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 | 10 | 10 | 10 | 15 | 9 | 14 | 10 | 9 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 0.90 | 1.40 | 1.00 | 0.90 | 1.10 |
time (sec) |
N/A | 0.136 | 0.035 | 0.238 | 0.239 | 0.238 | 0.062 | 0.287 | 15.220 |
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 | 28 | 0 | 62 | 32 | 53 | 49 | 24 | 49 | 129 |
N.S. |
1 | 0.00 | 2.21 | 1.14 | 1.89 | 1.75 | 0.86 | 1.75 | 4.61 |
time (sec) |
N/A | 0.000 | 0.211 | 1.431 | 0.318 | 0.244 | 0.085 | 0.355 | 16.237 |
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 | 19 | 110 | 19 | 16 | 19 | 28 | 15 | 0 | 20 |
N.S. |
1 | 5.79 | 1.00 | 0.84 | 1.00 | 1.47 | 0.79 | 0.00 | 1.05 |
time (sec) |
N/A | 0.438 | 0.685 | 0.776 | 0.355 | 0.246 | 7.246 | 0.000 | 14.521 |
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 | 22 | 38 | 38 | 38 | 37 | 41 | 42 | 37 | 37 |
N.S. |
1 | 1.73 | 1.73 | 1.73 | 1.68 | 1.86 | 1.91 | 1.68 | 1.68 |
time (sec) |
N/A | 0.024 | 0.009 | 0.273 | 0.183 | 0.247 | 0.038 | 0.277 | 15.228 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | F(-2) | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 22 | 20 | 21 | 69 | 0 | 157 | 0 |
N.S. |
1 | 0.00 | 0.88 | 0.80 | 0.84 | 2.76 | 0.00 | 6.28 | 0.00 |
time (sec) |
N/A | 0.000 | 2.018 | 5.179 | 0.479 | 0.290 | 0.000 | 3.687 | 0.000 |
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 | 25 | 73 | 34 | 21 | 21 | 21 | 20 | 21 | 0 |
N.S. |
1 | 2.92 | 1.36 | 0.84 | 0.84 | 0.84 | 0.80 | 0.84 | 0.00 |
time (sec) |
N/A | 0.255 | 0.189 | 0.203 | 0.303 | 0.241 | 0.113 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | A | B | B | B | B | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 41 | 0 | 37 | 220 | 96 | 94 | 137 | 0 |
N.S. |
1 | 1.64 | 0.00 | 1.48 | 8.80 | 3.84 | 3.76 | 5.48 | 0.00 |
time (sec) |
N/A | 1.449 | 0.000 | 69.160 | 0.546 | 0.262 | 1.444 | 2.441 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 235 | 141 | 145 | 327 | 147 | 163 | 178 | 142 |
N.S. |
1 | 7.83 | 4.70 | 4.83 | 10.90 | 4.90 | 5.43 | 5.93 | 4.73 |
time (sec) |
N/A | 0.468 | 6.089 | 0.108 | 0.240 | 0.247 | 0.149 | 0.311 | 0.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 33 | 33 | 30 | 33 | 48 | 27 | 33 | 29 |
N.S. |
1 | 1.38 | 1.38 | 1.25 | 1.38 | 2.00 | 1.12 | 1.38 | 1.21 |
time (sec) |
N/A | 7.720 | 0.495 | 49.652 | 0.259 | 0.273 | 2.092 | 0.487 | 14.746 |
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 | 19 | 26 | 17 | 18 | 20 | 19 | 18 | 18 |
N.S. |
1 | 0.68 | 0.93 | 0.61 | 0.64 | 0.71 | 0.68 | 0.64 | 0.64 |
time (sec) |
N/A | 0.435 | 0.713 | 0.061 | 0.218 | 0.254 | 0.079 | 0.295 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 18 | 17 | 42 | 15 | 44 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.81 | 2.00 | 0.71 | 2.10 | 0.81 |
time (sec) |
N/A | 0.034 | 0.034 | 0.099 | 0.175 | 0.243 | 0.101 | 0.293 | 14.681 |
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 | 20 | 18 | 20 | 20 | 20 | 20 | 24 |
N.S. |
1 | 0.00 | 0.80 | 0.72 | 0.80 | 0.80 | 0.80 | 0.80 | 0.96 |
time (sec) |
N/A | 0.000 | 0.663 | 0.072 | 0.225 | 0.230 | 0.070 | 0.296 | 15.442 |
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 | 25 | 0 | 25 | 24 | 0 | 46 | 24 | 0 | 23 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 0.00 | 1.84 | 0.96 | 0.00 | 0.92 |
time (sec) |
N/A | 0.000 | 1.493 | 2.374 | 0.000 | 0.247 | 0.161 | 0.000 | 15.974 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 63 | 33 | 33 | 39 | 35 | 0 | 39 | 34 |
N.S. |
1 | 2.17 | 1.14 | 1.14 | 1.34 | 1.21 | 0.00 | 1.34 | 1.17 |
time (sec) |
N/A | 0.906 | 0.505 | 15.056 | 0.249 | 0.245 | 0.000 | 1.197 | 16.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 47 | 51 | 44 | 43 | 64 | 44 | 0 | 44 |
N.S. |
1 | 1.74 | 1.89 | 1.63 | 1.59 | 2.37 | 1.63 | 0.00 | 1.63 |
time (sec) |
N/A | 0.133 | 1.027 | 0.463 | 0.268 | 0.264 | 0.152 | 0.000 | 15.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | F(-1) | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 20 | 37 | 53 | 0 | 37 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.87 | 1.61 | 2.30 | 0.00 | 1.61 | 0.00 |
time (sec) |
N/A | 0.000 | 2.197 | 0.779 | 0.333 | 0.263 | 0.000 | 0.330 | 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 | 27 | 0 | 27 | 32 | 28 | 30 | 24 | 28 | 30 |
N.S. |
1 | 0.00 | 1.00 | 1.19 | 1.04 | 1.11 | 0.89 | 1.04 | 1.11 |
time (sec) |
N/A | 0.000 | 0.173 | 4.431 | 0.241 | 0.249 | 0.422 | 0.408 | 15.917 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 51 | 47 | 32 | 152 | 52 | 26 | 34 | 34 |
N.S. |
1 | 2.22 | 2.04 | 1.39 | 6.61 | 2.26 | 1.13 | 1.48 | 1.48 |
time (sec) |
N/A | 0.503 | 0.089 | 0.133 | 0.254 | 0.244 | 0.082 | 0.341 | 15.406 |
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 | 24 | 20 | 18 | 15 | 23 | 15 | 15 | 15 | 15 |
N.S. |
1 | 0.83 | 0.75 | 0.62 | 0.96 | 0.62 | 0.62 | 0.62 | 0.62 |
time (sec) |
N/A | 0.029 | 0.027 | 0.053 | 0.232 | 0.255 | 0.059 | 0.311 | 0.057 |
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 | 25 | 0 | 23 | 23 | 22 | 22 | 20 | 0 | 209 |
N.S. |
1 | 0.00 | 0.92 | 0.92 | 0.88 | 0.88 | 0.80 | 0.00 | 8.36 |
time (sec) |
N/A | 0.000 | 0.120 | 37.431 | 0.264 | 0.252 | 0.158 | 0.000 | 13.707 |
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 | 23 | 35 | 22 | 20 | 35 | 22 |
N.S. |
1 | 0.00 | 1.00 | 0.88 | 1.35 | 0.85 | 0.77 | 1.35 | 0.85 |
time (sec) |
N/A | 0.000 | 0.078 | 1.968 | 0.327 | 0.242 | 0.131 | 0.404 | 13.707 |
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 | 291 | 124 | 124 | 112 | 109 | 134 | 109 | 26 |
N.S. |
1 | 10.39 | 4.43 | 4.43 | 4.00 | 3.89 | 4.79 | 3.89 | 0.93 |
time (sec) |
N/A | 0.401 | 10.195 | 0.434 | 0.269 | 0.242 | 0.164 | 0.356 | 14.141 |
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 | 11 | 11 | 8 | 9 | 9 | 7 | 9 | 9 |
N.S. |
1 | 0.52 | 0.52 | 0.38 | 0.43 | 0.43 | 0.33 | 0.43 | 0.43 |
time (sec) |
N/A | 0.002 | 0.002 | 0.334 | 0.193 | 0.236 | 0.035 | 0.306 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 107 | 89 | 129 | 119 | 144 | 0 | 137 |
N.S. |
1 | 0.00 | 4.46 | 3.71 | 5.38 | 4.96 | 6.00 | 0.00 | 5.71 |
time (sec) |
N/A | 0.000 | 0.396 | 4.269 | 0.650 | 0.275 | 1.478 | 0.000 | 14.255 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F(-2) | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 97 | 26 | 27 | 0 | 26 | 0 | 30 | 31 |
N.S. |
1 | 3.88 | 1.04 | 1.08 | 0.00 | 1.04 | 0.00 | 1.20 | 1.24 |
time (sec) |
N/A | 0.763 | 0.063 | 1.332 | 0.000 | 0.242 | 0.000 | 0.450 | 13.148 |
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 | 17 | 26 | 16 | 16 | 16 | 15 | 17 | 15 |
N.S. |
1 | 0.59 | 0.90 | 0.55 | 0.55 | 0.55 | 0.52 | 0.59 | 0.52 |
time (sec) |
N/A | 0.012 | 0.011 | 0.312 | 0.188 | 0.247 | 0.066 | 0.304 | 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 | 22 | 18 | 18 | 17 | 16 | 16 | 12 | 16 | 16 |
N.S. |
1 | 0.82 | 0.82 | 0.77 | 0.73 | 0.73 | 0.55 | 0.73 | 0.73 |
time (sec) |
N/A | 0.069 | 0.156 | 0.434 | 0.218 | 0.255 | 2.373 | 0.310 | 14.393 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 72 | 33 | 30 | 38 | 41 | 29 | 119 | 29 |
N.S. |
1 | 2.32 | 1.06 | 0.97 | 1.23 | 1.32 | 0.94 | 3.84 | 0.94 |
time (sec) |
N/A | 2.541 | 0.214 | 3.743 | 0.273 | 0.253 | 0.236 | 0.347 | 14.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 30 | 30 | 31 | 55 | 56 | 27 | 30 | 32 |
N.S. |
1 | 1.20 | 1.20 | 1.24 | 2.20 | 2.24 | 1.08 | 1.20 | 1.28 |
time (sec) |
N/A | 0.310 | 0.078 | 0.497 | 0.236 | 0.252 | 0.160 | 0.485 | 14.454 |
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 | 38 | 38 | 35 | 34 | 34 | 34 | 36 | 34 |
N.S. |
1 | 1.36 | 1.36 | 1.25 | 1.21 | 1.21 | 1.21 | 1.29 | 1.21 |
time (sec) |
N/A | 0.087 | 0.016 | 0.095 | 0.190 | 0.244 | 0.064 | 0.285 | 13.956 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 100 | 39 | 34 | 36 | 36 | 0 | 0 | 39 |
N.S. |
1 | 4.55 | 1.77 | 1.55 | 1.64 | 1.64 | 0.00 | 0.00 | 1.77 |
time (sec) |
N/A | 0.118 | 0.128 | 0.454 | 0.271 | 0.268 | 0.000 | 0.000 | 0.325 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 23 | 39 | 15 | 33 | 13 | 14 | 19 | 15 |
N.S. |
1 | 1.21 | 2.05 | 0.79 | 1.74 | 0.68 | 0.74 | 1.00 | 0.79 |
time (sec) |
N/A | 0.058 | 0.054 | 0.152 | 0.224 | 0.239 | 0.076 | 0.295 | 0.139 |
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 | 33 | 0 | 28 | 1052 | 0 | 39 | 39 | 0 | 43 |
N.S. |
1 | 0.00 | 0.85 | 31.88 | 0.00 | 1.18 | 1.18 | 0.00 | 1.30 |
time (sec) |
N/A | 0.000 | 0.053 | 7.932 | 0.000 | 0.258 | 0.270 | 0.000 | 14.539 |
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 | 26 | 21 | 25 | 25 | 25 | 24 | 26 | 25 |
N.S. |
1 | 1.24 | 1.00 | 1.19 | 1.19 | 1.19 | 1.14 | 1.24 | 1.19 |
time (sec) |
N/A | 0.355 | 3.552 | 0.171 | 0.238 | 0.253 | 0.148 | 0.881 | 13.208 |
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 | 30 | 0 | 35 | 37 | 139 | 35 | 32 | 35 | 26 |
N.S. |
1 | 0.00 | 1.17 | 1.23 | 4.63 | 1.17 | 1.07 | 1.17 | 0.87 |
time (sec) |
N/A | 0.000 | 0.034 | 1.274 | 0.201 | 0.242 | 0.095 | 0.315 | 14.285 |
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 | 29 | 29 | 27 | 26 | 26 | 24 | 28 | 26 |
N.S. |
1 | 0.97 | 0.97 | 0.90 | 0.87 | 0.87 | 0.80 | 0.93 | 0.87 |
time (sec) |
N/A | 2.934 | 0.087 | 2.667 | 0.347 | 0.261 | 0.219 | 0.362 | 0.799 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 134 | 135 | 39 | 106 | 21 | 41 | 39 | 41 |
N.S. |
1 | 6.09 | 6.14 | 1.77 | 4.82 | 0.95 | 1.86 | 1.77 | 1.86 |
time (sec) |
N/A | 0.205 | 0.101 | 0.209 | 0.355 | 0.249 | 0.143 | 0.351 | 14.398 |
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 | 9 | 12 | 9 | 9 | 8 | 8 | 5 | 8 | 8 |
N.S. |
1 | 1.33 | 1.00 | 1.00 | 0.89 | 0.89 | 0.56 | 0.89 | 0.89 |
time (sec) |
N/A | 0.002 | 0.000 | 0.013 | 0.188 | 0.236 | 0.016 | 0.289 | 0.002 |
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 | 15 | 14 | 14 | 12 | 14 | 10 |
N.S. |
1 | 0.93 | 0.93 | 1.00 | 0.93 | 0.93 | 0.80 | 0.93 | 0.67 |
time (sec) |
N/A | 0.003 | 0.002 | 0.033 | 0.178 | 0.241 | 0.043 | 0.298 | 14.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 28 | 28 | 58 | 58 | 54 | 60 | 0 |
N.S. |
1 | 0.00 | 0.90 | 0.90 | 1.87 | 1.87 | 1.74 | 1.94 | 0.00 |
time (sec) |
N/A | 0.000 | 0.536 | 0.367 | 0.245 | 0.248 | 0.127 | 0.362 | 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 | 38 | 19 | 19 | 18 | 18 | 19 | 18 | 18 |
N.S. |
1 | 1.73 | 0.86 | 0.86 | 0.82 | 0.82 | 0.86 | 0.82 | 0.82 |
time (sec) |
N/A | 0.030 | 0.106 | 0.131 | 0.179 | 0.237 | 0.082 | 0.309 | 13.560 |
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 | 20 | 0 | 20 | 20 | 19 | 19 | 20 | 19 | 19 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.95 | 0.95 | 1.00 | 0.95 | 0.95 |
time (sec) |
N/A | 0.000 | 0.374 | 0.653 | 0.249 | 0.244 | 0.133 | 0.330 | 13.261 |
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 | 31 | 16 | 16 | 25 | 18 | 14 | 18 | 15 |
N.S. |
1 | 1.63 | 0.84 | 0.84 | 1.32 | 0.95 | 0.74 | 0.95 | 0.79 |
time (sec) |
N/A | 0.014 | 0.013 | 0.118 | 0.187 | 0.243 | 0.045 | 0.300 | 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 | 26 | 25 | 24 | 19 | 26 | 35 | 19 | 26 | 20 |
N.S. |
1 | 0.96 | 0.92 | 0.73 | 1.00 | 1.35 | 0.73 | 1.00 | 0.77 |
time (sec) |
N/A | 0.027 | 0.027 | 0.386 | 0.193 | 0.236 | 0.084 | 0.290 | 0.103 |
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 | 18 | 0 | 18 | 16 | 17 | 15 | 14 | 17 | 77 |
N.S. |
1 | 0.00 | 1.00 | 0.89 | 0.94 | 0.83 | 0.78 | 0.94 | 4.28 |
time (sec) |
N/A | 0.000 | 0.304 | 1.069 | 0.305 | 0.255 | 0.298 | 0.322 | 14.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F(-1) | A | F(-1) | B | B | B | B | B |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 47 | 0 | 140 | 108 | 90 | 116 | 212 |
N.S. |
1 | 0.00 | 1.38 | 0.00 | 4.12 | 3.18 | 2.65 | 3.41 | 6.24 |
time (sec) |
N/A | 0.000 | 1.110 | 0.000 | 2.584 | 0.253 | 1.750 | 117.316 | 15.410 |
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 | 26 | 57 | 19 | 19 | 20 | 20 | 17 | 20 | 18 |
N.S. |
1 | 2.19 | 0.73 | 0.73 | 0.77 | 0.77 | 0.65 | 0.77 | 0.69 |
time (sec) |
N/A | 0.112 | 0.029 | 0.171 | 0.184 | 0.249 | 0.292 | 0.308 | 14.467 |
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 | 18 | 32 | 16 | 17 | 15 | 16 | 0 | 16 | 15 |
N.S. |
1 | 1.78 | 0.89 | 0.94 | 0.83 | 0.89 | 0.00 | 0.89 | 0.83 |
time (sec) |
N/A | 0.039 | 0.019 | 0.344 | 0.251 | 0.251 | 0.000 | 0.305 | 15.333 |
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 | 20 | 15 | 17 | 16 | 16 | 15 | 16 | 11 |
N.S. |
1 | 1.54 | 1.15 | 1.31 | 1.23 | 1.23 | 1.15 | 1.23 | 0.85 |
time (sec) |
N/A | 0.004 | 0.004 | 0.063 | 0.183 | 0.246 | 0.046 | 0.310 | 13.256 |
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 | 37 | 41 | 38 | 38 | 38 | 36 | 38 | 39 |
N.S. |
1 | 1.28 | 1.41 | 1.31 | 1.31 | 1.31 | 1.24 | 1.31 | 1.34 |
time (sec) |
N/A | 0.005 | 0.004 | 0.065 | 0.179 | 0.239 | 0.031 | 0.296 | 14.275 |
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 | 9 | 7 | 7 | 7 | 6 | 6 | 5 | 6 | 6 |
N.S. |
1 | 0.78 | 0.78 | 0.78 | 0.67 | 0.67 | 0.56 | 0.67 | 0.67 |
time (sec) |
N/A | 0.001 | 0.002 | 0.053 | 0.185 | 0.237 | 0.034 | 0.298 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 41 | 24 | 21 | 32 | 26 | 22 | 28 | 24 |
N.S. |
1 | 1.46 | 0.86 | 0.75 | 1.14 | 0.93 | 0.79 | 1.00 | 0.86 |
time (sec) |
N/A | 0.024 | 0.049 | 0.158 | 0.190 | 0.267 | 0.068 | 0.302 | 0.110 |
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 | 25 | 0 | 48 | 47 | 41 | 34 | 44 | 104 | 61 |
N.S. |
1 | 0.00 | 1.92 | 1.88 | 1.64 | 1.36 | 1.76 | 4.16 | 2.44 |
time (sec) |
N/A | 0.000 | 0.892 | 16.461 | 0.277 | 0.261 | 0.328 | 5.895 | 13.192 |
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 | 35 | 0 | 31 | 36 | 30 | 30 | 76 | 35 | 0 |
N.S. |
1 | 0.00 | 0.89 | 1.03 | 0.86 | 0.86 | 2.17 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 5.095 | 0.335 | 0.252 | 0.254 | 0.133 | 0.336 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | C | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 79 | 62 | 73 | 83 | 63 | 71 | 64 | 53 |
N.S. |
1 | 2.72 | 2.14 | 2.52 | 2.86 | 2.17 | 2.45 | 2.21 | 1.83 |
time (sec) |
N/A | 0.119 | 0.161 | 2.558 | 0.243 | 0.251 | 0.131 | 0.302 | 14.982 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F(-1) | F | A | A | A | A | A | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 0 | 41 | 30 | 40 | 32 | 40 | 68 |
N.S. |
1 | 0.00 | 0.00 | 1.28 | 0.94 | 1.25 | 1.00 | 1.25 | 2.12 |
time (sec) |
N/A | 0.000 | 0.000 | 19.145 | 0.468 | 0.254 | 0.735 | 2.060 | 15.443 |
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 | 28 | 0 | 58 | 34 | 27 | 29 | 29 | 27 | 86 |
N.S. |
1 | 0.00 | 2.07 | 1.21 | 0.96 | 1.04 | 1.04 | 0.96 | 3.07 |
time (sec) |
N/A | 0.000 | 5.106 | 1.177 | 0.334 | 0.240 | 0.129 | 0.307 | 14.762 |
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 | 8 | 6 | 6 | 7 | 17 | 6 | 5 | 6 | 6 |
N.S. |
1 | 0.75 | 0.75 | 0.88 | 2.12 | 0.75 | 0.62 | 0.75 | 0.75 |
time (sec) |
N/A | 0.007 | 0.001 | 0.031 | 0.199 | 0.246 | 0.042 | 0.281 | 13.395 |
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 | 30 | 28 | 39 | 74 | 59 | 24 | 22 | 21 |
N.S. |
1 | 1.36 | 1.27 | 1.77 | 3.36 | 2.68 | 1.09 | 1.00 | 0.95 |
time (sec) |
N/A | 0.218 | 0.079 | 0.233 | 0.210 | 0.258 | 0.070 | 0.287 | 14.239 |
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 | 30 | 22 | 19 | 26 | 26 | 27 | 26 | 29 |
N.S. |
1 | 1.36 | 1.00 | 0.86 | 1.18 | 1.18 | 1.23 | 1.18 | 1.32 |
time (sec) |
N/A | 0.050 | 0.039 | 0.085 | 0.178 | 0.260 | 0.087 | 0.281 | 14.751 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | B | A | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 0 | 28 | 53 | 59 | 27 | 10848 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.85 | 1.61 | 1.79 | 0.82 | 328.73 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.156 | 0.356 | 0.248 | 0.110 | 0.464 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | A | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 35 | 63 | 44 | 82 | 66 | 107 | 0 |
N.S. |
1 | 0.00 | 1.09 | 1.97 | 1.38 | 2.56 | 2.06 | 3.34 | 0.00 |
time (sec) |
N/A | 0.000 | 0.303 | 1.599 | 0.381 | 0.259 | 0.211 | 2.021 | 0.000 |
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 | 26 | 0 | 25 | 29 | 0 | 25 | 32 | 45 | 18 |
N.S. |
1 | 0.00 | 0.96 | 1.12 | 0.00 | 0.96 | 1.23 | 1.73 | 0.69 |
time (sec) |
N/A | 0.000 | 0.054 | 0.223 | 0.000 | 0.249 | 0.143 | 0.277 | 0.092 |
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 | 34 | 54 | 55 | 50 | 41 | 47 | 46 | 49 | 43 |
N.S. |
1 | 1.59 | 1.62 | 1.47 | 1.21 | 1.38 | 1.35 | 1.44 | 1.26 |
time (sec) |
N/A | 0.061 | 0.018 | 0.317 | 0.188 | 0.252 | 0.092 | 0.328 | 0.119 |
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 | 23 | 0 | 22 | 21 | 20 | 40 | 17 | 0 | 20 |
N.S. |
1 | 0.00 | 0.96 | 0.91 | 0.87 | 1.74 | 0.74 | 0.00 | 0.87 |
time (sec) |
N/A | 0.000 | 1.707 | 0.602 | 0.358 | 0.245 | 0.167 | 0.000 | 14.645 |
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 | 32 | 78 | 27 | 27 | 0 | 26 | 29 | 0 | 31 |
N.S. |
1 | 2.44 | 0.84 | 0.84 | 0.00 | 0.81 | 0.91 | 0.00 | 0.97 |
time (sec) |
N/A | 1.008 | 3.124 | 0.395 | 0.000 | 0.248 | 0.113 | 0.000 | 14.916 |
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 | 16 | 17 | 16 | 27 | 17 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.69 | 1.06 | 1.00 | 1.00 |
time (sec) |
N/A | 0.695 | 0.210 | 0.596 | 0.241 | 0.246 | 0.094 | 0.314 | 14.754 |
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 | 24 | 24 | 24 | 22 | 19 | 22 | 22 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.00 | 0.92 | 0.79 | 0.92 | 0.92 |
time (sec) |
N/A | 0.000 | 0.102 | 2.507 | 0.255 | 0.263 | 0.318 | 0.457 | 13.309 |
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 | 5 | 5 | 6 | 5 | 5 | 2 | 5 | 5 |
N.S. |
1 | 0.21 | 0.21 | 0.25 | 0.21 | 0.21 | 0.08 | 0.21 | 0.21 |
time (sec) |
N/A | 0.001 | 0.000 | 0.026 | 0.182 | 0.246 | 0.018 | 0.291 | 0.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | F(-1) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 32 | 25 | 37 | 43 | 48 | 0 | 42 |
N.S. |
1 | 0.00 | 1.78 | 1.39 | 2.06 | 2.39 | 2.67 | 0.00 | 2.33 |
time (sec) |
N/A | 0.000 | 2.908 | 2.726 | 0.327 | 0.247 | 0.463 | 0.000 | 13.248 |
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 | 26 | 26 | 26 | 25 | 25 | 24 | 25 | 27 |
N.S. |
1 | 0.93 | 0.93 | 0.93 | 0.89 | 0.89 | 0.86 | 0.89 | 0.96 |
time (sec) |
N/A | 0.288 | 0.315 | 0.224 | 0.230 | 0.248 | 0.203 | 0.302 | 13.581 |
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 | 23 | 0 | 20 | 22 | 26 | 22 | 20 | 0 | 20 |
N.S. |
1 | 0.00 | 0.87 | 0.96 | 1.13 | 0.96 | 0.87 | 0.00 | 0.87 |
time (sec) |
N/A | 0.000 | 0.504 | 104.010 | 0.346 | 0.250 | 0.446 | 0.000 | 14.406 |
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 | 24 | 26 | 28 | 28 | 26 | 23 | 25 |
N.S. |
1 | 1.12 | 1.00 | 1.08 | 1.17 | 1.17 | 1.08 | 0.96 | 1.04 |
time (sec) |
N/A | 0.036 | 0.221 | 0.059 | 0.182 | 0.260 | 0.050 | 0.278 | 0.166 |
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 | 20 | 0 | 27 | 16 | 23 | 23 | 12 | 23 | 15 |
N.S. |
1 | 0.00 | 1.35 | 0.80 | 1.15 | 1.15 | 0.60 | 1.15 | 0.75 |
time (sec) |
N/A | 0.000 | 0.897 | 0.076 | 0.224 | 0.237 | 0.057 | 0.278 | 0.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 82 | 52 | 60 | 0 | 59 | 60 | 67 | 140 |
N.S. |
1 | 2.34 | 1.49 | 1.71 | 0.00 | 1.69 | 1.71 | 1.91 | 4.00 |
time (sec) |
N/A | 1.315 | 0.128 | 0.236 | 0.000 | 0.262 | 0.128 | 0.275 | 14.913 |
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 | 18 | 13 | 13 | 12 | 12 | 10 | 12 | 9 |
N.S. |
1 | 1.12 | 0.81 | 0.81 | 0.75 | 0.75 | 0.62 | 0.75 | 0.56 |
time (sec) |
N/A | 0.007 | 0.004 | 0.032 | 0.187 | 0.243 | 0.040 | 0.262 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 53 | 27 | 34 | 30 | 36 | 26 | 36 | 31 |
N.S. |
1 | 3.53 | 1.80 | 2.27 | 2.00 | 2.40 | 1.73 | 2.40 | 2.07 |
time (sec) |
N/A | 0.250 | 0.032 | 0.375 | 0.191 | 0.245 | 0.670 | 0.271 | 0.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 35 | 34 | 83 | 39 | 30 | 31 | 32 | 33 |
N.S. |
1 | 1.13 | 1.10 | 2.68 | 1.26 | 0.97 | 1.00 | 1.03 | 1.06 |
time (sec) |
N/A | 1.538 | 0.106 | 0.602 | 0.322 | 0.236 | 0.340 | 0.327 | 14.805 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 22 | 55 | 18 | 20 | 19 | 21 | 20 |
N.S. |
1 | 0.00 | 1.16 | 2.89 | 0.95 | 1.05 | 1.00 | 1.11 | 1.05 |
time (sec) |
N/A | 0.000 | 0.085 | 2.797 | 0.220 | 0.252 | 0.394 | 0.306 | 13.715 |
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 | 15 | 0 | 15 | 16 | 15 | 15 | 14 | 15 | 13 |
N.S. |
1 | 0.00 | 1.00 | 1.07 | 1.00 | 1.00 | 0.93 | 1.00 | 0.87 |
time (sec) |
N/A | 0.000 | 0.141 | 0.796 | 0.347 | 0.251 | 0.171 | 0.597 | 13.539 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | F(-2) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 30 | 66 | 67 | 58 | 0 | 0 | 27 |
N.S. |
1 | 0.00 | 1.00 | 2.20 | 2.23 | 1.93 | 0.00 | 0.00 | 0.90 |
time (sec) |
N/A | 0.000 | 0.171 | 1.954 | 0.341 | 0.261 | 0.000 | 0.000 | 0.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 22 | 22 | 21 | 20 | 20 | 20 | 20 | 0 |
N.S. |
1 | 0.92 | 0.92 | 0.88 | 0.83 | 0.83 | 0.83 | 0.83 | 0.00 |
time (sec) |
N/A | 0.168 | 0.039 | 1.445 | 0.230 | 0.260 | 0.089 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 57 | 53 | 68 | 68 | 49 | 70 | 0 |
N.S. |
1 | 0.00 | 1.54 | 1.43 | 1.84 | 1.84 | 1.32 | 1.89 | 0.00 |
time (sec) |
N/A | 0.000 | 7.576 | 0.116 | 0.264 | 0.251 | 0.167 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 25 | 39 | 46 | 50 | 49 | 54 | 46 |
N.S. |
1 | 0.00 | 0.96 | 1.50 | 1.77 | 1.92 | 1.88 | 2.08 | 1.77 |
time (sec) |
N/A | 0.000 | 0.126 | 0.332 | 0.284 | 0.261 | 0.145 | 0.319 | 13.590 |
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 | 17 | 16 | 16 | 13 | 12 | 12 | 14 | 0 | 13 |
N.S. |
1 | 0.94 | 0.94 | 0.76 | 0.71 | 0.71 | 0.82 | 0.00 | 0.76 |
time (sec) |
N/A | 0.030 | 0.037 | 0.263 | 0.268 | 0.243 | 17.765 | 0.000 | 13.519 |
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 | 55 | 26 | 25 | 32 | 25 | 24 | 25 | 35 |
N.S. |
1 | 2.04 | 0.96 | 0.93 | 1.19 | 0.93 | 0.89 | 0.93 | 1.30 |
time (sec) |
N/A | 0.181 | 0.204 | 0.081 | 0.375 | 0.252 | 0.081 | 0.276 | 13.282 |
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 | 23 | 33 | 37 | 17 | 20 | 25 |
N.S. |
1 | 0.00 | 0.96 | 0.92 | 1.32 | 1.48 | 0.68 | 0.80 | 1.00 |
time (sec) |
N/A | 0.000 | 0.116 | 0.950 | 0.219 | 0.235 | 0.053 | 0.278 | 12.804 |
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 | 22 | 0 | 23 | 21 | 28 | 20 | 19 | 54 | 20 |
N.S. |
1 | 0.00 | 1.05 | 0.95 | 1.27 | 0.91 | 0.86 | 2.45 | 0.91 |
time (sec) |
N/A | 0.000 | 0.468 | 0.120 | 0.261 | 0.250 | 0.085 | 0.260 | 0.096 |
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 | 36 | 36 | 31 | 38 | 31 | 43 | 33 |
N.S. |
1 | 0.00 | 1.09 | 1.09 | 0.94 | 1.15 | 0.94 | 1.30 | 1.00 |
time (sec) |
N/A | 0.000 | 0.428 | 12.350 | 0.258 | 0.240 | 0.288 | 0.345 | 13.689 |
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 | 34 | 27 | 33 | 25 | 26 | 32 | 17 | 26 | 26 |
N.S. |
1 | 0.79 | 0.97 | 0.74 | 0.76 | 0.94 | 0.50 | 0.76 | 0.76 |
time (sec) |
N/A | 0.437 | 0.102 | 0.178 | 0.239 | 0.237 | 0.085 | 0.279 | 13.750 |
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 | 23 | 0 | 39 | 24 | 73 | 27 | 26 | 44 | 45 |
N.S. |
1 | 0.00 | 1.70 | 1.04 | 3.17 | 1.17 | 1.13 | 1.91 | 1.96 |
time (sec) |
N/A | 0.000 | 0.244 | 4.405 | 0.409 | 0.250 | 0.607 | 0.345 | 14.345 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | F(-2) | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 44 | 45 | 43 | 0 | 109 | 42 |
N.S. |
1 | 0.00 | 0.00 | 1.47 | 1.50 | 1.43 | 0.00 | 3.63 | 1.40 |
time (sec) |
N/A | 0.000 | 0.000 | 11.228 | 0.344 | 0.252 | 0.000 | 0.837 | 14.196 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 1296 | 76 | 73 | 485 | 90 | 165 | 358 | 170 |
N.S. |
1 | 49.85 | 2.92 | 2.81 | 18.65 | 3.46 | 6.35 | 13.77 | 6.54 |
time (sec) |
N/A | 12.426 | 5.139 | 1.223 | 0.341 | 0.243 | 0.460 | 0.320 | 14.202 |
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 | 27 | 28 | 20 | 21 | 29 | 19 | 20 | 20 |
N.S. |
1 | 1.23 | 1.27 | 0.91 | 0.95 | 1.32 | 0.86 | 0.91 | 0.91 |
time (sec) |
N/A | 0.020 | 0.032 | 0.493 | 0.182 | 0.243 | 0.060 | 0.270 | 13.871 |
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 | 29 | 27 | 26 | 29 | 26 | 26 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.90 | 1.00 | 0.90 | 0.90 | 0.90 |
time (sec) |
N/A | 0.010 | 0.012 | 0.130 | 0.185 | 0.232 | 0.035 | 0.263 | 14.274 |
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 | 28 | 67 | 34 | 36 | 36 | 62 | 34 | 34 | 55 |
N.S. |
1 | 2.39 | 1.21 | 1.29 | 1.29 | 2.21 | 1.21 | 1.21 | 1.96 |
time (sec) |
N/A | 0.260 | 0.056 | 0.423 | 0.190 | 0.251 | 0.349 | 0.336 | 13.405 |
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 | 10 | 10 | 10 | 8 | 8 | 7 | 9 | 8 |
N.S. |
1 | 0.62 | 0.62 | 0.62 | 0.50 | 0.50 | 0.44 | 0.56 | 0.50 |
time (sec) |
N/A | 0.002 | 0.001 | 0.062 | 0.190 | 0.229 | 0.020 | 0.280 | 14.044 |
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 | 16 | 16 | 14 | 11 | 11 | 12 | 11 | 15 |
N.S. |
1 | 0.84 | 0.84 | 0.74 | 0.58 | 0.58 | 0.63 | 0.58 | 0.79 |
time (sec) |
N/A | 0.003 | 0.003 | 0.039 | 0.194 | 0.244 | 0.019 | 0.259 | 13.841 |
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 | 23 | 118 | 34 | 47 | 565 | 85 | 68 | 84 | 82 |
N.S. |
1 | 5.13 | 1.48 | 2.04 | 24.57 | 3.70 | 2.96 | 3.65 | 3.57 |
time (sec) |
N/A | 0.931 | 0.398 | 0.191 | 0.446 | 0.266 | 0.099 | 0.311 | 0.255 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | B | A | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 0 | 67 | 528 | 55 | 53 | 256 | 55 |
N.S. |
1 | 0.00 | 0.00 | 2.31 | 18.21 | 1.90 | 1.83 | 8.83 | 1.90 |
time (sec) |
N/A | 0.000 | 0.000 | 4.175 | 0.338 | 0.246 | 0.154 | 0.393 | 14.819 |