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 | 20 | 25 | 25 | 26 | 27 | 25 | 22 | 27 | 22 |
N.S. |
1 | 1.25 | 1.25 | 1.30 | 1.35 | 1.25 | 1.10 | 1.35 | 1.10 |
time (sec) |
N/A | 0.347 | 0.138 | 1.859 | 0.310 | 0.243 | 0.160 | 0.295 | 12.212 |
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 | 37 | 0 | 99 | 48 | 154 | 154 | 94 | 525 | 0 |
N.S. |
1 | 0.00 | 2.68 | 1.30 | 4.16 | 4.16 | 2.54 | 14.19 | 0.00 |
time (sec) |
N/A | 0.000 | 10.242 | 1.042 | 0.472 | 0.254 | 0.288 | 0.680 | 0.000 |
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 | 29 | 23 | 48 | 24 | 70 | 26 | 24 | 26 | 18 |
N.S. |
1 | 0.79 | 1.66 | 0.83 | 2.41 | 0.90 | 0.83 | 0.90 | 0.62 |
time (sec) |
N/A | 0.127 | 0.063 | 0.252 | 0.435 | 0.237 | 0.077 | 0.286 | 0.475 |
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 | 30 | 0 | 30 | 29 | 34 | 28 | 24 | 28 | 26 |
N.S. |
1 | 0.00 | 1.00 | 0.97 | 1.13 | 0.93 | 0.80 | 0.93 | 0.87 |
time (sec) |
N/A | 0.000 | 0.358 | 0.236 | 0.218 | 0.254 | 0.148 | 0.300 | 11.495 |
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 | 13 | 11 | 11 | 9 | 43 | 8 | 8 | 8 | 8 |
N.S. |
1 | 0.85 | 0.85 | 0.69 | 3.31 | 0.62 | 0.62 | 0.62 | 0.62 |
time (sec) |
N/A | 0.023 | 0.007 | 0.194 | 0.205 | 0.231 | 0.053 | 0.287 | 11.642 |
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 | 21 | 17 | 17 | 17 | 17 | 17 | 17 | 17 |
N.S. |
1 | 0.91 | 0.74 | 0.74 | 0.74 | 0.74 | 0.74 | 0.74 | 0.74 |
time (sec) |
N/A | 0.011 | 0.006 | 0.481 | 0.179 | 0.240 | 0.091 | 0.270 | 11.909 |
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 | 26 | 25 | 38 | 34 | 33 | 55 | 31 | 33 | 43 |
N.S. |
1 | 0.96 | 1.46 | 1.31 | 1.27 | 2.12 | 1.19 | 1.27 | 1.65 |
time (sec) |
N/A | 0.347 | 0.254 | 0.678 | 0.319 | 0.244 | 0.207 | 0.288 | 12.127 |
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 | 26 | 25 | 25 | 20 | 25 | 25 |
N.S. |
1 | 0.96 | 0.96 | 0.96 | 0.93 | 0.93 | 0.74 | 0.93 | 0.93 |
time (sec) |
N/A | 0.036 | 0.012 | 0.095 | 0.178 | 0.237 | 0.050 | 0.278 | 11.618 |
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 | 25 | 27 | 16 | 19 | 20 | 12 | 13 | 19 |
N.S. |
1 | 1.04 | 1.12 | 0.67 | 0.79 | 0.83 | 0.50 | 0.54 | 0.79 |
time (sec) |
N/A | 0.069 | 0.235 | 0.048 | 0.182 | 0.239 | 0.051 | 0.273 | 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 | 14 | 11 | 11 | 10 | 11 | 11 | 8 | 11 | 11 |
N.S. |
1 | 0.79 | 0.79 | 0.71 | 0.79 | 0.79 | 0.57 | 0.79 | 0.79 |
time (sec) |
N/A | 0.003 | 0.004 | 0.025 | 0.179 | 0.242 | 0.031 | 0.267 | 11.779 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 11 | 10 | 10 | 5 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.00 | 1.00 | 0.50 | 1.00 | 1.00 |
time (sec) |
N/A | 0.079 | 0.017 | 0.373 | 0.229 | 0.248 | 0.054 | 0.277 | 11.769 |
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 | 27 | 0 | 25 | 27 | 60 | 60 | 65 | 100 | 92 |
N.S. |
1 | 0.00 | 0.93 | 1.00 | 2.22 | 2.22 | 2.41 | 3.70 | 3.41 |
time (sec) |
N/A | 0.000 | 0.637 | 1.772 | 0.258 | 0.254 | 0.156 | 0.362 | 11.519 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 15 | 16 | 13 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 1.25 | 1.33 | 1.08 | 1.17 | 1.17 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.002 | 0.002 | 0.033 | 0.183 | 0.225 | 0.020 | 0.281 | 0.044 |
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 | 14 | 14 | 14 | 13 | 12 | 14 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.86 | 1.00 | 0.86 | 0.86 | 0.86 |
time (sec) |
N/A | 0.020 | 0.013 | 0.204 | 0.248 | 0.252 | 0.100 | 0.274 | 12.289 |
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 | 26 | 0 | 25 | 110 | 165 | 100 | 39 | 466 | 0 |
N.S. |
1 | 0.00 | 0.96 | 4.23 | 6.35 | 3.85 | 1.50 | 17.92 | 0.00 |
time (sec) |
N/A | 0.000 | 0.130 | 7.274 | 0.276 | 0.247 | 0.186 | 1.925 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 49 | 51 | 50 | 47 | 69 | 75 | 100 | 55 |
N.S. |
1 | 1.63 | 1.70 | 1.67 | 1.57 | 2.30 | 2.50 | 3.33 | 1.83 |
time (sec) |
N/A | 0.136 | 0.232 | 0.766 | 0.220 | 0.248 | 0.075 | 0.285 | 12.599 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 63 | 27 | 200 | 24 | 26 | 67 | 0 |
N.S. |
1 | 0.00 | 2.25 | 0.96 | 7.14 | 0.86 | 0.93 | 2.39 | 0.00 |
time (sec) |
N/A | 0.000 | 0.388 | 0.542 | 0.407 | 0.243 | 0.263 | 0.490 | 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 | 13 | 13 | 12 | 11 | 16 | 10 | 11 | 12 |
N.S. |
1 | 0.81 | 0.81 | 0.75 | 0.69 | 1.00 | 0.62 | 0.69 | 0.75 |
time (sec) |
N/A | 0.041 | 0.017 | 0.053 | 0.201 | 0.248 | 0.063 | 0.274 | 0.091 |
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 | 15 | 14 | 13 | 13 | 12 | 13 | 13 |
N.S. |
1 | 0.68 | 0.68 | 0.64 | 0.59 | 0.59 | 0.55 | 0.59 | 0.59 |
time (sec) |
N/A | 0.036 | 0.065 | 0.084 | 0.179 | 0.254 | 0.066 | 0.275 | 11.432 |
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 | 23 | 0 | 23 | 24 | 60 | 48 | 65 | 60 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.04 | 2.61 | 2.09 | 2.83 | 2.61 | 0.00 |
time (sec) |
N/A | 0.000 | 0.486 | 0.278 | 0.316 | 0.252 | 0.096 | 0.299 | 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 | 19 | 15 | 12 | 14 | 13 | 13 | 12 | 13 | 14 |
N.S. |
1 | 0.79 | 0.63 | 0.74 | 0.68 | 0.68 | 0.63 | 0.68 | 0.74 |
time (sec) |
N/A | 0.004 | 0.003 | 0.036 | 0.193 | 0.236 | 0.034 | 0.274 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 0 | 32 | 27 | 27 | 32 | 29 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.23 | 1.04 | 1.04 | 1.23 | 1.12 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.903 | 0.304 | 0.240 | 0.135 | 0.307 | 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 | 29 | 33 | 28 | 33 | 55 | 46 | 36 | 53 | 32 |
N.S. |
1 | 1.14 | 0.97 | 1.14 | 1.90 | 1.59 | 1.24 | 1.83 | 1.10 |
time (sec) |
N/A | 0.658 | 0.789 | 0.238 | 0.221 | 0.241 | 0.095 | 0.294 | 11.806 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F(-1) | B | B | B | B | F(-1) | F(-1) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 110 | 312 | 292 | 154 | 0 | 0 | 308 |
N.S. |
1 | 0.00 | 3.55 | 10.06 | 9.42 | 4.97 | 0.00 | 0.00 | 9.94 |
time (sec) |
N/A | 0.000 | 1.070 | 3.736 | 3.887 | 0.281 | 0.000 | 0.000 | 12.711 |
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 | 20 | 0 | 20 | 30 | 17 | 33 | 37 | 20 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.50 | 0.85 | 1.65 | 1.85 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.563 | 0.587 | 0.279 | 0.274 | 0.169 | 0.286 | 0.000 |
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 | 28 | 0 | 32 | 30 | 34 | 40 | 31 | 2593 | 0 |
N.S. |
1 | 0.00 | 1.14 | 1.07 | 1.21 | 1.43 | 1.11 | 92.61 | 0.00 |
time (sec) |
N/A | 0.000 | 1.176 | 0.326 | 0.235 | 0.249 | 0.134 | 0.387 | 0.000 |
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 | 32 | 0 | 38 | 49 | 33 | 34 | 31 | 34 | 0 |
N.S. |
1 | 0.00 | 1.19 | 1.53 | 1.03 | 1.06 | 0.97 | 1.06 | 0.00 |
time (sec) |
N/A | 0.000 | 0.435 | 59.267 | 0.242 | 0.256 | 0.312 | 0.373 | 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 | 19 | 15 | 15 | 16 | 15 | 17 | 14 | 15 | 15 |
N.S. |
1 | 0.79 | 0.79 | 0.84 | 0.79 | 0.89 | 0.74 | 0.79 | 0.79 |
time (sec) |
N/A | 0.075 | 0.005 | 0.050 | 0.174 | 0.245 | 0.055 | 0.283 | 11.040 |
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 | 6 | 6 | 6 | 5 | 5 | 7 | 5 | 5 |
N.S. |
1 | 0.38 | 0.38 | 0.38 | 0.31 | 0.31 | 0.44 | 0.31 | 0.31 |
time (sec) |
N/A | 0.001 | 0.000 | 0.015 | 0.185 | 0.236 | 0.016 | 0.283 | 0.002 |
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 | 22 | 24 | 33 | 36 | 37 | 51 | 54 |
N.S. |
1 | 0.00 | 1.00 | 1.09 | 1.50 | 1.64 | 1.68 | 2.32 | 2.45 |
time (sec) |
N/A | 0.000 | 3.353 | 0.411 | 0.297 | 0.242 | 16.456 | 0.300 | 10.814 |
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 | 30 | 22 | 21 | 29 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.30 | 0.96 | 0.91 | 1.26 | 0.87 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.031 | 0.065 | 0.066 | 0.214 | 0.237 | 0.067 | 0.276 | 0.067 |
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 | 29 | 43 | 41 | 30 | 24 | 44 | 33 |
N.S. |
1 | 0.00 | 0.91 | 1.34 | 1.28 | 0.94 | 0.75 | 1.38 | 1.03 |
time (sec) |
N/A | 0.000 | 0.062 | 2.548 | 0.326 | 0.269 | 0.172 | 0.412 | 11.675 |
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 | 26 | 0 | 27 | 29 | 29 | 28 | 24 | 28 | 0 |
N.S. |
1 | 0.00 | 1.04 | 1.12 | 1.12 | 1.08 | 0.92 | 1.08 | 0.00 |
time (sec) |
N/A | 0.000 | 0.065 | 114.797 | 0.282 | 0.251 | 0.268 | 0.361 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 467 | 23 | 23 | 76 | 21 | 24 | 21 | 22 |
N.S. |
1 | 20.30 | 1.00 | 1.00 | 3.30 | 0.91 | 1.04 | 0.91 | 0.96 |
time (sec) |
N/A | 1.211 | 1.448 | 0.220 | 0.321 | 0.246 | 0.076 | 0.279 | 0.157 |
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 | 20 | 20 | 22 | 21 | 21 | 19 | 21 | 21 |
N.S. |
1 | 0.91 | 0.91 | 1.00 | 0.95 | 0.95 | 0.86 | 0.95 | 0.95 |
time (sec) |
N/A | 0.025 | 0.009 | 0.370 | 0.191 | 0.251 | 0.068 | 0.258 | 11.686 |
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 | 22 | 26 | 22 | 21 | 21 | 34 | 23 | 21 |
N.S. |
1 | 0.76 | 0.90 | 0.76 | 0.72 | 0.72 | 1.17 | 0.79 | 0.72 |
time (sec) |
N/A | 0.026 | 0.012 | 0.301 | 0.188 | 0.258 | 0.234 | 0.258 | 0.079 |
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 | 25 | 25 | 42 | 38 | 41 | 46 | 26 | 41 | 21 |
N.S. |
1 | 1.00 | 1.68 | 1.52 | 1.64 | 1.84 | 1.04 | 1.64 | 0.84 |
time (sec) |
N/A | 0.012 | 0.005 | 0.065 | 0.189 | 0.243 | 0.029 | 0.265 | 0.094 |
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 | 33 | 39 | 39 | 39 | 39 | 40 | 36 | 39 | 38 |
N.S. |
1 | 1.18 | 1.18 | 1.18 | 1.18 | 1.21 | 1.09 | 1.18 | 1.15 |
time (sec) |
N/A | 0.011 | 0.004 | 0.047 | 0.185 | 0.240 | 0.031 | 0.253 | 11.371 |
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 | 23 | 0 | 16 | 18 | 17 | 17 | 15 | 17 | 17 |
N.S. |
1 | 0.00 | 0.70 | 0.78 | 0.74 | 0.74 | 0.65 | 0.74 | 0.74 |
time (sec) |
N/A | 0.000 | 0.203 | 0.034 | 0.215 | 0.267 | 0.057 | 0.263 | 0.074 |
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 | 23 | 34 | 18 | 22 | 26 | 15 | 17 | 17 |
N.S. |
1 | 0.88 | 1.31 | 0.69 | 0.85 | 1.00 | 0.58 | 0.65 | 0.65 |
time (sec) |
N/A | 0.162 | 0.170 | 1.125 | 0.288 | 0.258 | 0.045 | 0.266 | 11.924 |
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 | 24 | 49 | 27 | 22 | 27 | 28 | 22 | 28 | 21 |
N.S. |
1 | 2.04 | 1.12 | 0.92 | 1.12 | 1.17 | 0.92 | 1.17 | 0.88 |
time (sec) |
N/A | 0.044 | 0.049 | 0.237 | 0.241 | 0.257 | 0.123 | 0.297 | 11.447 |
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 | 15 | 14 | 13 | 13 | 14 | 13 | 15 |
N.S. |
1 | 0.84 | 0.79 | 0.74 | 0.68 | 0.68 | 0.74 | 0.68 | 0.79 |
time (sec) |
N/A | 0.009 | 0.004 | 0.439 | 0.180 | 0.254 | 0.076 | 0.267 | 0.054 |
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 | 27 | 32 | 34 | 31 | 27 | 0 | 37 |
N.S. |
1 | 0.00 | 0.87 | 1.03 | 1.10 | 1.00 | 0.87 | 0.00 | 1.19 |
time (sec) |
N/A | 0.000 | 2.043 | 0.216 | 0.281 | 0.254 | 0.139 | 0.000 | 7.197 |
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 | 27 | 0 | 27 | 28 | 32 | 26 | 19 | 1559 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.04 | 1.19 | 0.96 | 0.70 | 57.74 | 0.00 |
time (sec) |
N/A | 0.000 | 0.062 | 2.876 | 0.311 | 0.261 | 0.299 | 1.073 | 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 | 21 | 20 | 18 | 16 | 17 | 17 | 17 | 18 | 17 |
N.S. |
1 | 0.95 | 0.86 | 0.76 | 0.81 | 0.81 | 0.81 | 0.86 | 0.81 |
time (sec) |
N/A | 0.003 | 0.007 | 0.405 | 0.175 | 0.259 | 0.109 | 0.270 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 10 | 12 | 13 | 10 | 13 | 12 | 10 | 10 |
N.S. |
1 | 0.83 | 1.00 | 1.08 | 0.83 | 1.08 | 1.00 | 0.83 | 0.83 |
time (sec) |
N/A | 0.002 | 0.000 | 0.015 | 0.180 | 0.253 | 0.015 | 0.263 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 102 | 151 | 27 | 51 | 49 | 56 | 51 | 95 |
N.S. |
1 | 3.52 | 5.21 | 0.93 | 1.76 | 1.69 | 1.93 | 1.76 | 3.28 |
time (sec) |
N/A | 0.186 | 0.303 | 0.584 | 0.197 | 0.264 | 5.992 | 0.274 | 12.783 |
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 | 19 | 0 | 19 | 18 | 0 | 19 | 27 | 23 | 19 |
N.S. |
1 | 0.00 | 1.00 | 0.95 | 0.00 | 1.00 | 1.42 | 1.21 | 1.00 |
time (sec) |
N/A | 0.000 | 0.838 | 0.060 | 0.000 | 0.249 | 0.081 | 0.275 | 0.205 |
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 | 19 | 15 | 14 | 14 | 15 | 14 | 17 |
N.S. |
1 | 1.18 | 1.12 | 0.88 | 0.82 | 0.82 | 0.88 | 0.82 | 1.00 |
time (sec) |
N/A | 0.003 | 0.003 | 0.041 | 0.172 | 0.242 | 0.019 | 0.267 | 12.157 |
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 | 20 | 33 | 33 | 21 | 15 | 40 | 21 |
N.S. |
1 | 0.83 | 0.67 | 1.10 | 1.10 | 0.70 | 0.50 | 1.33 | 0.70 |
time (sec) |
N/A | 0.149 | 0.239 | 0.665 | 0.311 | 0.252 | 0.084 | 0.299 | 12.717 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 37 | 64 | 74 | 86 | 53 | 205 | 35 |
N.S. |
1 | 0.00 | 1.28 | 2.21 | 2.55 | 2.97 | 1.83 | 7.07 | 1.21 |
time (sec) |
N/A | 0.000 | 0.173 | 0.689 | 0.313 | 0.275 | 0.883 | 0.379 | 12.514 |
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 | 19 | 28 | 41 | 124 | 33 | 31 | 96 | 38 |
N.S. |
1 | 1.00 | 1.47 | 2.16 | 6.53 | 1.74 | 1.63 | 5.05 | 2.00 |
time (sec) |
N/A | 0.344 | 1.308 | 1.019 | 0.328 | 0.254 | 0.116 | 0.330 | 12.388 |
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 | 5 | 4 | 4 | 3 | 4 | 4 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.80 | 0.80 | 0.60 | 0.80 | 0.80 |
time (sec) |
N/A | 0.001 | 0.001 | 0.026 | 0.185 | 0.244 | 0.038 | 0.266 | 0.031 |
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 | 17 | 16 | 31 | 14 | 0 | 16 |
N.S. |
1 | 0.00 | 0.96 | 0.74 | 0.70 | 1.35 | 0.61 | 0.00 | 0.70 |
time (sec) |
N/A | 0.000 | 0.112 | 0.073 | 0.245 | 0.240 | 0.111 | 0.000 | 11.684 |
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 | 27 | 22 | 20 | 26 | 87 | 22 | 20 | 60 | 22 |
N.S. |
1 | 0.81 | 0.74 | 0.96 | 3.22 | 0.81 | 0.74 | 2.22 | 0.81 |
time (sec) |
N/A | 0.469 | 0.026 | 0.100 | 0.301 | 0.242 | 0.117 | 0.283 | 13.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 39 | 35 | 64 | 55 | 53 | 68 | 38 |
N.S. |
1 | 0.00 | 1.26 | 1.13 | 2.06 | 1.77 | 1.71 | 2.19 | 1.23 |
time (sec) |
N/A | 0.000 | 0.469 | 0.705 | 0.330 | 0.246 | 0.216 | 0.284 | 12.224 |
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 | 29 | 0 | 34 | 35 | 38 | 35 | 34 | 66 | 22 |
N.S. |
1 | 0.00 | 1.17 | 1.21 | 1.31 | 1.21 | 1.17 | 2.28 | 0.76 |
time (sec) |
N/A | 0.000 | 2.400 | 0.260 | 0.336 | 0.244 | 0.096 | 0.287 | 11.888 |
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 | 33 | 45 | 47 | 48 | 60 | 53 | 46 | 59 | 40 |
N.S. |
1 | 1.36 | 1.42 | 1.45 | 1.82 | 1.61 | 1.39 | 1.79 | 1.21 |
time (sec) |
N/A | 0.111 | 0.076 | 0.165 | 0.218 | 0.245 | 0.094 | 0.278 | 12.061 |
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 | 23 | 25 | 25 | 22 | 20 | 30 | 23 |
N.S. |
1 | 0.00 | 0.92 | 1.00 | 1.00 | 0.88 | 0.80 | 1.20 | 0.92 |
time (sec) |
N/A | 0.000 | 0.718 | 0.336 | 0.280 | 0.242 | 0.141 | 0.295 | 0.302 |
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 | 33 | 65 | 33 | 33 | 51 | 42 | 27 | 63 | 38 |
N.S. |
1 | 1.97 | 1.00 | 1.00 | 1.55 | 1.27 | 0.82 | 1.91 | 1.15 |
time (sec) |
N/A | 0.267 | 0.136 | 0.242 | 0.222 | 0.237 | 0.082 | 0.279 | 11.387 |
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 | 17 | 16 | 24 | 15 | 16 | 19 |
N.S. |
1 | 0.00 | 1.00 | 0.94 | 0.89 | 1.33 | 0.83 | 0.89 | 1.06 |
time (sec) |
N/A | 0.000 | 0.311 | 1.712 | 0.222 | 0.240 | 0.064 | 0.263 | 12.352 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 44 | 59 | 49 | 50 | 53 | 58 | 51 |
N.S. |
1 | 0.00 | 1.83 | 2.46 | 2.04 | 2.08 | 2.21 | 2.42 | 2.12 |
time (sec) |
N/A | 0.000 | 0.076 | 0.670 | 0.185 | 0.247 | 3.287 | 0.288 | 12.634 |
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 | 16 | 14 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.00 | 0.88 | 1.00 | 1.00 |
time (sec) |
N/A | 0.126 | 0.023 | 0.078 | 0.179 | 0.257 | 0.048 | 0.289 | 12.193 |
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 | 32 | 30 | 33 | 598 | 188 | 31 | 22 | 178 | 26 |
N.S. |
1 | 0.94 | 1.03 | 18.69 | 5.88 | 0.97 | 0.69 | 5.56 | 0.81 |
time (sec) |
N/A | 0.162 | 0.135 | 11.228 | 0.272 | 0.243 | 0.118 | 0.410 | 12.198 |
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 | 7 | 7 | 7 | 6 | 6 | 5 | 6 | 6 |
N.S. |
1 | 0.64 | 0.64 | 0.64 | 0.55 | 0.55 | 0.45 | 0.55 | 0.55 |
time (sec) |
N/A | 0.001 | 0.000 | 0.034 | 0.177 | 0.239 | 0.023 | 0.257 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | A | F(-2) | F(-1) | F(-2) | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 122 | 24 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.00 | 4.52 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 60.194 | 0.339 | 0.000 | 0.000 | 0.000 | 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 | 31 | 0 | 33 | 32 | 32 | 47 | 32 | 59 | 36 |
N.S. |
1 | 0.00 | 1.06 | 1.03 | 1.03 | 1.52 | 1.03 | 1.90 | 1.16 |
time (sec) |
N/A | 0.000 | 0.293 | 26.258 | 0.312 | 0.258 | 0.305 | 0.425 | 0.806 |
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 | 29 | 28 | 30 | 27 | 24 | 33 | 27 |
N.S. |
1 | 0.00 | 1.12 | 1.08 | 1.15 | 1.04 | 0.92 | 1.27 | 1.04 |
time (sec) |
N/A | 0.000 | 0.797 | 3.465 | 0.414 | 0.256 | 0.173 | 0.307 | 11.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 30 | 25 | 29 | 24 | 19 | 0 | 0 |
N.S. |
1 | 0.00 | 1.15 | 0.96 | 1.12 | 0.92 | 0.73 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 5.147 | 4.457 | 0.363 | 0.246 | 0.269 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F(-1) | B | B | F | B | B | F(-2) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 77 | 81 | 0 | 79 | 80 | 0 | 232 |
N.S. |
1 | 0.00 | 2.14 | 2.25 | 0.00 | 2.19 | 2.22 | 0.00 | 6.44 |
time (sec) |
N/A | 0.000 | 0.680 | 0.068 | 0.000 | 0.269 | 1.187 | 0.000 | 12.186 |
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 | 27 | 28 | 36 | 35 | 34 | 37 | 25 |
N.S. |
1 | 2.11 | 1.00 | 1.04 | 1.33 | 1.30 | 1.26 | 1.37 | 0.93 |
time (sec) |
N/A | 1.182 | 1.698 | 0.332 | 0.220 | 0.243 | 0.075 | 0.269 | 12.489 |
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 | 15 | 14 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 0.88 | 0.82 | 0.82 | 0.82 | 0.82 | 0.82 | 0.82 |
time (sec) |
N/A | 0.003 | 0.004 | 0.040 | 0.196 | 0.266 | 0.035 | 0.266 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 137 | 33 | 27 | 0 | 26 | 24 | 26 | 36 |
N.S. |
1 | 4.42 | 1.06 | 0.87 | 0.00 | 0.84 | 0.77 | 0.84 | 1.16 |
time (sec) |
N/A | 13.663 | 0.145 | 12.892 | 0.000 | 0.263 | 0.357 | 0.421 | 13.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | C | A | A | F(-1) | B | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 216 | 476 | 47 | 46 | 0 | 108 | 0 |
N.S. |
1 | 0.00 | 7.20 | 15.87 | 1.57 | 1.53 | 0.00 | 3.60 | 0.00 |
time (sec) |
N/A | 0.000 | 0.219 | 3.429 | 0.329 | 0.266 | 0.000 | 0.401 | 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 | 19 | 57 | 56 | 51 | 47 | 48 | 46 | 47 | 42 |
N.S. |
1 | 3.00 | 2.95 | 2.68 | 2.47 | 2.53 | 2.42 | 2.47 | 2.21 |
time (sec) |
N/A | 0.016 | 0.010 | 0.065 | 0.186 | 0.245 | 0.026 | 0.257 | 15.258 |
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 | 26 | 22 | 20 | 22 | 30 | 20 | 44 | 22 |
N.S. |
1 | 0.90 | 0.76 | 0.69 | 0.76 | 1.03 | 0.69 | 1.52 | 0.76 |
time (sec) |
N/A | 0.445 | 0.129 | 0.129 | 0.253 | 0.257 | 0.098 | 0.278 | 15.164 |
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 | 23 | 23 | 19 | 18 | 18 | 17 | 18 | 18 |
N.S. |
1 | 1.05 | 1.05 | 0.86 | 0.82 | 0.82 | 0.77 | 0.82 | 0.82 |
time (sec) |
N/A | 0.045 | 0.072 | 0.060 | 0.194 | 0.243 | 0.043 | 0.267 | 0.056 |
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 | 35 | 664 | 181 | 253 | 855 | 205 | 291 | 349 | 229 |
N.S. |
1 | 18.97 | 5.17 | 7.23 | 24.43 | 5.86 | 8.31 | 9.97 | 6.54 |
time (sec) |
N/A | 13.083 | 0.326 | 0.156 | 0.318 | 0.252 | 0.230 | 0.270 | 16.316 |
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 | 35 | 24 | 57 | 18 | 17 | 17 | 15 | 17 | 17 |
N.S. |
1 | 0.69 | 1.63 | 0.51 | 0.49 | 0.49 | 0.43 | 0.49 | 0.49 |
time (sec) |
N/A | 0.040 | 0.065 | 0.078 | 0.180 | 0.242 | 0.068 | 0.260 | 0.095 |
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 | 42 | 27 | 36 | 26 | 24 | 26 | 28 |
N.S. |
1 | 0.00 | 1.31 | 0.84 | 1.12 | 0.81 | 0.75 | 0.81 | 0.88 |
time (sec) |
N/A | 0.000 | 0.122 | 0.186 | 0.269 | 0.241 | 0.103 | 0.344 | 15.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 0 | 62 | 64 | 72 | 65 | 99 | 0 |
N.S. |
1 | 0.00 | 0.00 | 2.48 | 2.56 | 2.88 | 2.60 | 3.96 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.224 | 0.322 | 0.243 | 0.126 | 0.287 | 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 | 24 | 29 | 25 | 33 | 29 | 32 | 31 | 32 | 29 |
N.S. |
1 | 1.21 | 1.04 | 1.38 | 1.21 | 1.33 | 1.29 | 1.33 | 1.21 |
time (sec) |
N/A | 0.439 | 0.326 | 0.664 | 0.305 | 0.251 | 0.154 | 0.283 | 15.550 |
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 | 25 | 36 | 24 | 22 | 73 | 38 | 17 | 39 | 21 |
N.S. |
1 | 1.44 | 0.96 | 0.88 | 2.92 | 1.52 | 0.68 | 1.56 | 0.84 |
time (sec) |
N/A | 0.166 | 1.240 | 0.571 | 0.227 | 0.254 | 0.098 | 0.276 | 15.415 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | F(-1) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 24 | 23 | 34 | 53 | 26 | 0 | 25 |
N.S. |
1 | 0.00 | 0.89 | 0.85 | 1.26 | 1.96 | 0.96 | 0.00 | 0.93 |
time (sec) |
N/A | 0.000 | 3.821 | 0.114 | 0.224 | 0.251 | 0.090 | 0.000 | 0.441 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 63 | 63 | 97 | 108 | 122 | 117 | 0 |
N.S. |
1 | 0.00 | 2.33 | 2.33 | 3.59 | 4.00 | 4.52 | 4.33 | 0.00 |
time (sec) |
N/A | 0.000 | 0.098 | 1.002 | 4.609 | 0.255 | 0.141 | 0.529 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 23 | 58 | 0 | 37 | 37 | 39 | 0 |
N.S. |
1 | 1.00 | 0.88 | 2.23 | 0.00 | 1.42 | 1.42 | 1.50 | 0.00 |
time (sec) |
N/A | 0.343 | 0.402 | 2.848 | 0.000 | 0.247 | 0.326 | 0.998 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 7 | 7 | 6 | 5 | 5 | 8 | 5 | 5 |
N.S. |
1 | 0.54 | 0.54 | 0.46 | 0.38 | 0.38 | 0.62 | 0.38 | 0.38 |
time (sec) |
N/A | 0.001 | 0.000 | 0.023 | 0.175 | 0.243 | 0.018 | 0.278 | 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 | 15 | 15 | 15 | 19 | 16 | 16 | 22 | 17 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.27 | 1.07 | 1.07 | 1.47 | 1.13 | 0.80 |
time (sec) |
N/A | 0.013 | 0.006 | 0.401 | 0.182 | 0.236 | 0.036 | 0.294 | 0.427 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 44 | 16 | 21 | 0 | 19 | 19 | 0 | 0 |
N.S. |
1 | 1.91 | 0.70 | 0.91 | 0.00 | 0.83 | 0.83 | 0.00 | 0.00 |
time (sec) |
N/A | 0.062 | 0.032 | 0.537 | 0.000 | 0.247 | 2.532 | 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 | 14 | 26 | 26 | 26 | 25 | 25 | 24 | 25 | 29 |
N.S. |
1 | 1.86 | 1.86 | 1.86 | 1.79 | 1.79 | 1.71 | 1.79 | 2.07 |
time (sec) |
N/A | 0.077 | 0.118 | 0.092 | 0.186 | 0.245 | 0.056 | 0.272 | 0.117 |
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 | 22 | 0 | 25 | 47 | 34 | 22 | 24 | 32 | 22 |
N.S. |
1 | 0.00 | 1.14 | 2.14 | 1.55 | 1.00 | 1.09 | 1.45 | 1.00 |
time (sec) |
N/A | 0.000 | 0.058 | 9.565 | 0.237 | 0.253 | 0.151 | 0.269 | 14.413 |
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 | 35 | 42 | 36 | 36 | 116 | 53 | 163 |
N.S. |
1 | 0.00 | 1.40 | 1.68 | 1.44 | 1.44 | 4.64 | 2.12 | 6.52 |
time (sec) |
N/A | 0.000 | 8.587 | 0.249 | 0.236 | 0.260 | 0.196 | 0.291 | 15.304 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 21 | 21 | 22 | 61 | 54 | 61 | 25 | 21 |
N.S. |
1 | 0.95 | 0.95 | 1.00 | 2.77 | 2.45 | 2.77 | 1.14 | 0.95 |
time (sec) |
N/A | 0.411 | 0.029 | 0.303 | 0.215 | 0.238 | 6.118 | 0.379 | 0.311 |
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 | 23 | 22 | 19 | 18 | 18 | 19 | 18 | 21 |
N.S. |
1 | 0.79 | 0.76 | 0.66 | 0.62 | 0.62 | 0.66 | 0.62 | 0.72 |
time (sec) |
N/A | 0.116 | 0.439 | 0.127 | 0.311 | 0.244 | 0.105 | 0.277 | 0.110 |
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 | 18 | 0 | 18 | 17 | 19 | 16 | 14 | 164 | 16 |
N.S. |
1 | 0.00 | 1.00 | 0.94 | 1.06 | 0.89 | 0.78 | 9.11 | 0.89 |
time (sec) |
N/A | 0.000 | 0.623 | 0.956 | 0.340 | 0.249 | 0.082 | 0.301 | 15.343 |
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 | 34 | 34 | 42 | 25 | 37 | 33 | 33 |
N.S. |
1 | 0.00 | 1.17 | 1.17 | 1.45 | 0.86 | 1.28 | 1.14 | 1.14 |
time (sec) |
N/A | 0.000 | 0.254 | 0.091 | 0.309 | 0.247 | 0.105 | 0.272 | 0.486 |
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 | 39 | 37 | 37 | 37 | 50 | 32 | 38 | 325 |
N.S. |
1 | 1.15 | 1.09 | 1.09 | 1.09 | 1.47 | 0.94 | 1.12 | 9.56 |
time (sec) |
N/A | 0.102 | 0.037 | 0.093 | 0.186 | 0.251 | 0.293 | 0.292 | 14.322 |
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 | 15 | 15 | 14 | 14 | 10 | 14 | 15 |
N.S. |
1 | 0.94 | 0.94 | 0.94 | 0.88 | 0.88 | 0.62 | 0.88 | 0.94 |
time (sec) |
N/A | 0.012 | 0.095 | 0.101 | 0.184 | 0.250 | 0.049 | 0.269 | 14.710 |
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 | 20 | 20 | 20 | 18 | 19 | 15 | 21 | 19 |
N.S. |
1 | 1.43 | 1.43 | 1.43 | 1.29 | 1.36 | 1.07 | 1.50 | 1.36 |
time (sec) |
N/A | 0.044 | 0.012 | 0.069 | 0.189 | 0.232 | 0.187 | 0.295 | 0.234 |
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 | 30 | 16 | 16 | 16 | 15 | 17 | 14 | 91 | 16 |
N.S. |
1 | 0.53 | 0.53 | 0.53 | 0.50 | 0.57 | 0.47 | 3.03 | 0.53 |
time (sec) |
N/A | 0.016 | 0.012 | 0.106 | 0.182 | 0.246 | 0.051 | 0.274 | 14.892 |