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 | B | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 47 | 0 | 43 | 42 | 74 | 46 |
N.S. |
1 | 1.00 | 1.00 | 2.47 | 0.00 | 2.26 | 2.21 | 3.89 | 2.42 |
time (sec) |
N/A | 0.162 | 0.044 | 0.398 | 0.000 | 0.236 | 0.202 | 0.281 | 0.302 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 17 | 15 | 12 | 12 | 12 | 10 | 12 | 11 |
N.S. |
1 | 0.68 | 0.60 | 0.48 | 0.48 | 0.48 | 0.40 | 0.48 | 0.44 |
time (sec) |
N/A | 0.005 | 0.007 | 0.092 | 0.186 | 0.232 | 0.037 | 0.271 | 11.743 |
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 | 26 | 31 | 25 | 27 | 25 | 25 |
N.S. |
1 | 0.84 | 0.84 | 0.81 | 0.97 | 0.78 | 0.84 | 0.78 | 0.78 |
time (sec) |
N/A | 0.054 | 0.029 | 0.163 | 0.304 | 0.245 | 0.082 | 0.313 | 12.327 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | B | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 126 | 52 | 18 | 0 | 0 | 18 |
N.S. |
1 | 0.00 | 1.00 | 5.48 | 2.26 | 0.78 | 0.00 | 0.00 | 0.78 |
time (sec) |
N/A | 0.000 | 0.176 | 0.262 | 0.415 | 0.262 | 0.000 | 0.000 | 12.893 |
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 | 21 | 0 | 26 | 47 | 27 | 32 | 53 | 63 | 27 |
N.S. |
1 | 0.00 | 1.24 | 2.24 | 1.29 | 1.52 | 2.52 | 3.00 | 1.29 |
time (sec) |
N/A | 0.000 | 2.652 | 0.540 | 0.243 | 0.259 | 0.214 | 0.283 | 12.575 |
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 | 17 | 0 | 17 | 16 | 15 | 15 | 17 | 20 | 18 |
N.S. |
1 | 0.00 | 1.00 | 0.94 | 0.88 | 0.88 | 1.00 | 1.18 | 1.06 |
time (sec) |
N/A | 0.000 | 0.336 | 0.100 | 0.261 | 0.243 | 0.124 | 0.271 | 0.226 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | B | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 46 | 25 | 41 | 45 | 37 | 31 | 29 |
N.S. |
1 | 0.00 | 2.42 | 1.32 | 2.16 | 2.37 | 1.95 | 1.63 | 1.53 |
time (sec) |
N/A | 0.000 | 0.305 | 0.322 | 0.191 | 0.263 | 0.126 | 0.269 | 12.459 |
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 | 7 | 7 | 7 | 9 | 8 | 8 | 7 | 9 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.29 | 1.14 | 1.14 | 1.00 | 1.29 | 1.14 |
time (sec) |
N/A | 0.001 | 0.001 | 0.351 | 0.197 | 0.244 | 0.030 | 0.267 | 0.036 |
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 | 8 | 8 | 9 | 8 | 8 | 7 | 9 | 8 |
N.S. |
1 | 0.42 | 0.42 | 0.47 | 0.42 | 0.42 | 0.37 | 0.47 | 0.42 |
time (sec) |
N/A | 0.002 | 0.001 | 0.042 | 0.184 | 0.247 | 0.030 | 0.262 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 46 | 71 | 31 | 27 | 45 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.77 | 2.73 | 1.19 | 1.04 | 1.73 | 0.00 |
time (sec) |
N/A | 0.000 | 0.400 | 5.492 | 0.362 | 0.242 | 0.179 | 0.864 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 19 | 19 | 15 | 14 | 41 | 15 | 0 | 14 |
N.S. |
1 | 0.86 | 0.86 | 0.68 | 0.64 | 1.86 | 0.68 | 0.00 | 0.64 |
time (sec) |
N/A | 0.026 | 0.045 | 0.117 | 0.196 | 0.257 | 0.259 | 0.000 | 0.163 |
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 | 24 | 24 | 21 | 162 | 20 | 20 | 68 | 20 |
N.S. |
1 | 0.73 | 0.73 | 0.64 | 4.91 | 0.61 | 0.61 | 2.06 | 0.61 |
time (sec) |
N/A | 0.202 | 0.060 | 0.545 | 0.310 | 0.242 | 0.128 | 0.286 | 11.862 |
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 | 12 | 12 | 19 | 10 | 18 | 8 | 10 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.58 | 0.83 | 1.50 | 0.67 | 0.83 | 1.00 |
time (sec) |
N/A | 0.131 | 0.068 | 1.777 | 0.238 | 0.247 | 0.092 | 0.270 | 11.955 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 139 | 28 | 122 | 576 | 127 | 153 | 126 | 0 |
N.S. |
1 | 6.04 | 1.22 | 5.30 | 25.04 | 5.52 | 6.65 | 5.48 | 0.00 |
time (sec) |
N/A | 17.041 | 0.795 | 2.600 | 0.371 | 0.275 | 0.715 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 33 | 19 | 18 | 231 | 17 | 15 | 17 | 19 |
N.S. |
1 | 1.74 | 1.00 | 0.95 | 12.16 | 0.89 | 0.79 | 0.89 | 1.00 |
time (sec) |
N/A | 0.030 | 0.802 | 0.167 | 0.269 | 0.255 | 0.066 | 0.291 | 11.834 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 14 | 14 | 15 | 25 | 14 | 12 | 14 | 11 |
N.S. |
1 | 0.61 | 0.61 | 0.65 | 1.09 | 0.61 | 0.52 | 0.61 | 0.48 |
time (sec) |
N/A | 0.005 | 0.003 | 0.056 | 0.195 | 0.246 | 0.046 | 0.272 | 11.403 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | A | F(-1) | F(-1) | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 52 | 27 | 36 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.00 | 2.17 | 1.12 | 1.50 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.160 | 0.614 | 0.636 | 0.243 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 49 | 47 | 35 | 34 | 34 | 37 | 36 | 36 |
N.S. |
1 | 1.63 | 1.57 | 1.17 | 1.13 | 1.13 | 1.23 | 1.20 | 1.20 |
time (sec) |
N/A | 0.057 | 0.066 | 0.085 | 0.182 | 0.246 | 0.125 | 0.282 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 38 | 53 | 23 | 45 | 29 | 32 | 29 | 29 |
N.S. |
1 | 1.81 | 2.52 | 1.10 | 2.14 | 1.38 | 1.52 | 1.38 | 1.38 |
time (sec) |
N/A | 2.371 | 9.287 | 0.129 | 0.290 | 0.263 | 0.096 | 0.312 | 12.018 |
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 | 19 | 0 | 20 | 20 | 25 | 22 | 22 | 19 | 26 |
N.S. |
1 | 0.00 | 1.05 | 1.05 | 1.32 | 1.16 | 1.16 | 1.00 | 1.37 |
time (sec) |
N/A | 0.000 | 0.455 | 0.211 | 0.356 | 0.248 | 0.145 | 0.305 | 12.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 37 | 17 | 33 | 31 | 31 | 31 | 31 | 13 |
N.S. |
1 | 2.31 | 1.06 | 2.06 | 1.94 | 1.94 | 1.94 | 1.94 | 0.81 |
time (sec) |
N/A | 0.036 | 0.166 | 0.145 | 0.190 | 0.255 | 0.066 | 0.286 | 0.148 |
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 | 31 | 0 | 22 | 27 | 54 | 52 | 53 | 53 | 0 |
N.S. |
1 | 0.00 | 0.71 | 0.87 | 1.74 | 1.68 | 1.71 | 1.71 | 0.00 |
time (sec) |
N/A | 0.000 | 0.381 | 0.387 | 0.339 | 0.269 | 0.163 | 0.342 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 35 | 36 | 34 | 34 | 30 | 34 | 36 | 34 |
N.S. |
1 | 1.35 | 1.38 | 1.31 | 1.31 | 1.15 | 1.31 | 1.38 | 1.31 |
time (sec) |
N/A | 0.009 | 0.012 | 0.083 | 0.197 | 0.251 | 0.061 | 0.286 | 0.062 |
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 | 22 | 20 | 19 | 22 | 19 | 22 | 28 |
N.S. |
1 | 0.00 | 0.96 | 0.87 | 0.83 | 0.96 | 0.83 | 0.96 | 1.22 |
time (sec) |
N/A | 0.000 | 0.126 | 0.366 | 0.247 | 0.263 | 0.211 | 0.336 | 13.268 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 20 | 22 | 34 | 0 | 36 | 19 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.10 | 1.70 | 0.00 | 1.80 | 0.95 |
time (sec) |
N/A | 0.000 | 0.351 | 11.850 | 0.259 | 0.266 | 0.000 | 0.318 | 13.089 |
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 | 21 | 20 | 20 | 22 | 25 | 20 |
N.S. |
1 | 1.25 | 1.25 | 1.05 | 1.00 | 1.00 | 1.10 | 1.25 | 1.00 |
time (sec) |
N/A | 0.060 | 0.050 | 0.096 | 0.220 | 0.250 | 0.141 | 0.293 | 12.705 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 134 | 24 | 22 | 20 | 26 | 26 | 37 | 21 |
N.S. |
1 | 4.19 | 0.75 | 0.69 | 0.62 | 0.81 | 0.81 | 1.16 | 0.66 |
time (sec) |
N/A | 0.184 | 0.049 | 1.183 | 0.316 | 0.258 | 0.052 | 0.291 | 11.961 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | F(-2) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 31 | 30 | 91 | 32 | 32 | 0 | 32 |
N.S. |
1 | 0.00 | 1.00 | 0.97 | 2.94 | 1.03 | 1.03 | 0.00 | 1.03 |
time (sec) |
N/A | 0.000 | 0.166 | 133.609 | 0.503 | 0.250 | 1.468 | 0.000 | 12.362 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 27 | 26 | 39 | 32 | 22 | 41 | 28 |
N.S. |
1 | 0.00 | 0.87 | 0.84 | 1.26 | 1.03 | 0.71 | 1.32 | 0.90 |
time (sec) |
N/A | 0.000 | 0.428 | 3.086 | 0.240 | 0.252 | 0.144 | 0.271 | 12.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 28 | 27 | 25 | 24 | 26 | 24 | 24 |
N.S. |
1 | 0.00 | 1.33 | 1.29 | 1.19 | 1.14 | 1.24 | 1.14 | 1.14 |
time (sec) |
N/A | 0.000 | 0.067 | 1.722 | 0.415 | 0.243 | 0.956 | 0.459 | 13.686 |
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 | 22 | 35 | 20 | 34 | 32 | 19 | 121 |
N.S. |
1 | 0.00 | 1.00 | 1.59 | 0.91 | 1.55 | 1.45 | 0.86 | 5.50 |
time (sec) |
N/A | 0.000 | 0.419 | 55.741 | 0.428 | 0.251 | 0.870 | 1.641 | 12.027 |
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 | 24 | 24 | 21 | 20 | 20 | 22 | 20 | 22 |
N.S. |
1 | 0.86 | 0.86 | 0.75 | 0.71 | 0.71 | 0.79 | 0.71 | 0.79 |
time (sec) |
N/A | 0.152 | 1.732 | 0.231 | 0.240 | 0.245 | 0.114 | 0.302 | 11.729 |
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 | 17 | 13 | 13 | 16 | 16 | 15 | 16 | 18 |
N.S. |
1 | 1.13 | 0.87 | 0.87 | 1.07 | 1.07 | 1.00 | 1.07 | 1.20 |
time (sec) |
N/A | 0.027 | 0.062 | 0.081 | 0.194 | 0.255 | 0.058 | 0.286 | 11.437 |
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 | 34 | 27 | 24 | 22 | 22 | 26 | 22 | 19 |
N.S. |
1 | 1.31 | 1.04 | 0.92 | 0.85 | 0.85 | 1.00 | 0.85 | 0.73 |
time (sec) |
N/A | 0.044 | 0.013 | 0.068 | 0.192 | 0.252 | 0.152 | 0.274 | 0.090 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | F(-1) | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 53 | 49 | 48 | 48 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 2.12 | 1.96 | 1.92 | 1.92 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.121 | 0.255 | 0.227 | 0.248 | 0.000 | 0.000 | 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 | 23 | 0 | 19 | 27 | 17 | 26 | 22 | 0 | 51 |
N.S. |
1 | 0.00 | 0.83 | 1.17 | 0.74 | 1.13 | 0.96 | 0.00 | 2.22 |
time (sec) |
N/A | 0.000 | 0.622 | 0.884 | 1.411 | 0.235 | 0.163 | 0.000 | 11.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 35 | 37 | 26 | 30 | 30 | 24 | 36 | 35 |
N.S. |
1 | 1.30 | 1.37 | 0.96 | 1.11 | 1.11 | 0.89 | 1.33 | 1.30 |
time (sec) |
N/A | 0.240 | 0.213 | 0.490 | 0.224 | 0.241 | 0.253 | 0.282 | 11.276 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | B | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 230 | 17 | 32 | 109 | 31 | 34 | 31 | 15 |
N.S. |
1 | 13.53 | 1.00 | 1.88 | 6.41 | 1.82 | 2.00 | 1.82 | 0.88 |
time (sec) |
N/A | 0.341 | 0.029 | 0.181 | 0.244 | 0.242 | 0.063 | 0.280 | 10.802 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 24 | 20 | 35 | 28 | 31 | 0 | 0 | 32 |
N.S. |
1 | 1.04 | 0.87 | 1.52 | 1.22 | 1.35 | 0.00 | 0.00 | 1.39 |
time (sec) |
N/A | 0.751 | 0.134 | 14.129 | 0.317 | 0.259 | 0.000 | 0.000 | 11.325 |
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 | 52 | 52 | 36 | 52 | 37 | 36 | 37 | 47 |
N.S. |
1 | 1.53 | 1.53 | 1.06 | 1.53 | 1.09 | 1.06 | 1.09 | 1.38 |
time (sec) |
N/A | 3.378 | 0.131 | 0.856 | 0.250 | 0.257 | 0.194 | 0.334 | 10.884 |
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 | 25 | 26 | 30 | 23 | 19 | 23 | 25 |
N.S. |
1 | 0.00 | 0.96 | 1.00 | 1.15 | 0.88 | 0.73 | 0.88 | 0.96 |
time (sec) |
N/A | 0.000 | 0.059 | 0.205 | 0.309 | 0.250 | 0.121 | 0.283 | 10.660 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | F | F | B | F(-1) | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 61 | 59 | 0 | 0 | 159 | 0 | 0 | 91 |
N.S. |
1 | 2.10 | 2.03 | 0.00 | 0.00 | 5.48 | 0.00 | 0.00 | 3.14 |
time (sec) |
N/A | 1.694 | 0.169 | 0.000 | 0.000 | 0.256 | 0.000 | 0.000 | 11.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 22 | 31 | 17 | 16 | 16 | 15 | 18 | 20 |
N.S. |
1 | 0.88 | 1.24 | 0.68 | 0.64 | 0.64 | 0.60 | 0.72 | 0.80 |
time (sec) |
N/A | 0.031 | 0.015 | 1.233 | 0.189 | 0.260 | 0.186 | 0.296 | 0.106 |
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 | 21 | 19 | 20 | 19 | 22 | 14 | 19 | 18 |
N.S. |
1 | 1.05 | 0.95 | 1.00 | 0.95 | 1.10 | 0.70 | 0.95 | 0.90 |
time (sec) |
N/A | 0.012 | 0.013 | 0.580 | 0.194 | 0.240 | 0.067 | 0.279 | 10.547 |
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 | 22 | 20 | 25 | 27 | 22 | 37 | 800 |
N.S. |
1 | 0.00 | 0.88 | 0.80 | 1.00 | 1.08 | 0.88 | 1.48 | 32.00 |
time (sec) |
N/A | 0.000 | 0.972 | 1.593 | 0.312 | 0.251 | 0.071 | 0.302 | 11.155 |
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 | 14 | 0 | 12 | 12 | 11 | 11 | 8 | 11 | 12 |
N.S. |
1 | 0.00 | 0.86 | 0.86 | 0.79 | 0.79 | 0.57 | 0.79 | 0.86 |
time (sec) |
N/A | 0.000 | 0.056 | 0.598 | 0.215 | 0.267 | 0.049 | 0.288 | 10.695 |
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 | 24 | 24 | 18 | 17 | 28 | 17 | 17 | 17 |
N.S. |
1 | 0.89 | 0.89 | 0.67 | 0.63 | 1.04 | 0.63 | 0.63 | 0.63 |
time (sec) |
N/A | 0.010 | 0.017 | 0.384 | 0.194 | 0.254 | 0.066 | 0.274 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 13 | 9 | 8 | 8 | 10 | 0 | 8 |
N.S. |
1 | 0.00 | 0.48 | 0.33 | 0.30 | 0.30 | 0.37 | 0.00 | 0.30 |
time (sec) |
N/A | 0.000 | 0.130 | 0.082 | 0.250 | 0.248 | 0.178 | 0.000 | 10.950 |
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 | 20 | 34 | 27 | 23 | 26 | 27 | 32 | 26 |
N.S. |
1 | 1.00 | 1.70 | 1.35 | 1.15 | 1.30 | 1.35 | 1.60 | 1.30 |
time (sec) |
N/A | 0.106 | 0.072 | 0.436 | 0.287 | 0.254 | 0.139 | 0.295 | 12.114 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | F(-2) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 31 | 63 | 44 | 42 | 0 | 90 |
N.S. |
1 | 0.00 | 1.00 | 1.29 | 2.62 | 1.83 | 1.75 | 0.00 | 3.75 |
time (sec) |
N/A | 0.000 | 0.145 | 3.093 | 0.444 | 0.251 | 0.268 | 0.000 | 11.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | A | B | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 58 | 179 | 32 | 38 | 58 | 178 | 54 |
N.S. |
1 | 0.00 | 1.87 | 5.77 | 1.03 | 1.23 | 1.87 | 5.74 | 1.74 |
time (sec) |
N/A | 0.000 | 0.948 | 26.056 | 0.388 | 0.263 | 0.556 | 2.407 | 11.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 29 | 29 | 25 | 52 | 45 | 22 | 48 | 24 |
N.S. |
1 | 0.85 | 0.85 | 0.74 | 1.53 | 1.32 | 0.65 | 1.41 | 0.71 |
time (sec) |
N/A | 0.115 | 0.111 | 0.491 | 0.252 | 0.254 | 0.118 | 0.287 | 10.918 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 28 | 28 | 29 | 28 | 31 | 24 | 30 | 26 |
N.S. |
1 | 1.17 | 1.17 | 1.21 | 1.17 | 1.29 | 1.00 | 1.25 | 1.08 |
time (sec) |
N/A | 0.141 | 0.016 | 0.101 | 0.191 | 0.246 | 0.072 | 0.280 | 11.071 |
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 | 26 | 28 | 46 | 41 | 22 | 33 | 85 |
N.S. |
1 | 0.00 | 0.96 | 1.04 | 1.70 | 1.52 | 0.81 | 1.22 | 3.15 |
time (sec) |
N/A | 0.000 | 0.316 | 1.647 | 0.303 | 0.260 | 0.085 | 0.290 | 11.777 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 26 | 36 | 42 | 42 | 0 | 42 | 23 |
N.S. |
1 | 0.00 | 1.08 | 1.50 | 1.75 | 1.75 | 0.00 | 1.75 | 0.96 |
time (sec) |
N/A | 0.000 | 5.157 | 0.048 | 0.257 | 0.257 | 0.000 | 0.319 | 12.037 |
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 | 21 | 20 | 21 | 21 | 19 | 23 | 21 |
N.S. |
1 | 0.91 | 0.91 | 0.87 | 0.91 | 0.91 | 0.83 | 1.00 | 0.91 |
time (sec) |
N/A | 0.034 | 0.012 | 0.128 | 0.191 | 0.221 | 0.052 | 0.270 | 0.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 13 | 12 | 11 | 22 | 8 | 22 | 11 |
N.S. |
1 | 0.00 | 0.62 | 0.57 | 0.52 | 1.05 | 0.38 | 1.05 | 0.52 |
time (sec) |
N/A | 0.000 | 0.081 | 0.153 | 0.249 | 0.246 | 0.081 | 0.281 | 10.770 |
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 | 30 | 26 | 33 | 29 | 58 | 28 | 26 | 69 | 29 |
N.S. |
1 | 0.87 | 1.10 | 0.97 | 1.93 | 0.93 | 0.87 | 2.30 | 0.97 |
time (sec) |
N/A | 2.215 | 0.837 | 7.075 | 0.334 | 0.263 | 0.328 | 0.347 | 11.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 20 | 20 | 19 | 45 | 18 | 17 | 18 | 20 |
N.S. |
1 | 0.80 | 0.80 | 0.76 | 1.80 | 0.72 | 0.68 | 0.72 | 0.80 |
time (sec) |
N/A | 0.053 | 0.049 | 0.741 | 0.319 | 0.261 | 0.076 | 0.275 | 12.072 |
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 | 19 | 18 | 17 | 21 | 14 | 21 | 17 |
N.S. |
1 | 0.00 | 0.73 | 0.69 | 0.65 | 0.81 | 0.54 | 0.81 | 0.65 |
time (sec) |
N/A | 0.000 | 1.256 | 0.260 | 0.216 | 0.248 | 0.066 | 0.283 | 0.151 |
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 | 25 | 25 | 24 | 26 | 30 | 24 |
N.S. |
1 | 0.00 | 1.00 | 1.25 | 1.25 | 1.20 | 1.30 | 1.50 | 1.20 |
time (sec) |
N/A | 0.000 | 0.429 | 33.027 | 0.325 | 0.249 | 2.345 | 0.337 | 12.444 |
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 | 11 | 11 | 12 | 11 | 11 | 8 | 11 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 1.00 | 0.73 | 1.00 | 0.91 |
time (sec) |
N/A | 0.025 | 0.008 | 0.075 | 0.210 | 0.268 | 0.106 | 0.286 | 11.704 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 62 | 122 | 51 | 63 | 61 | 0 | 55 |
N.S. |
1 | 1.00 | 2.38 | 4.69 | 1.96 | 2.42 | 2.35 | 0.00 | 2.12 |
time (sec) |
N/A | 0.560 | 0.171 | 90.924 | 0.268 | 0.266 | 11.449 | 0.000 | 11.813 |
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 | 27 | 26 | 23 | 25 | 15 | 19 | 21 |
N.S. |
1 | 0.00 | 1.23 | 1.18 | 1.05 | 1.14 | 0.68 | 0.86 | 0.95 |
time (sec) |
N/A | 0.000 | 0.432 | 0.271 | 0.212 | 0.263 | 0.096 | 0.303 | 11.158 |
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 | 33 | 89 | 35 | 70 | 80 | 59 | 63 | 0 | 58 |
N.S. |
1 | 2.70 | 1.06 | 2.12 | 2.42 | 1.79 | 1.91 | 0.00 | 1.76 |
time (sec) |
N/A | 0.154 | 0.263 | 4.947 | 0.194 | 0.250 | 6.889 | 0.000 | 11.318 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | B | A | A | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 0 | 54 | 105 | 103 | 46 | 48 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.64 | 3.18 | 3.12 | 1.39 | 1.45 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.277 | 0.332 | 0.260 | 0.161 | 0.582 | 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 | 18 | 18 | 18 | 21 | 21 | 20 | 19 | 21 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.17 | 1.17 | 1.11 | 1.06 | 1.17 | 1.11 |
time (sec) |
N/A | 0.839 | 0.232 | 0.713 | 0.224 | 0.257 | 0.136 | 0.295 | 13.329 |
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 | 27 | 29 | 29 | 31 | 189 | 29 | 26 | 29 | 26 |
N.S. |
1 | 1.07 | 1.07 | 1.15 | 7.00 | 1.07 | 0.96 | 1.07 | 0.96 |
time (sec) |
N/A | 0.031 | 0.404 | 0.094 | 0.320 | 0.263 | 0.080 | 0.282 | 0.129 |
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 | 30 | 0 | 52 | 37 | 0 | 40 | 44 | 39 | 39 |
N.S. |
1 | 0.00 | 1.73 | 1.23 | 0.00 | 1.33 | 1.47 | 1.30 | 1.30 |
time (sec) |
N/A | 0.000 | 0.556 | 0.171 | 0.000 | 0.253 | 0.306 | 0.328 | 12.249 |
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 | 23 | 23 | 22 | 21 | 21 | 20 | 21 | 17 |
N.S. |
1 | 1.28 | 1.28 | 1.22 | 1.17 | 1.17 | 1.11 | 1.17 | 0.94 |
time (sec) |
N/A | 0.011 | 0.020 | 0.147 | 0.184 | 0.266 | 0.110 | 0.276 | 11.821 |
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 | 26 | 24 | 23 | 25 | 29 | 22 | 35 | 0 |
N.S. |
1 | 1.08 | 1.00 | 0.96 | 1.04 | 1.21 | 0.92 | 1.46 | 0.00 |
time (sec) |
N/A | 0.427 | 0.244 | 0.184 | 0.238 | 0.261 | 0.145 | 0.290 | 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 | 33 | 27 | 30 | 27 | 66 | 27 | 24 | 27 | 25 |
N.S. |
1 | 0.82 | 0.91 | 0.82 | 2.00 | 0.82 | 0.73 | 0.82 | 0.76 |
time (sec) |
N/A | 0.224 | 0.088 | 0.627 | 0.216 | 0.240 | 0.118 | 0.287 | 0.210 |
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 | 30 | 0 | 49 | 44 | 45 | 38 | 42 | 0 | 42 |
N.S. |
1 | 0.00 | 1.63 | 1.47 | 1.50 | 1.27 | 1.40 | 0.00 | 1.40 |
time (sec) |
N/A | 0.000 | 0.266 | 0.173 | 0.221 | 0.257 | 0.166 | 0.000 | 12.172 |
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 | 22 | 21 | 21 | 22 | 19 | 20 | 21 |
N.S. |
1 | 1.05 | 1.00 | 0.95 | 0.95 | 1.00 | 0.86 | 0.91 | 0.95 |
time (sec) |
N/A | 0.009 | 0.006 | 0.085 | 0.192 | 0.250 | 0.052 | 0.289 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F(-1) | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 242 | 243 | 352 | 352 | 170 | 242 | 0 |
N.S. |
1 | 0.00 | 8.34 | 8.38 | 12.14 | 12.14 | 5.86 | 8.34 | 0.00 |
time (sec) |
N/A | 0.000 | 0.767 | 7.596 | 0.861 | 0.308 | 2.030 | 7.179 | 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 | 12 | 11 | 12 | 8 | 11 | 12 |
N.S. |
1 | 0.79 | 0.79 | 0.63 | 0.58 | 0.63 | 0.42 | 0.58 | 0.63 |
time (sec) |
N/A | 0.003 | 0.002 | 0.016 | 0.179 | 0.257 | 0.034 | 0.270 | 0.025 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 18 | 17 | 16 | 26 | 15 | 16 | 16 |
N.S. |
1 | 0.00 | 0.86 | 0.81 | 0.76 | 1.24 | 0.71 | 0.76 | 0.76 |
time (sec) |
N/A | 0.000 | 0.131 | 0.061 | 0.235 | 0.250 | 0.095 | 0.275 | 11.563 |
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 | 8 | 8 | 8 | 9 | 8 | 8 | 7 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 1.12 | 1.00 | 1.00 | 0.88 | 1.00 | 1.00 |
time (sec) |
N/A | 0.001 | 0.000 | 0.078 | 0.173 | 0.250 | 0.023 | 0.311 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 30 | 30 | 0 | 30 | 0 | 0 | 48 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.00 | 1.00 | 0.00 | 0.00 | 1.60 |
time (sec) |
N/A | 0.000 | 0.281 | 196.254 | 0.000 | 0.266 | 0.000 | 0.000 | 0.386 |
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 | 27 | 0 | 49 | 64 | 75 | 75 | 60 | 76 | 68 |
N.S. |
1 | 0.00 | 1.81 | 2.37 | 2.78 | 2.78 | 2.22 | 2.81 | 2.52 |
time (sec) |
N/A | 0.000 | 0.060 | 11.361 | 0.215 | 0.250 | 0.087 | 0.339 | 11.950 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 63 | 20 | 41 | 40 | 36 | 42 | 36 | 18 |
N.S. |
1 | 3.00 | 0.95 | 1.95 | 1.90 | 1.71 | 2.00 | 1.71 | 0.86 |
time (sec) |
N/A | 0.050 | 0.184 | 0.219 | 0.187 | 0.247 | 0.084 | 0.289 | 0.149 |
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 | 35 | 31 | 29 | 28 | 28 | 27 | 28 | 26 |
N.S. |
1 | 1.67 | 1.48 | 1.38 | 1.33 | 1.33 | 1.29 | 1.33 | 1.24 |
time (sec) |
N/A | 0.027 | 0.075 | 0.050 | 0.178 | 0.236 | 0.059 | 0.315 | 11.103 |
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 | 38 | 0 | 41 | 44 | 48 | 40 | 37 | 88 | 0 |
N.S. |
1 | 0.00 | 1.08 | 1.16 | 1.26 | 1.05 | 0.97 | 2.32 | 0.00 |
time (sec) |
N/A | 0.000 | 0.293 | 95.365 | 1.058 | 0.255 | 3.358 | 1.414 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 27 | 26 | 24 | 63 | 65 | 73 | 66 | 118 |
N.S. |
1 | 1.08 | 1.04 | 0.96 | 2.52 | 2.60 | 2.92 | 2.64 | 4.72 |
time (sec) |
N/A | 0.191 | 0.071 | 0.738 | 0.310 | 0.274 | 0.167 | 0.349 | 7.729 |
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 | 22 | 21 | 20 | 18 | 18 | 15 | 19 | 19 |
N.S. |
1 | 1.00 | 0.95 | 0.91 | 0.82 | 0.82 | 0.68 | 0.86 | 0.86 |
time (sec) |
N/A | 0.016 | 0.018 | 0.438 | 0.177 | 0.246 | 0.095 | 0.259 | 0.084 |
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 | 36 | 60 | 63 | 35 | 42 | 42 | 34 | 124 | 57 |
N.S. |
1 | 1.67 | 1.75 | 0.97 | 1.17 | 1.17 | 0.94 | 3.44 | 1.58 |
time (sec) |
N/A | 1.250 | 0.252 | 1.388 | 0.225 | 0.252 | 0.291 | 0.286 | 0.432 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 23 | 58 | 24 | 29 | 30 | 27 | 29 | 29 |
N.S. |
1 | 1.44 | 3.62 | 1.50 | 1.81 | 1.88 | 1.69 | 1.81 | 1.81 |
time (sec) |
N/A | 0.009 | 0.000 | 0.008 | 0.182 | 0.228 | 0.022 | 0.267 | 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 | 27 | 37 | 37 | 30 | 31 | 33 | 27 | 28 | 23 |
N.S. |
1 | 1.37 | 1.37 | 1.11 | 1.15 | 1.22 | 1.00 | 1.04 | 0.85 |
time (sec) |
N/A | 0.036 | 0.012 | 0.080 | 0.187 | 0.242 | 0.074 | 0.276 | 12.847 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 40 | 23 | 20 | 20 | 20 | 26 | 0 | 19 |
N.S. |
1 | 1.74 | 1.00 | 0.87 | 0.87 | 0.87 | 1.13 | 0.00 | 0.83 |
time (sec) |
N/A | 0.049 | 0.084 | 4.789 | 0.317 | 0.249 | 0.938 | 0.000 | 12.604 |
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 | 40 | 34 | 38 | 41 | 39 | 43 | 55 |
N.S. |
1 | 0.00 | 1.33 | 1.13 | 1.27 | 1.37 | 1.30 | 1.43 | 1.83 |
time (sec) |
N/A | 0.000 | 0.125 | 1.365 | 0.247 | 0.257 | 0.158 | 0.306 | 13.673 |
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 | 41 | 51 | 48 | 37 | 37 | 47 | 42 |
N.S. |
1 | 0.00 | 1.28 | 1.59 | 1.50 | 1.16 | 1.16 | 1.47 | 1.31 |
time (sec) |
N/A | 0.000 | 0.108 | 12.876 | 0.214 | 0.247 | 0.422 | 0.387 | 13.432 |
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 | 17 | 0 | 15 | 14 | 13 | 13 | 10 | 13 | 13 |
N.S. |
1 | 0.00 | 0.88 | 0.82 | 0.76 | 0.76 | 0.59 | 0.76 | 0.76 |
time (sec) |
N/A | 0.000 | 0.252 | 0.113 | 0.210 | 0.262 | 0.062 | 0.270 | 13.226 |
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 | 17 | 19 | 19 | 17 | 18 | 18 | 141 | 18 | 18 |
N.S. |
1 | 1.12 | 1.12 | 1.00 | 1.06 | 1.06 | 8.29 | 1.06 | 1.06 |
time (sec) |
N/A | 0.165 | 0.232 | 0.446 | 0.213 | 0.251 | 0.204 | 0.263 | 11.504 |
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 | 19 | 24 | 18 | 18 | 20 | 15 | 18 | 17 |
N.S. |
1 | 0.70 | 0.89 | 0.67 | 0.67 | 0.74 | 0.56 | 0.67 | 0.63 |
time (sec) |
N/A | 0.017 | 0.010 | 0.062 | 0.178 | 0.231 | 0.059 | 0.304 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 35 | 29 | 40 | 71 | 31 | 936 | 87 |
N.S. |
1 | 0.00 | 1.13 | 0.94 | 1.29 | 2.29 | 1.00 | 30.19 | 2.81 |
time (sec) |
N/A | 0.000 | 0.235 | 0.493 | 0.226 | 0.270 | 0.155 | 0.310 | 11.263 |
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 | 34 | 46 | 25 | 42 | 28 | 29 | 28 | 95 |
N.S. |
1 | 1.06 | 1.44 | 0.78 | 1.31 | 0.88 | 0.91 | 0.88 | 2.97 |
time (sec) |
N/A | 2.545 | 3.590 | 0.658 | 0.270 | 0.257 | 0.139 | 0.467 | 11.888 |
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 | 22 | 16 | 18 | 18 | 32 | 18 | 15 |
N.S. |
1 | 0.82 | 1.00 | 0.73 | 0.82 | 0.82 | 1.45 | 0.82 | 0.68 |
time (sec) |
N/A | 0.003 | 0.003 | 0.050 | 0.171 | 0.247 | 0.027 | 0.277 | 11.870 |
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 | 9 | 9 | 10 | 9 | 9 | 10 | 9 | 10 |
N.S. |
1 | 0.56 | 0.56 | 0.62 | 0.56 | 0.56 | 0.62 | 0.56 | 0.62 |
time (sec) |
N/A | 0.003 | 0.001 | 0.059 | 0.175 | 0.258 | 0.024 | 0.262 | 0.039 |
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 | 33 | 11592 | 14593 | 128 | 39766 | 124 | 139 | 497 | 127 |
N.S. |
1 | 351.27 | 442.21 | 3.88 | 1205.03 | 3.76 | 4.21 | 15.06 | 3.85 |
time (sec) |
N/A | 19.804 | 41.564 | 1.218 | 0.716 | 0.266 | 0.248 | 1.234 | 11.944 |
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 | 18 | 18 | 18 | 61 | 17 | 15 | 17 | 18 |
N.S. |
1 | 0.75 | 0.75 | 0.75 | 2.54 | 0.71 | 0.62 | 0.71 | 0.75 |
time (sec) |
N/A | 0.082 | 0.036 | 0.079 | 0.301 | 0.262 | 0.054 | 0.279 | 0.101 |