | 12.684 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | A | A | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 0 | 47 | 37 | 31 | 27 | 62 | 29 |
N.S. |
1 | 0.00 | 0.00 | 2.04 | 1.61 | 1.35 | 1.17 | 2.70 | 1.26 |
time (sec) |
N/A | 0.000 | 0.000 | 0.528 | 0.302 | 0.240 | 0.169 | 0.294 | 12.999 |
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 | 26 | 26 | 30 | 30 | 29 | 26 | 30 | 30 |
N.S. |
1 | 0.96 | 0.96 | 1.11 | 1.11 | 1.07 | 0.96 | 1.11 | 1.11 |
time (sec) |
N/A | 2.632 | 0.100 | 15.798 | 0.249 | 0.256 | 0.338 | 0.375 | 12.863 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 17 | 52 | 84 | 33 | 36 | 77 | 29 |
N.S. |
1 | 1.00 | 0.85 | 2.60 | 4.20 | 1.65 | 1.80 | 3.85 | 1.45 |
time (sec) |
N/A | 0.308 | 0.028 | 0.595 | 0.282 | 0.246 | 0.151 | 0.301 | 13.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 62 | 61 | 314 | 285 | 1217 | 616 | 0 |
N.S. |
1 | 0.00 | 1.77 | 1.74 | 8.97 | 8.14 | 34.77 | 17.60 | 0.00 |
time (sec) |
N/A | 0.000 | 0.273 | 1.706 | 0.429 | 0.255 | 0.596 | 0.573 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 29 | 40 | 60 | 59 | 27 | 31 | 41 |
N.S. |
1 | 0.00 | 1.12 | 1.54 | 2.31 | 2.27 | 1.04 | 1.19 | 1.58 |
time (sec) |
N/A | 0.000 | 0.066 | 2.406 | 0.305 | 0.233 | 0.206 | 0.301 | 12.613 |
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 | 14 | 16 | 15 | 13 | 12 | 13 | 14 | 12 | 12 |
N.S. |
1 | 1.14 | 1.07 | 0.93 | 0.86 | 0.93 | 1.00 | 0.86 | 0.86 |
time (sec) |
N/A | 0.139 | 0.000 | 0.059 | 0.188 | 0.237 | 0.016 | 0.281 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 96 | 22 | 37 | 36 | 61 | 34 | 21 | 21 |
N.S. |
1 | 3.69 | 0.85 | 1.42 | 1.38 | 2.35 | 1.31 | 0.81 | 0.81 |
time (sec) |
N/A | 0.448 | 0.024 | 0.149 | 0.190 | 0.235 | 0.197 | 0.273 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-1) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 25 | 23 | 21 | 23 | 20 | 24 | 0 | 22 |
N.S. |
1 | 0.86 | 0.79 | 0.72 | 0.79 | 0.69 | 0.83 | 0.00 | 0.76 |
time (sec) |
N/A | 0.212 | 0.626 | 0.824 | 0.265 | 0.244 | 0.146 | 0.000 | 11.788 |
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 | 19 | 0 | 19 | 18 | 50 | 26 | 19 | 17 | 17 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 2.63 | 1.37 | 1.00 | 0.89 | 0.89 |
time (sec) |
N/A | 0.000 | 0.374 | 0.087 | 0.233 | 0.259 | 0.139 | 0.282 | 12.235 |
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 | 28 | 81 | 112 | 73 | 72 | 97 | 97 | 73 | 97 |
N.S. |
1 | 2.89 | 4.00 | 2.61 | 2.57 | 3.46 | 3.46 | 2.61 | 3.46 |
time (sec) |
N/A | 1.587 | 0.209 | 2.062 | 0.209 | 0.319 | 19.805 | 0.317 | 14.533 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 48 | 47 | 17 | 0 | 22 | 19 | 22 | 16 |
N.S. |
1 | 2.40 | 2.35 | 0.85 | 0.00 | 1.10 | 0.95 | 1.10 | 0.80 |
time (sec) |
N/A | 0.946 | 0.234 | 0.560 | 0.000 | 0.236 | 0.123 | 0.268 | 0.385 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | B | B | B | F(-1) | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 0 | 82 | 116 | 96 | 83 | 0 | 134 |
N.S. |
1 | 0.00 | 0.00 | 2.41 | 3.41 | 2.82 | 2.44 | 0.00 | 3.94 |
time (sec) |
N/A | 0.000 | 0.000 | 0.804 | 0.299 | 0.245 | 24.559 | 0.000 | 0.533 |
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 | 16 | 16 | 15 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 1.07 | 1.07 | 1.00 | 0.93 | 0.93 | 0.93 | 0.93 | 0.93 |
time (sec) |
N/A | 0.158 | 0.007 | 0.152 | 0.188 | 0.225 | 0.080 | 0.269 | 0.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | A | A | A | A | A | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 26 | 0 | 21 | 28 | 26 | 26 | 28 | 28 |
N.S. |
1 | 1.30 | 0.00 | 1.05 | 1.40 | 1.30 | 1.30 | 1.40 | 1.40 |
time (sec) |
N/A | 0.273 | 0.000 | 0.160 | 0.349 | 0.241 | 0.075 | 0.267 | 11.511 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | B | A | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 36 | 27 | 31 | 397 | 52 | 29 | 134 | 34 |
N.S. |
1 | 1.38 | 1.04 | 1.19 | 15.27 | 2.00 | 1.12 | 5.15 | 1.31 |
time (sec) |
N/A | 1.467 | 1.199 | 0.120 | 0.368 | 0.236 | 0.083 | 0.300 | 0.233 |
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 | 26 | 68 | 66 | 56 | 60 | 60 | 44 | 60 | 34 |
N.S. |
1 | 2.62 | 2.54 | 2.15 | 2.31 | 2.31 | 1.69 | 2.31 | 1.31 |
time (sec) |
N/A | 0.200 | 0.012 | 0.090 | 0.175 | 0.229 | 0.036 | 0.260 | 11.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 14 | 32 | 26 | 35 | 33 | 31 | 30 | 36 |
N.S. |
1 | 0.93 | 2.13 | 1.73 | 2.33 | 2.20 | 2.07 | 2.00 | 2.40 |
time (sec) |
N/A | 0.380 | 0.073 | 0.143 | 0.182 | 0.237 | 0.097 | 0.279 | 11.473 |
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 | 28 | 27 | 27 | 107 | 319 | 85 | 109 | 85 | 88 |
N.S. |
1 | 0.96 | 0.96 | 3.82 | 11.39 | 3.04 | 3.89 | 3.04 | 3.14 |
time (sec) |
N/A | 0.661 | 0.051 | 1.435 | 0.316 | 0.237 | 0.373 | 0.293 | 11.867 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 43 | 43 | 38 | 38 | 61 | 70 | 46 |
N.S. |
1 | 0.00 | 1.26 | 1.26 | 1.12 | 1.12 | 1.79 | 2.06 | 1.35 |
time (sec) |
N/A | 0.000 | 0.541 | 0.834 | 0.221 | 0.229 | 0.193 | 0.279 | 12.336 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 129 | 29 | 63 | 123 | 33 | 0 | 0 | 103 |
N.S. |
1 | 4.30 | 0.97 | 2.10 | 4.10 | 1.10 | 0.00 | 0.00 | 3.43 |
time (sec) |
N/A | 0.314 | 0.101 | 6.434 | 0.433 | 0.237 | 0.000 | 0.000 | 12.673 |
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 | 51 | 47 | 105 | 79 | 155 | 88 | 135 | 48 |
N.S. |
1 | 2.32 | 2.14 | 4.77 | 3.59 | 7.05 | 4.00 | 6.14 | 2.18 |
time (sec) |
N/A | 0.381 | 0.095 | 0.589 | 0.201 | 0.238 | 2.700 | 0.265 | 12.121 |
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 | 29 | 26 | 24 | 21 | 0 | 36 | 20 | 36 | 33 |
N.S. |
1 | 0.90 | 0.83 | 0.72 | 0.00 | 1.24 | 0.69 | 1.24 | 1.14 |
time (sec) |
N/A | 0.486 | 0.049 | 0.184 | 0.000 | 0.242 | 0.101 | 0.279 | 0.180 |
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 | 14 | 14 | 11 | 10 | 21 | 12 | 10 | 10 |
N.S. |
1 | 0.78 | 0.78 | 0.61 | 0.56 | 1.17 | 0.67 | 0.56 | 0.56 |
time (sec) |
N/A | 0.278 | 0.044 | 0.305 | 0.214 | 0.233 | 0.088 | 0.266 | 12.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 36 | 59 | 22 | 34 | 43 | 34 | 34 | 34 |
N.S. |
1 | 2.12 | 3.47 | 1.29 | 2.00 | 2.53 | 2.00 | 2.00 | 2.00 |
time (sec) |
N/A | 0.233 | 0.030 | 0.797 | 0.183 | 0.223 | 0.153 | 0.267 | 0.147 |
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 | 33 | 0 | 37 | 46 | 50 | 55 | 27 | 66 | 69 |
N.S. |
1 | 0.00 | 1.12 | 1.39 | 1.52 | 1.67 | 0.82 | 2.00 | 2.09 |
time (sec) |
N/A | 0.000 | 0.546 | 9.193 | 0.369 | 0.252 | 0.299 | 0.390 | 12.641 |
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 | 32 | 30 | 30 | 25 | 44 | 25 | 22 | 25 | 23 |
N.S. |
1 | 0.94 | 0.94 | 0.78 | 1.38 | 0.78 | 0.69 | 0.78 | 0.72 |
time (sec) |
N/A | 0.236 | 0.039 | 0.085 | 0.218 | 0.232 | 0.098 | 0.275 | 12.241 |
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 | 18 | 98 | 76 | 57 | 91 | 62 | 60 | 80 | 20 |
N.S. |
1 | 5.44 | 4.22 | 3.17 | 5.06 | 3.44 | 3.33 | 4.44 | 1.11 |
time (sec) |
N/A | 0.228 | 0.050 | 0.219 | 0.200 | 0.232 | 0.123 | 0.295 | 12.112 |
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 | 20 | 14 | 14 | 13 | 12 | 23 | 12 | 12 | 12 |
N.S. |
1 | 0.70 | 0.70 | 0.65 | 0.60 | 1.15 | 0.60 | 0.60 | 0.60 |
time (sec) |
N/A | 0.143 | 0.013 | 0.018 | 0.192 | 0.241 | 0.049 | 0.280 | 0.058 |
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 | 24 | 24 | 24 | 19 | 29 | 19 | 15 | 0 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 1.21 | 0.79 | 0.62 | 0.00 | 0.75 |
time (sec) |
N/A | 1.016 | 0.375 | 0.390 | 0.352 | 0.227 | 0.197 | 0.000 | 12.594 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 38 | 18 | 29 | 26 | 26 | 29 | 45 | 33 |
N.S. |
1 | 2.11 | 1.00 | 1.61 | 1.44 | 1.44 | 1.61 | 2.50 | 1.83 |
time (sec) |
N/A | 0.188 | 0.031 | 0.190 | 0.193 | 0.233 | 0.099 | 0.273 | 0.077 |
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 | 11 | 13 | 16 | 13 | 11 | 11 | 10 | 11 | 12 |
N.S. |
1 | 1.18 | 1.45 | 1.18 | 1.00 | 1.00 | 0.91 | 1.00 | 1.09 |
time (sec) |
N/A | 0.158 | 0.008 | 0.139 | 0.191 | 0.236 | 0.032 | 0.281 | 0.052 |
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 | 29 | 0 | 31 | 31 | 34 | 30 | 0 | 34 | 27 |
N.S. |
1 | 0.00 | 1.07 | 1.07 | 1.17 | 1.03 | 0.00 | 1.17 | 0.93 |
time (sec) |
N/A | 0.000 | 0.427 | 23.071 | 0.339 | 0.249 | 0.000 | 0.454 | 12.467 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 30 | 26 | 61 | 318 | 35 | 58 | 44 | 32 |
N.S. |
1 | 1.07 | 0.93 | 2.18 | 11.36 | 1.25 | 2.07 | 1.57 | 1.14 |
time (sec) |
N/A | 1.018 | 0.350 | 2.778 | 0.333 | 0.253 | 1.111 | 0.357 | 12.525 |
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 | 32 | 0 | 27 | 35 | 39 | 39 | 24 | 43 | 38 |
N.S. |
1 | 0.00 | 0.84 | 1.09 | 1.22 | 1.22 | 0.75 | 1.34 | 1.19 |
time (sec) |
N/A | 0.000 | 4.583 | 0.103 | 0.237 | 0.255 | 0.092 | 0.278 | 12.040 |
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 | 28 | 41 | 23 | 21 | 55 | 23 | 20 | 23 | 22 |
N.S. |
1 | 1.46 | 0.82 | 0.75 | 1.96 | 0.82 | 0.71 | 0.82 | 0.79 |
time (sec) |
N/A | 0.267 | 0.082 | 0.099 | 0.190 | 0.234 | 0.067 | 0.259 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 24 | 22 | 24 | 78 | 73 | 82 | 88 | 0 |
N.S. |
1 | 0.89 | 0.81 | 0.89 | 2.89 | 2.70 | 3.04 | 3.26 | 0.00 |
time (sec) |
N/A | 0.715 | 0.048 | 1.039 | 0.355 | 0.231 | 0.181 | 0.564 | 0.000 |
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 | 23 | 23 | 23 | 21 | 31 | 20 | 19 | 0 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 1.35 | 0.87 | 0.83 | 0.00 | 0.91 |
time (sec) |
N/A | 6.450 | 0.152 | 7.710 | 0.376 | 0.250 | 37.102 | 0.000 | 13.716 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 32 | 22 | 18 | 26 | 17 | 0 | 0 | 17 |
N.S. |
1 | 1.45 | 1.00 | 0.82 | 1.18 | 0.77 | 0.00 | 0.00 | 0.77 |
time (sec) |
N/A | 0.150 | 0.019 | 0.604 | 0.280 | 0.240 | 0.000 | 0.000 | 0.363 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | F | A | A | F | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 31 | 622 | 0 | 50 | 42 | 0 | 100 |
N.S. |
1 | 0.00 | 0.97 | 19.44 | 0.00 | 1.56 | 1.31 | 0.00 | 3.12 |
time (sec) |
N/A | 0.000 | 0.503 | 0.188 | 0.000 | 0.240 | 24.628 | 0.000 | 15.161 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | F(-1) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 62 | 71 | 106 | 73 | 0 | 77 | 69 |
N.S. |
1 | 0.00 | 1.68 | 1.92 | 2.86 | 1.97 | 0.00 | 2.08 | 1.86 |
time (sec) |
N/A | 0.000 | 0.130 | 1.457 | 0.236 | 0.240 | 0.000 | 0.835 | 13.276 |
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 | 20 | 19 | 17 | 17 | 16 | 23 | 14 | 16 | 59 |
N.S. |
1 | 0.95 | 0.85 | 0.85 | 0.80 | 1.15 | 0.70 | 0.80 | 2.95 |
time (sec) |
N/A | 0.186 | 0.013 | 0.861 | 0.186 | 0.236 | 0.073 | 0.269 | 12.007 |
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 | 13 | 27 | 20 | 19 | 18 | 18 | 19 | 18 | 18 |
N.S. |
1 | 2.08 | 1.54 | 1.46 | 1.38 | 1.38 | 1.46 | 1.38 | 1.38 |
time (sec) |
N/A | 0.160 | 0.014 | 0.086 | 0.181 | 0.240 | 0.059 | 0.280 | 12.174 |
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 | 20 | 32 | 25 | 24 | 35 | 21 | 26 | 31 | 25 |
N.S. |
1 | 1.60 | 1.25 | 1.20 | 1.75 | 1.05 | 1.30 | 1.55 | 1.25 |
time (sec) |
N/A | 0.216 | 0.292 | 0.122 | 0.219 | 0.246 | 0.074 | 0.273 | 0.092 |
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 | 27 | 20 | 95 | 19 | 33 | 77 | 34 | 18 | 34 |
N.S. |
1 | 0.74 | 3.52 | 0.70 | 1.22 | 2.85 | 1.26 | 0.67 | 1.26 |
time (sec) |
N/A | 0.288 | 0.062 | 0.123 | 0.187 | 0.240 | 0.227 | 0.270 | 11.816 |
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 | 19 | 15 | 16 | 15 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.12 | 0.88 | 0.94 | 0.88 | 0.94 | 0.94 |
time (sec) |
N/A | 0.319 | 0.063 | 0.365 | 0.254 | 0.240 | 0.130 | 0.287 | 12.499 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 41 | 29 | 63 | 28 | 24 | 28 | 28 |
N.S. |
1 | 0.00 | 1.24 | 0.88 | 1.91 | 0.85 | 0.73 | 0.85 | 0.85 |
time (sec) |
N/A | 0.000 | 0.196 | 0.044 | 0.237 | 0.234 | 0.052 | 0.285 | 11.410 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 118 | 27 | 84 | 133 | 87 | 87 | 116 | 27 |
N.S. |
1 | 4.21 | 0.96 | 3.00 | 4.75 | 3.11 | 3.11 | 4.14 | 0.96 |
time (sec) |
N/A | 1.214 | 0.744 | 0.105 | 0.271 | 0.233 | 0.081 | 0.294 | 11.530 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | A | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 52 | 60 | 47 | 46 | 57 | 60 |
N.S. |
1 | 0.00 | 0.00 | 1.93 | 2.22 | 1.74 | 1.70 | 2.11 | 2.22 |
time (sec) |
N/A | 0.000 | 0.000 | 205.265 | 0.600 | 0.257 | 3.136 | 8.905 | 12.337 |
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 | 20 | 4 | 4 | 5 | 4 | 4 | 3 | 4 | 4 |
N.S. |
1 | 0.20 | 0.20 | 0.25 | 0.20 | 0.20 | 0.15 | 0.20 | 0.20 |
time (sec) |
N/A | 0.121 | 0.000 | 0.039 | 0.191 | 0.230 | 0.023 | 0.273 | 0.003 |
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 | 16 | 15 | 20 | 13 | 12 | 12 | 10 | 12 | 12 |
N.S. |
1 | 0.94 | 1.25 | 0.81 | 0.75 | 0.75 | 0.62 | 0.75 | 0.75 |
time (sec) |
N/A | 0.257 | 0.096 | 1.075 | 0.214 | 0.234 | 0.046 | 0.261 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 31 | 34 | 28 | 39 | 24 | 48 | 41 |
N.S. |
1 | 0.00 | 1.03 | 1.13 | 0.93 | 1.30 | 0.80 | 1.60 | 1.37 |
time (sec) |
N/A | 0.000 | 0.243 | 39.846 | 0.309 | 0.275 | 0.164 | 0.405 | 0.541 |
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 | 20 | 20 | 17 | 18 | 18 | 17 | 20 | 12 |
N.S. |
1 | 0.95 | 0.95 | 0.81 | 0.86 | 0.86 | 0.81 | 0.95 | 0.57 |
time (sec) |
N/A | 0.235 | 0.012 | 0.871 | 0.190 | 0.246 | 0.086 | 0.265 | 12.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F(-1) | F(-2) | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 31 | 31 | 0 | 31 | 42 | 0 | 0 | 40 |
N.S. |
1 | 1.19 | 1.19 | 0.00 | 1.19 | 1.62 | 0.00 | 0.00 | 1.54 |
time (sec) |
N/A | 3.518 | 0.675 | 0.000 | 0.436 | 0.261 | 0.000 | 0.000 | 13.622 |
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 | 19 | 18 | 18 | 38 | 22 | 34 | 37 | 41 | 38 |
N.S. |
1 | 0.95 | 0.95 | 2.00 | 1.16 | 1.79 | 1.95 | 2.16 | 2.00 |
time (sec) |
N/A | 0.466 | 0.168 | 0.996 | 0.305 | 0.244 | 0.206 | 0.355 | 14.243 |
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 | 24 | 0 | 22 | 27 | 0 | 21 | 34 | 26 | 17 |
N.S. |
1 | 0.00 | 0.92 | 1.12 | 0.00 | 0.88 | 1.42 | 1.08 | 0.71 |
time (sec) |
N/A | 0.000 | 0.228 | 0.191 | 0.000 | 0.241 | 0.106 | 0.277 | 12.656 |
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 | 12 | 12 | 12 | 11 | 11 | 8 | 11 | 11 |
N.S. |
1 | 0.71 | 0.71 | 0.71 | 0.65 | 0.65 | 0.47 | 0.65 | 0.65 |
time (sec) |
N/A | 0.137 | 0.003 | 0.011 | 0.174 | 0.229 | 0.036 | 0.256 | 12.400 |
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 | 23 | 0 | 26 | 17 | 23 | 26 | 24 | 44 | 30 |
N.S. |
1 | 0.00 | 1.13 | 0.74 | 1.00 | 1.13 | 1.04 | 1.91 | 1.30 |
time (sec) |
N/A | 0.000 | 0.215 | 1.474 | 0.219 | 0.223 | 0.111 | 0.283 | 13.093 |
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 | 20 | 22 | 20 | 22 | 71 | 21 | 19 | 21 | 22 |
N.S. |
1 | 1.10 | 1.00 | 1.10 | 3.55 | 1.05 | 0.95 | 1.05 | 1.10 |
time (sec) |
N/A | 0.238 | 0.277 | 0.194 | 0.294 | 0.232 | 0.056 | 0.267 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 37 | 25 | 30 | 30 | 24 | 34 | 35 |
N.S. |
1 | 0.00 | 2.06 | 1.39 | 1.67 | 1.67 | 1.33 | 1.89 | 1.94 |
time (sec) |
N/A | 0.000 | 5.335 | 0.381 | 0.241 | 0.236 | 0.279 | 0.276 | 12.647 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 23 | 22 | 19 | 13 | 18 | 15 | 0 | 13 |
N.S. |
1 | 0.92 | 0.88 | 0.76 | 0.52 | 0.72 | 0.60 | 0.00 | 0.52 |
time (sec) |
N/A | 0.303 | 0.078 | 0.078 | 1.770 | 0.219 | 0.065 | 0.000 | 12.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | C | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 45 | 28 | 24 | 0 | 19 | 32 | 128 | 0 |
N.S. |
1 | 1.73 | 1.08 | 0.92 | 0.00 | 0.73 | 1.23 | 4.92 | 0.00 |
time (sec) |
N/A | 1.116 | 6.451 | 0.717 | 0.000 | 0.235 | 0.330 | 0.301 | 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 | 16 | 16 | 22 | 15 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.38 | 0.94 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.143 | 0.007 | 0.125 | 0.196 | 0.261 | 0.057 | 0.258 | 11.744 |
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 | 20 | 0 | 18 | 23 | 18 | 18 | 15 | 22 | 0 |
N.S. |
1 | 0.00 | 0.90 | 1.15 | 0.90 | 0.90 | 0.75 | 1.10 | 0.00 |
time (sec) |
N/A | 0.000 | 0.654 | 1.287 | 0.261 | 0.235 | 0.144 | 0.297 | 0.000 |