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 | 27 | 36 | 18 | 19 | 33 | 27 | 19 | 29 | 19 |
N.S. |
1 | 1.33 | 0.67 | 0.70 | 1.22 | 1.00 | 0.70 | 1.07 | 0.70 |
time (sec) |
N/A | 0.197 | 0.041 | 0.071 | 0.211 | 0.237 | 0.071 | 0.258 | 8.776 |
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 | 17 | 15 | 15 | 18 | 47 | 17 | 15 | 17 | 15 |
N.S. |
1 | 0.88 | 0.88 | 1.06 | 2.76 | 1.00 | 0.88 | 1.00 | 0.88 |
time (sec) |
N/A | 0.298 | 0.052 | 0.373 | 0.275 | 0.238 | 0.061 | 0.270 | 9.247 |
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 | 17 | 18 | 15 | 13 | 20 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.06 | 0.88 | 0.76 | 1.18 | 0.71 | 0.59 | 0.71 | 0.71 |
time (sec) |
N/A | 0.169 | 0.017 | 0.100 | 0.218 | 0.253 | 0.040 | 0.278 | 9.061 |
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 | 20 | 20 | 17 | 18 | 18 | 15 | 20 | 16 |
N.S. |
1 | 1.11 | 1.11 | 0.94 | 1.00 | 1.00 | 0.83 | 1.11 | 0.89 |
time (sec) |
N/A | 0.185 | 0.008 | 0.028 | 0.298 | 0.236 | 0.047 | 0.261 | 9.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 24 | 24 | 21 | 26 | 0 | 24 | 0 | 21 |
N.S. |
1 | 1.04 | 1.04 | 0.91 | 1.13 | 0.00 | 1.04 | 0.00 | 0.91 |
time (sec) |
N/A | 0.487 | 0.393 | 0.363 | 0.320 | 0.000 | 0.122 | 0.000 | 9.669 |
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 | 29 | 0 | 33 | 40 | 120 | 120 | 216 | 148 | 32 |
N.S. |
1 | 0.00 | 1.14 | 1.38 | 4.14 | 4.14 | 7.45 | 5.10 | 1.10 |
time (sec) |
N/A | 0.000 | 0.186 | 4.240 | 0.275 | 0.259 | 0.279 | 0.311 | 9.707 |
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 | 33 | 602 | 92 | 89 | 422 | 144 | 114 | 1222 | 0 |
N.S. |
1 | 18.24 | 2.79 | 2.70 | 12.79 | 4.36 | 3.45 | 37.03 | 0.00 |
time (sec) |
N/A | 5.767 | 0.236 | 0.510 | 0.351 | 0.288 | 0.199 | 0.323 | 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 | 22 | 61 | 24 | 26 | 25 | 25 | 24 | 25 | 27 |
N.S. |
1 | 2.77 | 1.09 | 1.18 | 1.14 | 1.14 | 1.09 | 1.14 | 1.23 |
time (sec) |
N/A | 0.234 | 1.021 | 0.073 | 0.289 | 0.243 | 0.049 | 0.261 | 9.081 |
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 | 35 | 53 | 40 | 47 | 50 | 49 | 48 | 53 | 39 |
N.S. |
1 | 1.51 | 1.14 | 1.34 | 1.43 | 1.40 | 1.37 | 1.51 | 1.11 |
time (sec) |
N/A | 0.487 | 0.110 | 0.243 | 0.206 | 0.240 | 1.718 | 0.264 | 0.334 |
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 | 20 | 77 | 221 | 80 | 105 | 131 | 114 | 90 | 135 |
N.S. |
1 | 3.85 | 11.05 | 4.00 | 5.25 | 6.55 | 5.70 | 4.50 | 6.75 |
time (sec) |
N/A | 0.430 | 0.120 | 0.144 | 0.206 | 0.236 | 0.253 | 0.262 | 9.508 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 20 | 22 | 19 | 0 | 19 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.71 | 0.79 | 0.68 | 0.00 | 0.68 | 0.71 |
time (sec) |
N/A | 1.406 | 0.137 | 1.762 | 0.509 | 0.255 | 0.000 | 0.270 | 10.560 |
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 | 25 | 27 | 27 | 26 | 42 | 42 | 20 | 0 | 25 |
N.S. |
1 | 1.08 | 1.08 | 1.04 | 1.68 | 1.68 | 0.80 | 0.00 | 1.00 |
time (sec) |
N/A | 0.524 | 0.075 | 0.919 | 0.254 | 0.239 | 0.843 | 0.000 | 28.260 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 70 | 30 | 33 | 0 | 36 | 39 | 25 | 32 |
N.S. |
1 | 2.12 | 0.91 | 1.00 | 0.00 | 1.09 | 1.18 | 0.76 | 0.97 |
time (sec) |
N/A | 0.908 | 0.080 | 1.309 | 0.000 | 0.242 | 0.231 | 0.328 | 10.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 79 | 17 | 20 | 33 | 33 | 39 | 16 | 39 |
N.S. |
1 | 3.29 | 0.71 | 0.83 | 1.38 | 1.38 | 1.62 | 0.67 | 1.62 |
time (sec) |
N/A | 0.291 | 0.011 | 0.061 | 0.199 | 0.247 | 0.180 | 0.261 | 8.823 |
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 | 32 | 16 | 18 | 49 | 20 | 19 | 28 | 14 |
N.S. |
1 | 1.68 | 0.84 | 0.95 | 2.58 | 1.05 | 1.00 | 1.47 | 0.74 |
time (sec) |
N/A | 0.688 | 0.089 | 0.030 | 0.241 | 0.230 | 0.041 | 0.265 | 10.160 |
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 | 21 | 20 | 17 | 18 | 20 | 22 | 16 | 16 |
N.S. |
1 | 0.91 | 0.87 | 0.74 | 0.78 | 0.87 | 0.96 | 0.70 | 0.70 |
time (sec) |
N/A | 0.190 | 0.059 | 0.139 | 0.321 | 0.253 | 0.089 | 0.270 | 0.082 |
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 | 480 | 510 | 418 | 390 | 364 | 471 | 663 | 365 |
N.S. |
1 | 17.14 | 18.21 | 14.93 | 13.93 | 13.00 | 16.82 | 23.68 | 13.04 |
time (sec) |
N/A | 1.125 | 3.560 | 2.117 | 0.297 | 0.282 | 0.742 | 0.331 | 11.537 |
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 | 29 | 599 | 235 | 212 | 569 | 263 | 333 | 298 | 335 |
N.S. |
1 | 20.66 | 8.10 | 7.31 | 19.62 | 9.07 | 11.48 | 10.28 | 11.55 |
time (sec) |
N/A | 1.125 | 0.171 | 0.197 | 0.230 | 0.261 | 0.489 | 0.267 | 10.830 |
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 | 13 | 11 | 11 | 11 | 11 | 10 | 11 | 9 |
N.S. |
1 | 0.54 | 0.46 | 0.46 | 0.46 | 0.46 | 0.42 | 0.46 | 0.38 |
time (sec) |
N/A | 0.129 | 0.002 | 0.025 | 0.202 | 0.237 | 0.025 | 0.254 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 273 | 27 | 29 | 70 | 83 | 83 | 30 | 525 |
N.S. |
1 | 8.03 | 0.79 | 0.85 | 2.06 | 2.44 | 2.44 | 0.88 | 15.44 |
time (sec) |
N/A | 0.777 | 0.039 | 0.673 | 0.216 | 0.249 | 2.685 | 0.280 | 10.572 |
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 | 18 | 0 | 16 | 28 | 13 | 13 | 20 | 0 | 15 |
N.S. |
1 | 0.00 | 0.89 | 1.56 | 0.72 | 0.72 | 1.11 | 0.00 | 0.83 |
time (sec) |
N/A | 0.000 | 0.245 | 0.163 | 0.511 | 0.258 | 0.238 | 0.000 | 9.470 |
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 | 37 | 31 | 35 | 34 | 31 | 34 | 33 | 34 |
N.S. |
1 | 1.54 | 1.29 | 1.46 | 1.42 | 1.29 | 1.42 | 1.38 | 1.42 |
time (sec) |
N/A | 0.211 | 0.015 | 0.060 | 0.203 | 0.232 | 0.165 | 0.247 | 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 | 24 | 24 | 24 | 22 | 21 | 21 | 19 | 35 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.88 | 0.88 | 0.79 | 1.46 | 0.88 |
time (sec) |
N/A | 0.860 | 0.126 | 0.120 | 0.241 | 0.263 | 0.091 | 0.265 | 9.346 |
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 | 28 | 27 | 23 | 20 | 20 | 20 | 25 | 31 |
N.S. |
1 | 0.97 | 0.93 | 0.79 | 0.69 | 0.69 | 0.69 | 0.86 | 1.07 |
time (sec) |
N/A | 0.173 | 0.013 | 0.055 | 0.208 | 0.243 | 0.074 | 0.250 | 9.633 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 94 | 0 | 55 | 51 | 0 | 24 |
N.S. |
1 | 1.00 | 1.00 | 5.22 | 0.00 | 3.06 | 2.83 | 0.00 | 1.33 |
time (sec) |
N/A | 0.509 | 0.060 | 10.863 | 0.000 | 0.256 | 0.231 | 0.000 | 11.881 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 25 | 117 | 23 | 36 | 22 | 22 | 24 | 20 |
N.S. |
1 | 1.25 | 5.85 | 1.15 | 1.80 | 1.10 | 1.10 | 1.20 | 1.00 |
time (sec) |
N/A | 0.442 | 0.109 | 0.269 | 0.246 | 0.242 | 0.090 | 0.271 | 0.358 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 34 | 40 | 29 | 32 | 53 | 0 | 109 |
N.S. |
1 | 0.00 | 1.21 | 1.43 | 1.04 | 1.14 | 1.89 | 0.00 | 3.89 |
time (sec) |
N/A | 0.000 | 0.130 | 20.720 | 0.388 | 0.255 | 0.252 | 0.000 | 10.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 40 | 12 | 17 | 55 | 16 | 15 | 16 | 12 |
N.S. |
1 | 3.33 | 1.00 | 1.42 | 4.58 | 1.33 | 1.25 | 1.33 | 1.00 |
time (sec) |
N/A | 0.200 | 0.011 | 0.135 | 0.229 | 0.237 | 0.077 | 0.265 | 9.497 |
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 | 19 | 18 | 17 | 16 | 47 | 17 | 14 | 129 | 19 |
N.S. |
1 | 0.95 | 0.89 | 0.84 | 2.47 | 0.89 | 0.74 | 6.79 | 1.00 |
time (sec) |
N/A | 0.199 | 0.043 | 0.141 | 0.213 | 0.259 | 0.061 | 0.318 | 9.494 |
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 | 33 | 0 | 32 | 38 | 28 | 36 | 34 | 0 | 40 |
N.S. |
1 | 0.00 | 0.97 | 1.15 | 0.85 | 1.09 | 1.03 | 0.00 | 1.21 |
time (sec) |
N/A | 0.000 | 1.233 | 10.033 | 0.299 | 0.241 | 0.964 | 0.000 | 10.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 288 | 29 | 58 | 57 | 80 | 60 | 0 | 51 |
N.S. |
1 | 12.00 | 1.21 | 2.42 | 2.38 | 3.33 | 2.50 | 0.00 | 2.12 |
time (sec) |
N/A | 4.150 | 0.215 | 61.115 | 0.364 | 0.268 | 9.553 | 0.000 | 9.759 |
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 | 34 | 37 | 21 | 25 | 29 | 22 | 25 | 27 |
N.S. |
1 | 1.70 | 1.85 | 1.05 | 1.25 | 1.45 | 1.10 | 1.25 | 1.35 |
time (sec) |
N/A | 0.226 | 0.018 | 0.334 | 0.195 | 0.255 | 0.092 | 0.277 | 9.959 |
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 | 17 | 18 | 17 | 12 | 14 | 16 | 12 |
N.S. |
1 | 1.14 | 1.21 | 1.29 | 1.21 | 0.86 | 1.00 | 1.14 | 0.86 |
time (sec) |
N/A | 0.174 | 0.010 | 0.047 | 0.193 | 0.242 | 0.049 | 0.264 | 9.324 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | B | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 839 | 42 | 41 | 1714 | 84 | 155 | 0 | 0 |
N.S. |
1 | 34.96 | 1.75 | 1.71 | 71.42 | 3.50 | 6.46 | 0.00 | 0.00 |
time (sec) |
N/A | 11.730 | 0.196 | 0.684 | 0.392 | 0.245 | 0.251 | 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 | 17 | 16 | 16 | 12 | 11 | 17 | 10 | 17 | 11 |
N.S. |
1 | 0.94 | 0.94 | 0.71 | 0.65 | 1.00 | 0.59 | 1.00 | 0.65 |
time (sec) |
N/A | 0.158 | 0.012 | 0.043 | 0.204 | 0.236 | 0.047 | 0.271 | 8.947 |
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 | 22 | 30 | 27 | 23 | 48 | 28 | 19 | 29 | 25 |
N.S. |
1 | 1.36 | 1.23 | 1.05 | 2.18 | 1.27 | 0.86 | 1.32 | 1.14 |
time (sec) |
N/A | 0.597 | 0.844 | 0.082 | 0.302 | 0.251 | 0.064 | 0.269 | 0.118 |
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 | 10 | 13 | 11 | 10 | 10 | 8 | 15 | 10 |
N.S. |
1 | 0.56 | 0.72 | 0.61 | 0.56 | 0.56 | 0.44 | 0.83 | 0.56 |
time (sec) |
N/A | 0.141 | 0.006 | 0.201 | 0.208 | 0.237 | 0.053 | 0.269 | 8.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 26 | 26 | 22 | 0 | 21 | 17 | 55 | 25 |
N.S. |
1 | 0.84 | 0.84 | 0.71 | 0.00 | 0.68 | 0.55 | 1.77 | 0.81 |
time (sec) |
N/A | 0.240 | 0.055 | 0.225 | 0.000 | 0.250 | 0.071 | 0.282 | 8.639 |
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 | 15 | 11 | 10 | 10 | 14 | 10 | 12 |
N.S. |
1 | 1.00 | 0.94 | 0.69 | 0.62 | 0.62 | 0.88 | 0.62 | 0.75 |
time (sec) |
N/A | 0.148 | 0.114 | 0.042 | 0.204 | 0.240 | 0.037 | 0.268 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 18 | 17 | 17 | 23 | 17 | 19 | 52 | 0 |
N.S. |
1 | 0.95 | 0.89 | 0.89 | 1.21 | 0.89 | 1.00 | 2.74 | 0.00 |
time (sec) |
N/A | 0.193 | 0.007 | 0.058 | 0.200 | 0.249 | 0.099 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | A | A | F | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 56 | 549 | 28 | 29 | 48 | 0 | 48 |
N.S. |
1 | 0.00 | 1.70 | 16.64 | 0.85 | 0.88 | 1.45 | 0.00 | 1.45 |
time (sec) |
N/A | 0.000 | 0.411 | 2.269 | 0.363 | 0.246 | 1.647 | 0.000 | 10.006 |
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 | 27 | 0 | 20 | 21 | 31 | 31 | 19 | 20 | 41 |
N.S. |
1 | 0.00 | 0.74 | 0.78 | 1.15 | 1.15 | 0.70 | 0.74 | 1.52 |
time (sec) |
N/A | 0.000 | 0.514 | 0.490 | 0.239 | 0.240 | 0.075 | 0.273 | 0.319 |
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 | 21 | 21 | 21 | 19 | 18 | 29 | 31 | 52 | 30 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.86 | 1.38 | 1.48 | 2.48 | 1.43 |
time (sec) |
N/A | 0.159 | 0.066 | 0.374 | 0.199 | 0.242 | 0.091 | 0.252 | 9.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | F | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 64 | 67 | 0 | 234 | 60 | 0 | 165 |
N.S. |
1 | 0.00 | 2.06 | 2.16 | 0.00 | 7.55 | 1.94 | 0.00 | 5.32 |
time (sec) |
N/A | 0.000 | 1.647 | 0.187 | 0.000 | 0.253 | 2.095 | 0.000 | 9.400 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | F(-2) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 80 | 51 | 49 | 75 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 4.71 | 3.00 | 2.88 | 4.41 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.607 | 23.145 | 0.330 | 0.254 | 0.000 | 0.000 | 0.000 |
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 | 25 | 258 | 55 | 60 | 205 | 57 | 105 | 63 | 52 |
N.S. |
1 | 10.32 | 2.20 | 2.40 | 8.20 | 2.28 | 4.20 | 2.52 | 2.08 |
time (sec) |
N/A | 2.022 | 9.078 | 0.525 | 0.261 | 0.239 | 0.108 | 0.265 | 8.821 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 175 | 13 | 11 | 0 | 12 | 0 | 0 | 10 |
N.S. |
1 | 9.72 | 0.72 | 0.61 | 0.00 | 0.67 | 0.00 | 0.00 | 0.56 |
time (sec) |
N/A | 0.609 | 0.061 | 0.206 | 0.000 | 0.232 | 0.000 | 0.000 | 8.464 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 31 | 31 | 23 | 27 | 32 | 15 | 87 | 24 |
N.S. |
1 | 1.03 | 1.03 | 0.77 | 0.90 | 1.07 | 0.50 | 2.90 | 0.80 |
time (sec) |
N/A | 0.415 | 0.603 | 0.195 | 0.222 | 0.235 | 0.054 | 0.254 | 8.742 |
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 | 17 | 0 | 17 | 17 | 28 | 26 | 14 | 46 | 25 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.65 | 1.53 | 0.82 | 2.71 | 1.47 |
time (sec) |
N/A | 0.000 | 0.051 | 0.669 | 0.250 | 0.248 | 0.076 | 0.300 | 9.011 |
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 | 28 | 0 | 25 | 26 | 44 | 36 | 17 | 110 | 25 |
N.S. |
1 | 0.00 | 0.89 | 0.93 | 1.57 | 1.29 | 0.61 | 3.93 | 0.89 |
time (sec) |
N/A | 0.000 | 2.142 | 3.305 | 0.229 | 0.245 | 0.050 | 0.270 | 9.042 |
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 | 25 | 0 | 47 | 56 | 70 | 55 | 0 | 55 | 184 |
N.S. |
1 | 0.00 | 1.88 | 2.24 | 2.80 | 2.20 | 0.00 | 2.20 | 7.36 |
time (sec) |
N/A | 0.000 | 0.099 | 0.435 | 0.266 | 0.250 | 0.000 | 0.427 | 12.253 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 21 | 24 | 0 | 19 | 42 | 58 | 17 |
N.S. |
1 | 1.00 | 0.88 | 1.00 | 0.00 | 0.79 | 1.75 | 2.42 | 0.71 |
time (sec) |
N/A | 0.185 | 0.008 | 0.156 | 0.000 | 0.239 | 0.154 | 0.252 | 8.972 |
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 | 40 | 27 | 27 | 32 | 32 | 26 | 32 | 24 |
N.S. |
1 | 1.67 | 1.12 | 1.12 | 1.33 | 1.33 | 1.08 | 1.33 | 1.00 |
time (sec) |
N/A | 0.183 | 0.019 | 0.043 | 0.194 | 0.242 | 0.020 | 0.263 | 8.555 |
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 | 17 | 17 | 19 | 0 | 22 | 12 | 22 | 17 |
N.S. |
1 | 0.74 | 0.74 | 0.83 | 0.00 | 0.96 | 0.52 | 0.96 | 0.74 |
time (sec) |
N/A | 0.399 | 0.117 | 0.297 | 0.000 | 0.257 | 0.060 | 0.259 | 8.963 |
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 | 38 | 34 | 28 | 36 | 36 | 27 | 36 | 25 |
N.S. |
1 | 1.90 | 1.70 | 1.40 | 1.80 | 1.80 | 1.35 | 1.80 | 1.25 |
time (sec) |
N/A | 0.163 | 0.010 | 0.047 | 0.206 | 0.252 | 0.026 | 0.251 | 0.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 60 | 34 | 34 | 52 | 58 | 32 | 58 | 51 |
N.S. |
1 | 2.40 | 1.36 | 1.36 | 2.08 | 2.32 | 1.28 | 2.32 | 2.04 |
time (sec) |
N/A | 0.382 | 0.089 | 0.074 | 0.287 | 0.236 | 0.079 | 0.266 | 8.828 |
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 | 27 | 27 | 23 | 25 | 29 | 17 | 29 | 22 |
N.S. |
1 | 0.84 | 0.84 | 0.72 | 0.78 | 0.91 | 0.53 | 0.91 | 0.69 |
time (sec) |
N/A | 0.203 | 0.012 | 0.064 | 0.198 | 0.242 | 0.066 | 0.255 | 0.072 |
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 | 25 | 23 | 21 | 20 | 23 | 17 | 20 | 20 |
N.S. |
1 | 0.83 | 0.77 | 0.70 | 0.67 | 0.77 | 0.57 | 0.67 | 0.67 |
time (sec) |
N/A | 0.415 | 0.060 | 0.334 | 0.199 | 0.242 | 0.081 | 0.265 | 8.979 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 64 | 54 | 20 | 35 | 34 | 31 | 62 | 342 |
N.S. |
1 | 2.56 | 2.16 | 0.80 | 1.40 | 1.36 | 1.24 | 2.48 | 13.68 |
time (sec) |
N/A | 0.345 | 0.075 | 0.171 | 0.194 | 0.249 | 0.926 | 0.262 | 11.820 |
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 | 10 | 9 | 9 | 10 | 9 | 38 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.90 | 0.90 | 1.00 | 0.90 | 3.80 |
time (sec) |
N/A | 0.219 | 0.041 | 0.059 | 0.188 | 0.229 | 0.078 | 0.255 | 9.035 |
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 | 21 | 21 | 13 | 12 | 20 | 12 | 12 | 12 |
N.S. |
1 | 0.95 | 0.95 | 0.59 | 0.55 | 0.91 | 0.55 | 0.55 | 0.55 |
time (sec) |
N/A | 0.215 | 0.018 | 0.327 | 0.199 | 0.236 | 0.049 | 0.259 | 0.071 |
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 | 5 | 5 | 5 | 4 | 3 | 3 | 3 | 3 | 3 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.60 | 0.60 | 0.60 | 0.60 | 0.60 |
time (sec) |
N/A | 0.154 | 0.002 | 0.055 | 0.195 | 0.243 | 0.061 | 0.248 | 0.033 |
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 | 29 | 18 | 18 | 26 | 15 | 19 | 15 | 17 |
N.S. |
1 | 1.45 | 0.90 | 0.90 | 1.30 | 0.75 | 0.95 | 0.75 | 0.85 |
time (sec) |
N/A | 0.161 | 0.012 | 0.052 | 0.191 | 0.261 | 0.054 | 0.252 | 0.064 |
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 | 25 | 637 | 73 | 76 | 773 | 75 | 70 | 75 | 82 |
N.S. |
1 | 25.48 | 2.92 | 3.04 | 30.92 | 3.00 | 2.80 | 3.00 | 3.28 |
time (sec) |
N/A | 2.511 | 0.048 | 0.246 | 0.219 | 0.236 | 0.124 | 0.278 | 8.882 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 25 | 39 | 115 | 110 | 41 | 0 | 103 |
N.S. |
1 | 0.00 | 0.74 | 1.15 | 3.38 | 3.24 | 1.21 | 0.00 | 3.03 |
time (sec) |
N/A | 0.000 | 1.285 | 0.285 | 1.672 | 0.247 | 0.444 | 0.000 | 0.473 |
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 | 6 | 6 | 5 | 6 | 6 | 5 | 7 | 4 |
N.S. |
1 | 0.27 | 0.27 | 0.23 | 0.27 | 0.27 | 0.23 | 0.32 | 0.18 |
time (sec) |
N/A | 0.121 | 0.001 | 0.192 | 0.192 | 0.220 | 0.022 | 0.251 | 8.585 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | C | C | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 35 | 41 | 41 | 79 | 58 | 139 | 49 |
N.S. |
1 | 0.00 | 1.67 | 1.95 | 1.95 | 3.76 | 2.76 | 6.62 | 2.33 |
time (sec) |
N/A | 0.000 | 0.159 | 0.817 | 0.198 | 0.239 | 0.077 | 0.264 | 8.780 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 37 | 18 | 18 | 26 | 20 | 14 | 66 | 17 |
N.S. |
1 | 1.76 | 0.86 | 0.86 | 1.24 | 0.95 | 0.67 | 3.14 | 0.81 |
time (sec) |
N/A | 0.196 | 0.043 | 0.168 | 0.231 | 0.238 | 0.046 | 0.255 | 8.945 |
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 | 19 | 19 | 18 | 17 | 17 | 17 | 19 | 19 |
N.S. |
1 | 1.19 | 1.19 | 1.12 | 1.06 | 1.06 | 1.06 | 1.19 | 1.19 |
time (sec) |
N/A | 0.365 | 0.386 | 0.351 | 0.228 | 0.232 | 0.130 | 0.272 | 8.956 |
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 | 32 | 14 | 13 | 29 | 15 | 14 | 15 | 12 |
N.S. |
1 | 1.39 | 0.61 | 0.57 | 1.26 | 0.65 | 0.61 | 0.65 | 0.52 |
time (sec) |
N/A | 0.196 | 0.099 | 0.110 | 0.195 | 0.228 | 0.043 | 0.263 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 26 | 22 | 25 | 20 | 397 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.04 | 0.88 | 1.00 | 0.80 | 15.88 | 0.00 |
time (sec) |
N/A | 0.000 | 0.623 | 22.540 | 0.336 | 0.244 | 0.231 | 1.071 | 0.000 |
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 | 28 | 31 | 27 | 22 | 53 | 37 |
N.S. |
1 | 0.00 | 1.13 | 1.22 | 1.35 | 1.17 | 0.96 | 2.30 | 1.61 |
time (sec) |
N/A | 0.000 | 0.533 | 0.427 | 0.319 | 0.232 | 0.134 | 0.260 | 8.236 |
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 | 24 | 22 | 17 | 16 | 16 | 17 | 16 | 14 |
N.S. |
1 | 1.09 | 1.00 | 0.77 | 0.73 | 0.73 | 0.77 | 0.73 | 0.64 |
time (sec) |
N/A | 0.158 | 0.021 | 0.051 | 0.186 | 0.243 | 0.048 | 0.253 | 0.059 |
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 | 24 | 22 | 20 | 19 | 22 | 22 | 29 | 20 |
N.S. |
1 | 1.00 | 0.92 | 0.83 | 0.79 | 0.92 | 0.92 | 1.21 | 0.83 |
time (sec) |
N/A | 0.684 | 0.132 | 0.095 | 0.240 | 0.246 | 0.069 | 0.258 | 8.889 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 35 | 35 | 31 | 30 | 30 | 26 | 30 | 28 |
N.S. |
1 | 1.35 | 1.35 | 1.19 | 1.15 | 1.15 | 1.00 | 1.15 | 1.08 |
time (sec) |
N/A | 0.214 | 0.026 | 0.194 | 0.200 | 0.236 | 0.051 | 0.264 | 8.510 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 39 | 46 | 43 | 41 | 71 | 45 | 0 |
N.S. |
1 | 0.00 | 1.50 | 1.77 | 1.65 | 1.58 | 2.73 | 1.73 | 0.00 |
time (sec) |
N/A | 0.000 | 0.099 | 0.395 | 0.398 | 0.247 | 0.222 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 61 | 24 | 23 | 0 | 58 | 24 | 65 | 22 |
N.S. |
1 | 2.44 | 0.96 | 0.92 | 0.00 | 2.32 | 0.96 | 2.60 | 0.88 |
time (sec) |
N/A | 0.649 | 0.640 | 0.177 | 0.000 | 0.260 | 0.148 | 0.274 | 8.929 |
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 | 21 | 21 | 31 | 31 | 15 | 31 | 0 |
N.S. |
1 | 0.00 | 0.91 | 0.91 | 1.35 | 1.35 | 0.65 | 1.35 | 0.00 |
time (sec) |
N/A | 0.000 | 0.064 | 0.156 | 0.248 | 0.247 | 0.075 | 0.317 | 0.000 |
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 | 31 | 0 | 49 | 30 | 39 | 30 | 27 | 0 | 166 |
N.S. |
1 | 0.00 | 1.58 | 0.97 | 1.26 | 0.97 | 0.87 | 0.00 | 5.35 |
time (sec) |
N/A | 0.000 | 0.148 | 0.309 | 0.336 | 0.237 | 0.165 | 0.000 | 10.563 |
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 | 30 | 29 | 30 | 32 | 27 | 31 | 31 |
N.S. |
1 | 0.00 | 1.36 | 1.32 | 1.36 | 1.45 | 1.23 | 1.41 | 1.41 |
time (sec) |
N/A | 0.000 | 0.327 | 0.109 | 0.321 | 0.256 | 0.112 | 0.255 | 0.338 |
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 | 30 | 71 | 69 | 63 | 64 | 73 | 70 | 76 | 63 |
N.S. |
1 | 2.37 | 2.30 | 2.10 | 2.13 | 2.43 | 2.33 | 2.53 | 2.10 |
time (sec) |
N/A | 0.263 | 0.034 | 0.082 | 0.200 | 0.238 | 1.032 | 0.257 | 9.757 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 197 | 24 | 57 | 53 | 27 | 53 | 33 |
N.S. |
1 | 0.00 | 7.30 | 0.89 | 2.11 | 1.96 | 1.00 | 1.96 | 1.22 |
time (sec) |
N/A | 0.000 | 14.582 | 0.082 | 0.242 | 0.256 | 0.079 | 0.285 | 0.602 |
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 | 27 | 0 | 28 | 45 | 31 | 43 | 39 | 44 | 0 |
N.S. |
1 | 0.00 | 1.04 | 1.67 | 1.15 | 1.59 | 1.44 | 1.63 | 0.00 |
time (sec) |
N/A | 0.000 | 0.145 | 2.915 | 0.331 | 0.236 | 0.308 | 1.285 | 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 | 22 | 33 | 33 | 31 | 31 | 31 | 32 | 31 | 33 |
N.S. |
1 | 1.50 | 1.50 | 1.41 | 1.41 | 1.41 | 1.45 | 1.41 | 1.50 |
time (sec) |
N/A | 0.728 | 0.921 | 1.336 | 0.404 | 0.239 | 0.336 | 0.297 | 9.449 |
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 | 14 | 14 | 12 | 13 | 11 | 8 | 13 | 11 |
N.S. |
1 | 0.93 | 0.93 | 0.80 | 0.87 | 0.73 | 0.53 | 0.87 | 0.73 |
time (sec) |
N/A | 0.145 | 0.002 | 0.056 | 0.193 | 0.228 | 0.031 | 0.253 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | F | B | B | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 32 | 151 | 0 | 103 | 116 | 0 | 0 |
N.S. |
1 | 0.00 | 1.10 | 5.21 | 0.00 | 3.55 | 4.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.323 | 0.951 | 0.000 | 0.254 | 44.588 | 0.000 | 0.000 |
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 | 25 | 119 | 89 | 88 | 90 | 84 | 99 | 92 | 90 |
N.S. |
1 | 4.76 | 3.56 | 3.52 | 3.60 | 3.36 | 3.96 | 3.68 | 3.60 |
time (sec) |
N/A | 0.363 | 5.111 | 0.079 | 0.291 | 0.242 | 0.121 | 0.255 | 0.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 99 | 33 | 46 | 50 | 45 | 48 | 45 | 38 |
N.S. |
1 | 3.81 | 1.27 | 1.77 | 1.92 | 1.73 | 1.85 | 1.73 | 1.46 |
time (sec) |
N/A | 0.277 | 0.270 | 0.151 | 0.223 | 0.234 | 0.080 | 0.248 | 9.648 |
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 | 22 | 20 | 62 | 19 | 15 | 19 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 2.82 | 0.86 | 0.68 | 0.86 | 0.91 |
time (sec) |
N/A | 0.156 | 0.007 | 0.046 | 0.194 | 0.254 | 0.058 | 0.256 | 8.511 |
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 | 18 | 16 | 15 | 14 | 14 | 15 | 14 | 12 |
N.S. |
1 | 1.06 | 0.94 | 0.88 | 0.82 | 0.82 | 0.88 | 0.82 | 0.71 |
time (sec) |
N/A | 0.140 | 0.004 | 0.033 | 0.194 | 0.234 | 0.042 | 0.259 | 8.763 |
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 | 12 | 12 | 10 | 9 | 9 | 8 | 10 | 9 |
N.S. |
1 | 0.40 | 0.40 | 0.33 | 0.30 | 0.30 | 0.27 | 0.33 | 0.30 |
time (sec) |
N/A | 0.165 | 0.018 | 0.049 | 0.194 | 0.233 | 0.039 | 0.273 | 0.107 |
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 | 15 | 15 | 9 | 14 | 14 | 12 | 14 | 12 |
N.S. |
1 | 1.36 | 1.36 | 0.82 | 1.27 | 1.27 | 1.09 | 1.27 | 1.09 |
time (sec) |
N/A | 0.121 | 0.000 | 0.026 | 0.194 | 0.226 | 0.034 | 0.252 | 9.324 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 5 | 21 | 18 | 29 | 57 | 19 | 17 | 17 |
N.S. |
1 | 0.20 | 0.84 | 0.72 | 1.16 | 2.28 | 0.76 | 0.68 | 0.68 |
time (sec) |
N/A | 0.868 | 0.874 | 9.503 | 0.310 | 0.247 | 0.481 | 1.791 | 10.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 53 | 28 | 36 | 45 | 45 | 44 | 45 | 43 |
N.S. |
1 | 2.41 | 1.27 | 1.64 | 2.05 | 2.05 | 2.00 | 2.05 | 1.95 |
time (sec) |
N/A | 0.188 | 0.012 | 0.142 | 0.194 | 0.231 | 0.025 | 0.261 | 9.290 |
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 | 13 | 12 | 12 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.92 | 0.92 | 0.77 | 0.92 | 0.92 |
time (sec) |
N/A | 0.163 | 0.009 | 1.514 | 0.206 | 0.231 | 0.046 | 0.258 | 9.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | F(-1) | B | F(-1) | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 42 | 118 | 0 | 116 | 0 | 672 | 0 |
N.S. |
1 | 0.00 | 1.31 | 3.69 | 0.00 | 3.62 | 0.00 | 21.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.402 | 11.345 | 0.000 | 0.253 | 0.000 | 3.039 | 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 | 25 | 23 | 11 | 11 | 10 | 11 | 35 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 0.44 | 0.44 | 0.40 | 0.44 | 1.40 |
time (sec) |
N/A | 0.000 | 3.583 | 0.692 | 0.252 | 0.244 | 0.078 | 0.270 | 9.890 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | F | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 0 | 25 | 35 | 27 | 26 | 0 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.00 | 1.40 | 1.08 | 1.04 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 10.478 | 0.344 | 0.232 | 0.205 | 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 | 20 | 25 | 18 | 22 | 25 | 21 | 22 | 21 | 21 |
N.S. |
1 | 1.25 | 0.90 | 1.10 | 1.25 | 1.05 | 1.10 | 1.05 | 1.05 |
time (sec) |
N/A | 0.323 | 0.079 | 0.094 | 0.310 | 0.236 | 0.166 | 0.271 | 9.570 |
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 | 28 | 0 | 30 | 25 | 26 | 43 | 19 | 410 | 26 |
N.S. |
1 | 0.00 | 1.07 | 0.89 | 0.93 | 1.54 | 0.68 | 14.64 | 0.93 |
time (sec) |
N/A | 0.000 | 0.098 | 0.176 | 0.243 | 0.243 | 0.091 | 0.308 | 9.399 |