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 | F | A | C | B | B | B | F(-2) | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 32 | 578 | 500 | 62 | 61 | 0 | 94 |
N.S. |
1 | 0.00 | 1.33 | 24.08 | 20.83 | 2.58 | 2.54 | 0.00 | 3.92 |
time (sec) |
N/A | 0.000 | 0.368 | 0.066 | 4.959 | 0.249 | 3.381 | 0.000 | 10.487 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 0 | 23 | 28 | 29 | 15 | 27 | 28 | 15 |
N.S. |
1 | 0.00 | 1.77 | 2.15 | 2.23 | 1.15 | 2.08 | 2.15 | 1.15 |
time (sec) |
N/A | 0.000 | 0.332 | 0.531 | 0.232 | 0.238 | 0.275 | 0.323 | 8.622 |
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 | 29 | 24 | 32 | 25 | 24 | 29 | 26 |
N.S. |
1 | 0.00 | 0.97 | 0.80 | 1.07 | 0.83 | 0.80 | 0.97 | 0.87 |
time (sec) |
N/A | 0.000 | 9.555 | 0.158 | 1.414 | 0.252 | 0.112 | 0.316 | 0.174 |
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 | 31 | 0 | 28 | 31 | 33 | 43 | 34 | 36 | 42 |
N.S. |
1 | 0.00 | 0.90 | 1.00 | 1.06 | 1.39 | 1.10 | 1.16 | 1.35 |
time (sec) |
N/A | 0.000 | 0.123 | 274.354 | 0.288 | 0.244 | 0.203 | 0.319 | 8.586 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 57 | 22 | 29 | 0 | 28 | 29 | 19 | 62 |
N.S. |
1 | 2.59 | 1.00 | 1.32 | 0.00 | 1.27 | 1.32 | 0.86 | 2.82 |
time (sec) |
N/A | 2.133 | 0.657 | 5.795 | 0.000 | 0.241 | 0.282 | 0.748 | 8.669 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 0 | 24 | 30 | 23 | 22 | 73 | 21 |
N.S. |
1 | 0.00 | 0.00 | 1.09 | 1.36 | 1.05 | 1.00 | 3.32 | 0.95 |
time (sec) |
N/A | 0.000 | 0.000 | 62.118 | 0.322 | 0.244 | 0.736 | 3.234 | 9.930 |
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 | 3 | 3 | 4 | 3 | 3 | 3 | 4 | 3 |
N.S. |
1 | 0.60 | 0.60 | 0.80 | 0.60 | 0.60 | 0.60 | 0.80 | 0.60 |
time (sec) |
N/A | 0.143 | 0.001 | 0.020 | 0.182 | 0.232 | 0.036 | 0.283 | 9.633 |
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 | 31 | 50 | 26 | 18 | 23 | 28 | 15 | 30 | 19 |
N.S. |
1 | 1.61 | 0.84 | 0.58 | 0.74 | 0.90 | 0.48 | 0.97 | 0.61 |
time (sec) |
N/A | 0.340 | 0.490 | 0.056 | 0.292 | 0.252 | 0.068 | 0.292 | 0.215 |
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 | 26 | 24 | 25 | 27 | 14 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.62 | 1.50 | 1.56 | 1.69 | 0.88 | 0.94 |
time (sec) |
N/A | 0.206 | 0.029 | 0.064 | 0.171 | 0.244 | 0.094 | 0.289 | 9.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 20 | 0 | 19 | 17 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.00 | 0.86 | 0.77 | 0.86 | 0.86 |
time (sec) |
N/A | 0.407 | 0.184 | 0.081 | 0.000 | 0.240 | 0.073 | 0.277 | 8.540 |
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 | 31 | 0 | 26 | 26 | 35 | 29 | 27 | 35 | 143 |
N.S. |
1 | 0.00 | 0.84 | 0.84 | 1.13 | 0.94 | 0.87 | 1.13 | 4.61 |
time (sec) |
N/A | 0.000 | 0.156 | 5.060 | 0.270 | 0.247 | 0.178 | 0.503 | 9.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 35 | 35 | 31 | 57 | 27 | 35 | 69 |
N.S. |
1 | 0.00 | 1.09 | 1.09 | 0.97 | 1.78 | 0.84 | 1.09 | 2.16 |
time (sec) |
N/A | 0.000 | 1.137 | 1.777 | 0.261 | 0.265 | 0.101 | 0.299 | 8.881 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 11 | 13 | 7 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 1.00 | 0.54 | 0.85 | 0.85 |
time (sec) |
N/A | 0.153 | 0.005 | 0.023 | 0.176 | 0.219 | 0.036 | 0.277 | 0.040 |
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 | 24 | 33 | 33 | 18 | 18 | 30 | 15 | 18 | 17 |
N.S. |
1 | 1.38 | 1.38 | 0.75 | 0.75 | 1.25 | 0.62 | 0.75 | 0.71 |
time (sec) |
N/A | 0.337 | 0.020 | 0.081 | 0.170 | 0.252 | 0.115 | 0.283 | 9.000 |
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 | 29 | 41 | 39 | 29 | 33 | 33 | 27 | 33 | 33 |
N.S. |
1 | 1.41 | 1.34 | 1.00 | 1.14 | 1.14 | 0.93 | 1.14 | 1.14 |
time (sec) |
N/A | 0.169 | 0.004 | 0.023 | 0.168 | 0.226 | 0.022 | 0.278 | 9.036 |
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 | 24 | 30 | 36 | 28 | 22 | 43 | 1156 |
N.S. |
1 | 0.00 | 0.92 | 1.15 | 1.38 | 1.08 | 0.85 | 1.65 | 44.46 |
time (sec) |
N/A | 0.000 | 1.234 | 122.320 | 0.363 | 0.240 | 0.832 | 0.433 | 11.067 |
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 | 29 | 27 | 27 | 82 | 57 | 49 | 19 | 1737 | 27 |
N.S. |
1 | 0.93 | 0.93 | 2.83 | 1.97 | 1.69 | 0.66 | 59.90 | 0.93 |
time (sec) |
N/A | 5.128 | 0.181 | 2.059 | 0.376 | 0.259 | 0.161 | 2.304 | 9.755 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | F(-2) | A | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 0 | 31 | 30 | 34 | 0 | 34 | 51 |
N.S. |
1 | 0.00 | 0.00 | 1.35 | 1.30 | 1.48 | 0.00 | 1.48 | 2.22 |
time (sec) |
N/A | 0.000 | 0.000 | 0.280 | 0.341 | 0.250 | 0.000 | 0.312 | 9.279 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 108 | 26 | 44 | 96 | 43 | 46 | 51 | 43 |
N.S. |
1 | 4.70 | 1.13 | 1.91 | 4.17 | 1.87 | 2.00 | 2.22 | 1.87 |
time (sec) |
N/A | 1.330 | 1.599 | 0.099 | 0.224 | 0.249 | 0.105 | 0.293 | 8.452 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 55 | 55 | 60 | 61 | 57 | 65 | 65 | 56 |
N.S. |
1 | 1.83 | 1.83 | 2.00 | 2.03 | 1.90 | 2.17 | 2.17 | 1.87 |
time (sec) |
N/A | 0.288 | 0.026 | 0.049 | 0.174 | 0.229 | 0.236 | 0.279 | 0.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 80 | 37 | 38 | 100 | 38 | 60 | 74 | 58 |
N.S. |
1 | 2.76 | 1.28 | 1.31 | 3.45 | 1.31 | 2.07 | 2.55 | 2.00 |
time (sec) |
N/A | 0.337 | 0.593 | 0.081 | 0.236 | 0.238 | 0.077 | 0.297 | 0.137 |
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 | 11 | 11 | 11 | 12 | 23 | 11 | 12 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 2.09 | 1.00 | 1.09 | 1.00 | 1.00 |
time (sec) |
N/A | 0.408 | 0.286 | 0.076 | 0.295 | 0.259 | 0.061 | 0.302 | 8.643 |
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 | 22 | 26 | 31 | 26 | 17 | 26 | 25 |
N.S. |
1 | 0.00 | 0.85 | 1.00 | 1.19 | 1.00 | 0.65 | 1.00 | 0.96 |
time (sec) |
N/A | 0.000 | 0.343 | 0.766 | 0.324 | 0.238 | 0.072 | 0.300 | 9.527 |
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 | 21 | 51 | 32 | 26 | 27 | 31 | 27 | 31 | 24 |
N.S. |
1 | 2.43 | 1.52 | 1.24 | 1.29 | 1.48 | 1.29 | 1.48 | 1.14 |
time (sec) |
N/A | 0.897 | 0.248 | 0.082 | 0.223 | 0.248 | 0.131 | 0.305 | 9.142 |
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 | 17 | 43 | 43 | 41 | 49 | 35 | 37 | 38 | 43 |
N.S. |
1 | 2.53 | 2.53 | 2.41 | 2.88 | 2.06 | 2.18 | 2.24 | 2.53 |
time (sec) |
N/A | 0.231 | 0.020 | 0.025 | 0.199 | 0.246 | 0.074 | 0.281 | 8.570 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 54 | 54 | 53 | 54 | 52 | 51 | 56 | 52 |
N.S. |
1 | 2.45 | 2.45 | 2.41 | 2.45 | 2.36 | 2.32 | 2.55 | 2.36 |
time (sec) |
N/A | 1.061 | 0.063 | 0.042 | 0.182 | 0.268 | 0.077 | 0.299 | 8.612 |
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 | 20 | 20 | 18 | 17 | 19 | 19 | 20 | 17 |
N.S. |
1 | 0.71 | 0.71 | 0.64 | 0.61 | 0.68 | 0.68 | 0.71 | 0.61 |
time (sec) |
N/A | 0.255 | 0.016 | 0.046 | 0.203 | 0.228 | 0.252 | 0.284 | 8.520 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 31 | 36 | 38 | 42 | 46 | 0 | 41 |
N.S. |
1 | 0.00 | 1.00 | 1.16 | 1.23 | 1.35 | 1.48 | 0.00 | 1.32 |
time (sec) |
N/A | 0.000 | 2.548 | 0.847 | 0.318 | 0.243 | 0.173 | 0.000 | 9.387 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | B | B | F(-1) | F(-1) | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 61 | 828 | 1058 | 114 | 0 | 0 | 76 |
N.S. |
1 | 0.00 | 1.74 | 23.66 | 30.23 | 3.26 | 0.00 | 0.00 | 2.17 |
time (sec) |
N/A | 0.000 | 0.452 | 0.137 | 3.738 | 0.256 | 0.000 | 0.000 | 10.530 |
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 | 30 | 20 | 18 | 19 | 32 | 17 | 19 | 19 |
N.S. |
1 | 1.30 | 0.87 | 0.78 | 0.83 | 1.39 | 0.74 | 0.83 | 0.83 |
time (sec) |
N/A | 0.777 | 0.036 | 0.271 | 0.223 | 0.249 | 0.091 | 0.309 | 8.515 |
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 | 37 | 40 | 35 | 32 | 43 | 29 | 32 | 31 |
N.S. |
1 | 1.23 | 1.33 | 1.17 | 1.07 | 1.43 | 0.97 | 1.07 | 1.03 |
time (sec) |
N/A | 0.514 | 0.064 | 0.067 | 0.185 | 0.242 | 0.169 | 0.309 | 8.463 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 17 | 17 | 46 | 14 | 17 | 17 |
N.S. |
1 | 0.00 | 1.00 | 0.81 | 0.81 | 2.19 | 0.67 | 0.81 | 0.81 |
time (sec) |
N/A | 0.000 | 0.136 | 0.028 | 0.294 | 0.244 | 0.081 | 0.305 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 41 | 27 | 38 | 32 | 31 | 86 | 0 |
N.S. |
1 | 1.00 | 1.64 | 1.08 | 1.52 | 1.28 | 1.24 | 3.44 | 0.00 |
time (sec) |
N/A | 0.477 | 7.321 | 0.207 | 0.285 | 0.268 | 0.167 | 0.326 | 0.000 |
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 | 35 | 0 | 36 | 33 | 0 | 58 | 27 | 58 | 32 |
N.S. |
1 | 0.00 | 1.03 | 0.94 | 0.00 | 1.66 | 0.77 | 1.66 | 0.91 |
time (sec) |
N/A | 0.000 | 0.457 | 89.719 | 0.000 | 0.259 | 1.398 | 0.610 | 9.804 |
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 | 26 | 0 | 22 | 32 | 20 | 29 | 22 | 0 | 54 |
N.S. |
1 | 0.00 | 0.85 | 1.23 | 0.77 | 1.12 | 0.85 | 0.00 | 2.08 |
time (sec) |
N/A | 0.000 | 0.509 | 0.202 | 0.307 | 0.279 | 0.177 | 0.000 | 8.903 |
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 | 24 | 21 | 76 | 25 | 22 | 27 | 27 |
N.S. |
1 | 0.00 | 0.80 | 0.70 | 2.53 | 0.83 | 0.73 | 0.90 | 0.90 |
time (sec) |
N/A | 0.000 | 1.686 | 4.732 | 0.451 | 0.258 | 0.261 | 0.302 | 9.144 |
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 | 22 | 0 | 22 | 28 | 0 | 27 | 20 | 100 | 26 |
N.S. |
1 | 0.00 | 1.00 | 1.27 | 0.00 | 1.23 | 0.91 | 4.55 | 1.18 |
time (sec) |
N/A | 0.000 | 0.164 | 0.156 | 0.000 | 0.248 | 0.081 | 0.328 | 0.158 |
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 | 36 | 37 | 26 | 35 | 35 | 37 | 37 | 48 |
N.S. |
1 | 1.64 | 1.68 | 1.18 | 1.59 | 1.59 | 1.68 | 1.68 | 2.18 |
time (sec) |
N/A | 0.233 | 0.025 | 0.100 | 0.182 | 0.249 | 0.087 | 0.299 | 8.446 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 69 | 46 | 44 | 77 | 47 | 42 | 55 | 93 |
N.S. |
1 | 2.65 | 1.77 | 1.69 | 2.96 | 1.81 | 1.62 | 2.12 | 3.58 |
time (sec) |
N/A | 0.365 | 0.189 | 0.072 | 0.332 | 0.272 | 0.110 | 0.388 | 8.510 |
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 | 35 | 0 | 63 | 103 | 467 | 81 | 75 | 104 | 76 |
N.S. |
1 | 0.00 | 1.80 | 2.94 | 13.34 | 2.31 | 2.14 | 2.97 | 2.17 |
time (sec) |
N/A | 0.000 | 0.187 | 22.370 | 0.331 | 0.271 | 0.292 | 10.329 | 8.838 |
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 | 17 | 0 | 17 | 18 | 83 | 83 | 95 | 7896 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.06 | 4.88 | 4.88 | 5.59 | 464.47 | 0.00 |
time (sec) |
N/A | 0.000 | 0.157 | 0.654 | 0.609 | 0.263 | 0.175 | 3.141 | 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 | 27 | 23 | 20 | 19 | 19 | 20 | 19 | 16 |
N.S. |
1 | 1.29 | 1.10 | 0.95 | 0.90 | 0.90 | 0.95 | 0.90 | 0.76 |
time (sec) |
N/A | 0.156 | 0.002 | 0.020 | 0.189 | 0.234 | 0.042 | 0.295 | 8.476 |
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 | 28 | 29 | 24 | 28 | 29 | 0 | 29 |
N.S. |
1 | 0.00 | 0.93 | 0.97 | 0.80 | 0.93 | 0.97 | 0.00 | 0.97 |
time (sec) |
N/A | 0.000 | 0.745 | 0.160 | 0.299 | 0.240 | 0.104 | 0.000 | 0.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | C | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 188 | 120 | 31 | 92 | 30 | 32 | 69 | 17 |
N.S. |
1 | 10.44 | 6.67 | 1.72 | 5.11 | 1.67 | 1.78 | 3.83 | 0.94 |
time (sec) |
N/A | 0.457 | 2.530 | 0.123 | 0.194 | 0.302 | 0.068 | 0.275 | 9.004 |
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 | 21 | 23 | 29 | 29 | 26 | 30 | 20 |
N.S. |
1 | 0.00 | 0.88 | 0.96 | 1.21 | 1.21 | 1.08 | 1.25 | 0.83 |
time (sec) |
N/A | 0.000 | 1.486 | 0.138 | 0.313 | 0.286 | 0.102 | 0.270 | 0.244 |
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 | 20 | 16 | 15 | 15 | 19 | 15 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.75 | 0.75 | 0.95 | 0.75 | 0.90 |
time (sec) |
N/A | 0.348 | 0.542 | 0.072 | 0.172 | 0.267 | 0.134 | 0.292 | 0.125 |
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 | 19 | 11 | 13 | 16 | 21 | 17 | 17 | 13 |
N.S. |
1 | 1.58 | 0.92 | 1.08 | 1.33 | 1.75 | 1.42 | 1.42 | 1.08 |
time (sec) |
N/A | 0.178 | 0.003 | 0.025 | 0.168 | 0.251 | 0.056 | 0.262 | 0.050 |
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 | 70 | 43 | 41 | 41 | 37 | 44 | 38 | 40 |
N.S. |
1 | 2.59 | 1.59 | 1.52 | 1.52 | 1.37 | 1.63 | 1.41 | 1.48 |
time (sec) |
N/A | 0.247 | 0.117 | 0.356 | 0.188 | 0.245 | 0.167 | 0.286 | 7.838 |
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 | 36 | 0 | 52 | 61 | 54 | 58 | 27 | 61 | 68 |
N.S. |
1 | 0.00 | 1.44 | 1.69 | 1.50 | 1.61 | 0.75 | 1.69 | 1.89 |
time (sec) |
N/A | 0.000 | 0.210 | 0.256 | 0.254 | 0.280 | 0.114 | 0.371 | 7.703 |
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 | 6 | 6 | 6 | 5 | 5 | 5 | 5 | 5 |
N.S. |
1 | 0.29 | 0.29 | 0.29 | 0.24 | 0.24 | 0.24 | 0.24 | 0.24 |
time (sec) |
N/A | 0.127 | 0.000 | 0.009 | 0.181 | 0.224 | 0.013 | 0.263 | 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 | 23 | 21 | 23 | 21 | 20 | 25 | 20 | 20 | 20 |
N.S. |
1 | 0.91 | 1.00 | 0.91 | 0.87 | 1.09 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.404 | 0.232 | 0.042 | 0.236 | 0.247 | 0.115 | 0.289 | 7.654 |
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 | 20 | 20 | 30 | 29 | 29 | 29 | 29 | 29 |
N.S. |
1 | 0.87 | 0.87 | 1.30 | 1.26 | 1.26 | 1.26 | 1.26 | 1.26 |
time (sec) |
N/A | 2.668 | 0.651 | 0.511 | 0.238 | 0.244 | 0.192 | 0.422 | 0.264 |
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 | 23 | 23 | 18 | 18 | 17 | 22 | 18 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.78 | 0.74 | 0.96 | 0.78 | 0.83 |
time (sec) |
N/A | 0.261 | 0.084 | 0.026 | 0.273 | 0.250 | 0.076 | 0.275 | 7.907 |
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 | 21 | 22 | 22 | 22 | 23 | 21 |
N.S. |
1 | 0.91 | 0.91 | 0.91 | 0.96 | 0.96 | 0.96 | 1.00 | 0.91 |
time (sec) |
N/A | 0.803 | 0.349 | 0.319 | 0.321 | 0.251 | 0.446 | 0.362 | 8.557 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 14 | 14 | 28 | 66 | 49 | 15 | 12 | 12 |
N.S. |
1 | 0.88 | 0.88 | 1.75 | 4.12 | 3.06 | 0.94 | 0.75 | 0.75 |
time (sec) |
N/A | 0.287 | 0.066 | 4.335 | 0.183 | 0.241 | 0.052 | 0.266 | 7.988 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 156 | 47 | 35 | 0 | 49 | 31 | 52 | 30 |
N.S. |
1 | 6.24 | 1.88 | 1.40 | 0.00 | 1.96 | 1.24 | 2.08 | 1.20 |
time (sec) |
N/A | 0.830 | 0.217 | 0.164 | 0.000 | 0.243 | 0.116 | 0.270 | 0.294 |
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 | 9 | 9 | 9 | 8 | 8 | 8 | 8 | 8 |
N.S. |
1 | 0.50 | 0.50 | 0.50 | 0.44 | 0.44 | 0.44 | 0.44 | 0.44 |
time (sec) |
N/A | 0.135 | 0.001 | 0.020 | 0.180 | 0.235 | 0.028 | 0.276 | 8.064 |
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 | 20 | 0 | 18 | 28 | 20 | 27 | 22 | 56 | 60 |
N.S. |
1 | 0.00 | 0.90 | 1.40 | 1.00 | 1.35 | 1.10 | 2.80 | 3.00 |
time (sec) |
N/A | 0.000 | 1.467 | 0.156 | 0.294 | 0.238 | 0.084 | 0.278 | 8.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | F | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 94 | 0 | 50 | 71 | 46 | 0 | 42 | 47 |
N.S. |
1 | 2.94 | 0.00 | 1.56 | 2.22 | 1.44 | 0.00 | 1.31 | 1.47 |
time (sec) |
N/A | 0.730 | 0.000 | 3.355 | 0.390 | 0.245 | 0.000 | 0.592 | 8.701 |
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 | 25 | 19 | 17 | 16 | 16 | 15 | 16 | 16 |
N.S. |
1 | 1.19 | 0.90 | 0.81 | 0.76 | 0.76 | 0.71 | 0.76 | 0.76 |
time (sec) |
N/A | 0.147 | 0.017 | 0.021 | 0.168 | 0.243 | 0.043 | 0.268 | 0.065 |
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 | 21 | 20 | 24 | 26 | 24 | 22 |
N.S. |
1 | 0.00 | 1.00 | 0.81 | 0.77 | 0.92 | 1.00 | 0.92 | 0.85 |
time (sec) |
N/A | 0.000 | 0.660 | 0.036 | 0.212 | 0.241 | 0.133 | 0.295 | 8.248 |
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 | 20 | 0 | 20 | 24 | 31 | 27 | 15 | 23 | 18 |
N.S. |
1 | 0.00 | 1.00 | 1.20 | 1.55 | 1.35 | 0.75 | 1.15 | 0.90 |
time (sec) |
N/A | 0.000 | 0.091 | 0.173 | 0.230 | 0.244 | 0.090 | 0.274 | 8.441 |
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 | 25 | 29 | 21 | 18 | 26 | 19 | 18 | 22 |
N.S. |
1 | 1.14 | 1.32 | 0.95 | 0.82 | 1.18 | 0.86 | 0.82 | 1.00 |
time (sec) |
N/A | 0.184 | 0.016 | 0.110 | 0.182 | 0.227 | 0.072 | 0.271 | 8.361 |
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 | 26 | 0 | 38 | 46 | 44 | 44 | 42 | 51 | 101 |
N.S. |
1 | 0.00 | 1.46 | 1.77 | 1.69 | 1.69 | 1.62 | 1.96 | 3.88 |
time (sec) |
N/A | 0.000 | 0.095 | 1.425 | 0.327 | 0.265 | 0.167 | 0.530 | 1.560 |
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 | 24 | 24 | 24 | 30 | 33 | 22 | 33 | 23 |
N.S. |
1 | 0.96 | 0.96 | 0.96 | 1.20 | 1.32 | 0.88 | 1.32 | 0.92 |
time (sec) |
N/A | 2.270 | 0.136 | 4.305 | 0.243 | 0.261 | 0.238 | 0.286 | 8.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 9 | 9 | 7 | 6 | 6 | 7 | 6 | 6 |
N.S. |
1 | 0.82 | 0.82 | 0.64 | 0.55 | 0.55 | 0.64 | 0.55 | 0.55 |
time (sec) |
N/A | 0.148 | 0.009 | 0.019 | 0.172 | 0.229 | 0.028 | 0.259 | 0.027 |
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 | 23 | 0 | 25 | 19 | 0 | 18 | 19 | 34 | 18 |
N.S. |
1 | 0.00 | 1.09 | 0.83 | 0.00 | 0.78 | 0.83 | 1.48 | 0.78 |
time (sec) |
N/A | 0.000 | 0.116 | 0.165 | 0.000 | 0.243 | 0.101 | 0.301 | 7.964 |
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 | 13 | 13 | 16 | 15 | 13 | 17 | 15 | 13 |
N.S. |
1 | 0.52 | 0.52 | 0.64 | 0.60 | 0.52 | 0.68 | 0.60 | 0.52 |
time (sec) |
N/A | 0.418 | 0.074 | 0.117 | 0.202 | 0.272 | 0.238 | 0.285 | 8.101 |
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 | 13 | 15 | 20 | 11 | 21 | 10 | 10 | 10 | 10 |
N.S. |
1 | 1.15 | 1.54 | 0.85 | 1.62 | 0.77 | 0.77 | 0.77 | 0.77 |
time (sec) |
N/A | 0.154 | 0.017 | 0.035 | 0.259 | 0.248 | 0.042 | 0.285 | 8.430 |
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 | 25 | 0 | 25 | 38 | 34 | 36 | 32 | 86 | 53 |
N.S. |
1 | 0.00 | 1.00 | 1.52 | 1.36 | 1.44 | 1.28 | 3.44 | 2.12 |
time (sec) |
N/A | 0.000 | 3.237 | 3.860 | 0.360 | 0.258 | 0.291 | 0.507 | 8.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 36 | 0 | 20 | 114 | 54 | 0 | 54 | 68 |
N.S. |
1 | 1.38 | 0.00 | 0.77 | 4.38 | 2.08 | 0.00 | 2.08 | 2.62 |
time (sec) |
N/A | 3.079 | 0.000 | 0.579 | 0.645 | 0.268 | 0.000 | 0.285 | 8.606 |
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 | 25 | 25 | 21 | 21 | 19 | 19 | 21 | 18 |
N.S. |
1 | 0.93 | 0.93 | 0.78 | 0.78 | 0.70 | 0.70 | 0.78 | 0.67 |
time (sec) |
N/A | 0.171 | 0.007 | 0.022 | 0.187 | 0.236 | 0.053 | 0.264 | 7.796 |
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 | 14 | 13 | 15 | 12 | 14 | 13 |
N.S. |
1 | 0.94 | 0.94 | 0.88 | 0.81 | 0.94 | 0.75 | 0.88 | 0.81 |
time (sec) |
N/A | 0.144 | 0.003 | 0.017 | 0.190 | 0.233 | 0.032 | 0.262 | 0.029 |
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 | 22 | 22 | 21 | 20 | 22 | 15 | 20 | 20 |
N.S. |
1 | 0.96 | 0.96 | 0.91 | 0.87 | 0.96 | 0.65 | 0.87 | 0.87 |
time (sec) |
N/A | 0.199 | 0.030 | 0.059 | 0.198 | 0.262 | 0.075 | 0.269 | 7.906 |
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 | 32 | 0 | 33 | 40 | 48 | 40 | 0 | 48 | 32 |
N.S. |
1 | 0.00 | 1.03 | 1.25 | 1.50 | 1.25 | 0.00 | 1.50 | 1.00 |
time (sec) |
N/A | 0.000 | 0.204 | 105.990 | 0.339 | 0.263 | 0.000 | 0.350 | 9.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | B | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 0 | 36 | 41 | 36 | 49 | 609 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.38 | 1.58 | 1.38 | 1.88 | 23.42 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.234 | 0.366 | 0.242 | 0.162 | 0.595 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 380 | 162 | 38 | 641 | 37 | 31 | 546 | 27 |
N.S. |
1 | 14.62 | 6.23 | 1.46 | 24.65 | 1.42 | 1.19 | 21.00 | 1.04 |
time (sec) |
N/A | 1.595 | 0.142 | 0.319 | 0.264 | 0.232 | 0.116 | 0.390 | 1.374 |
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 | 19 | 87 | 19 | 27 | 28 | 17 | 19 | 30 | 17 |
N.S. |
1 | 4.58 | 1.00 | 1.42 | 1.47 | 0.89 | 1.00 | 1.58 | 0.89 |
time (sec) |
N/A | 0.602 | 0.122 | 0.265 | 0.287 | 0.231 | 0.165 | 0.283 | 8.420 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 30 | 24 | 28 | 24 | 26 | 36 | 24 |
N.S. |
1 | 0.00 | 0.97 | 0.77 | 0.90 | 0.77 | 0.84 | 1.16 | 0.77 |
time (sec) |
N/A | 0.000 | 1.962 | 0.234 | 0.265 | 0.248 | 0.076 | 0.261 | 0.223 |
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 | 36 | 21 | 33 | 32 | 32 | 41 | 32 | 34 |
N.S. |
1 | 1.71 | 1.00 | 1.57 | 1.52 | 1.52 | 1.95 | 1.52 | 1.62 |
time (sec) |
N/A | 0.203 | 0.052 | 8.933 | 0.243 | 0.248 | 0.179 | 0.282 | 8.053 |
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 | 15 | 16 | 16 | 16 | 43 | 15 | 14 | 15 | 15 |
N.S. |
1 | 1.07 | 1.07 | 1.07 | 2.87 | 1.00 | 0.93 | 1.00 | 1.00 |
time (sec) |
N/A | 0.319 | 0.026 | 0.074 | 0.191 | 0.254 | 0.060 | 0.265 | 0.269 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 119 | 26 | 59 | 72 | 57 | 51 | 75 | 20 |
N.S. |
1 | 5.17 | 1.13 | 2.57 | 3.13 | 2.48 | 2.22 | 3.26 | 0.87 |
time (sec) |
N/A | 0.276 | 0.356 | 0.087 | 0.188 | 0.253 | 0.145 | 0.278 | 7.782 |
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 | 30 | 0 | 43 | 31 | 55 | 44 | 44 | 57 | 34 |
N.S. |
1 | 0.00 | 1.43 | 1.03 | 1.83 | 1.47 | 1.47 | 1.90 | 1.13 |
time (sec) |
N/A | 0.000 | 2.871 | 0.256 | 0.240 | 0.238 | 0.148 | 0.300 | 8.002 |
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 | 26 | 0 | 21 | 21 | 74 | 23 | 17 | 23 | 23 |
N.S. |
1 | 0.00 | 0.81 | 0.81 | 2.85 | 0.88 | 0.65 | 0.88 | 0.88 |
time (sec) |
N/A | 0.000 | 0.169 | 12.861 | 0.280 | 0.260 | 0.167 | 0.334 | 8.430 |
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 | 42 | 32 | 23 | 43 | 27 | 24 | 35 | 33 |
N.S. |
1 | 1.91 | 1.45 | 1.05 | 1.95 | 1.23 | 1.09 | 1.59 | 1.50 |
time (sec) |
N/A | 0.288 | 0.137 | 0.096 | 0.172 | 0.256 | 0.110 | 0.281 | 8.366 |
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 | 24 | 0 | 37 | 47 | 34 | 32 | 34 | 34 | 30 |
N.S. |
1 | 0.00 | 1.54 | 1.96 | 1.42 | 1.33 | 1.42 | 1.42 | 1.25 |
time (sec) |
N/A | 0.000 | 0.250 | 0.138 | 0.302 | 0.229 | 0.691 | 0.287 | 8.634 |
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 | 18 | 18 | 18 | 60 | 18 | 14 | 18 | 18 |
N.S. |
1 | 0.67 | 0.67 | 0.67 | 2.22 | 0.67 | 0.52 | 0.67 | 0.67 |
time (sec) |
N/A | 0.177 | 0.032 | 0.032 | 0.240 | 0.232 | 0.049 | 0.295 | 0.096 |
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 | 17 | 17 | 16 | 15 | 21 | 15 | 15 | 15 |
N.S. |
1 | 0.94 | 0.94 | 0.89 | 0.83 | 1.17 | 0.83 | 0.83 | 0.83 |
time (sec) |
N/A | 0.169 | 0.008 | 0.035 | 0.185 | 0.241 | 0.057 | 0.284 | 8.158 |
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 | 31 | 0 | 27 | 42 | 23 | 40 | 39 | 30 | 103 |
N.S. |
1 | 0.00 | 0.87 | 1.35 | 0.74 | 1.29 | 1.26 | 0.97 | 3.32 |
time (sec) |
N/A | 0.000 | 1.529 | 0.169 | 0.458 | 0.232 | 0.143 | 0.401 | 8.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | C | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 24 | 56 | 53 | 38 | 19 | 25 | 25 |
N.S. |
1 | 0.00 | 0.96 | 2.24 | 2.12 | 1.52 | 0.76 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.099 | 0.347 | 0.313 | 0.251 | 0.134 | 0.822 | 9.103 |
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 | 11 | 10 | 10 | 8 | 11 | 8 |
N.S. |
1 | 0.62 | 0.62 | 0.69 | 0.62 | 0.62 | 0.50 | 0.69 | 0.50 |
time (sec) |
N/A | 0.133 | 0.004 | 0.071 | 0.180 | 0.234 | 0.029 | 0.287 | 0.060 |
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 | 21 | 39 | 39 | 40 | 39 | 32 | 39 | 39 | 39 |
N.S. |
1 | 1.86 | 1.86 | 1.90 | 1.86 | 1.52 | 1.86 | 1.86 | 1.86 |
time (sec) |
N/A | 0.203 | 0.010 | 0.031 | 0.187 | 0.228 | 0.056 | 0.292 | 7.858 |
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 | 26 | 52 | 32 | 28 | 60 | 27 | 27 | 36 | 26 |
N.S. |
1 | 2.00 | 1.23 | 1.08 | 2.31 | 1.04 | 1.04 | 1.38 | 1.00 |
time (sec) |
N/A | 0.393 | 0.324 | 0.056 | 0.266 | 0.243 | 0.113 | 0.295 | 8.007 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | F(-2) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 33 | 41 | 50 | 48 | 0 | 40 | 104 |
N.S. |
1 | 0.00 | 1.27 | 1.58 | 1.92 | 1.85 | 0.00 | 1.54 | 4.00 |
time (sec) |
N/A | 0.000 | 0.419 | 0.355 | 0.307 | 0.242 | 0.000 | 0.426 | 0.635 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 125 | 34 | 34 | 117 | 45 | 31 | 52 | 37 |
N.S. |
1 | 4.03 | 1.10 | 1.10 | 3.77 | 1.45 | 1.00 | 1.68 | 1.19 |
time (sec) |
N/A | 3.046 | 10.179 | 0.125 | 0.263 | 0.242 | 0.099 | 0.282 | 8.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 62 | 55 | 74 | 116 | 83 | 110 | 86 | 112 |
N.S. |
1 | 1.94 | 1.72 | 2.31 | 3.62 | 2.59 | 3.44 | 2.69 | 3.50 |
time (sec) |
N/A | 0.475 | 0.064 | 0.225 | 0.251 | 0.242 | 0.149 | 0.289 | 7.945 |
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 | 24 | 0 | 24 | 26 | 28 | 28 | 29 | 28 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.08 | 1.17 | 1.17 | 1.21 | 1.17 | 0.00 |
time (sec) |
N/A | 0.000 | 0.106 | 25.331 | 0.368 | 0.238 | 0.356 | 0.753 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 27 | 124 | 30 | 39 | 0 | 0 | 39 |
N.S. |
1 | 0.00 | 0.93 | 4.28 | 1.03 | 1.34 | 0.00 | 0.00 | 1.34 |
time (sec) |
N/A | 0.000 | 0.269 | 0.099 | 0.489 | 0.262 | 0.000 | 0.000 | 8.731 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 112 | 35 | 108 | 128 | 91 | 87 | 113 | 107 |
N.S. |
1 | 4.67 | 1.46 | 4.50 | 5.33 | 3.79 | 3.62 | 4.71 | 4.46 |
time (sec) |
N/A | 0.523 | 0.115 | 0.092 | 0.196 | 0.242 | 0.154 | 0.292 | 7.922 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | A | F(-2) | F(-2) | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 40 | 147 | 32 | 31 | 0 | 0 | 31 |
N.S. |
1 | 0.00 | 1.18 | 4.32 | 0.94 | 0.91 | 0.00 | 0.00 | 0.91 |
time (sec) |
N/A | 0.000 | 0.113 | 0.139 | 0.358 | 0.284 | 0.000 | 0.000 | 17.286 |