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 | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 110 | 25 | 56 | 49 | 49 | 114 | 51 | 18 |
N.S. |
1 | 4.40 | 1.00 | 2.24 | 1.96 | 1.96 | 4.56 | 2.04 | 0.72 |
time (sec) |
N/A | 0.237 | 2.329 | 1.968 | 0.274 | 0.264 | 0.114 | 0.250 | 0.201 |
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 | 27 | 17 | 17 | 34 | 33 | 29 | 42 | 33 | 33 |
N.S. |
1 | 0.63 | 0.63 | 1.26 | 1.22 | 1.07 | 1.56 | 1.22 | 1.22 |
time (sec) |
N/A | 0.388 | 0.037 | 3.510 | 0.241 | 0.243 | 10.583 | 0.277 | 10.149 |
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 | 18 | 23 | 18 | 20 | 19 | 19 | 20 | 19 | 20 |
N.S. |
1 | 1.28 | 1.00 | 1.11 | 1.06 | 1.06 | 1.11 | 1.06 | 1.11 |
time (sec) |
N/A | 0.079 | 0.024 | 1.427 | 0.184 | 0.235 | 0.097 | 0.245 | 10.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | A | F(-2) | A | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 26 | 51 | 25 | 0 | 25 | 67 |
N.S. |
1 | 0.00 | 0.00 | 1.08 | 2.12 | 1.04 | 0.00 | 1.04 | 2.79 |
time (sec) |
N/A | 0.000 | 0.000 | 9.440 | 0.331 | 0.233 | 0.000 | 0.312 | 10.387 |
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 | 22 | 0 | 21 | 20 | 19 | 26 | 15 | 30 | 19 |
N.S. |
1 | 0.00 | 0.95 | 0.91 | 0.86 | 1.18 | 0.68 | 1.36 | 0.86 |
time (sec) |
N/A | 0.000 | 0.201 | 1.139 | 0.235 | 0.232 | 0.127 | 0.250 | 10.242 |
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 | 12 | 11 | 11 | 15 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.79 | 0.79 | 1.07 | 0.79 | 0.79 |
time (sec) |
N/A | 0.002 | 0.001 | 0.508 | 0.191 | 0.234 | 0.022 | 0.248 | 10.169 |
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 | 30 | 0 | 19 | 22 | 42 | 42 | 41 | 114 | 62 |
N.S. |
1 | 0.00 | 0.63 | 0.73 | 1.40 | 1.40 | 1.37 | 3.80 | 2.07 |
time (sec) |
N/A | 0.000 | 0.346 | 3.122 | 0.251 | 0.232 | 0.151 | 0.263 | 10.779 |
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 | 30 | 0 | 45 | 50 | 49 | 47 | 53 | 49 | 0 |
N.S. |
1 | 0.00 | 1.50 | 1.67 | 1.63 | 1.57 | 1.77 | 1.63 | 0.00 |
time (sec) |
N/A | 0.000 | 0.093 | 2.418 | 0.357 | 0.248 | 0.138 | 0.288 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | A | B | B | F(-2) | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 0 | 86 | 37 | 80 | 87 | 0 | 138 |
N.S. |
1 | 0.00 | 0.00 | 2.61 | 1.12 | 2.42 | 2.64 | 0.00 | 4.18 |
time (sec) |
N/A | 0.000 | 0.000 | 36.271 | 1.541 | 0.242 | 0.840 | 0.000 | 12.303 |
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 | 8 | 7 | 7 | 7 | 7 | 7 |
N.S. |
1 | 0.42 | 0.42 | 0.42 | 0.37 | 0.37 | 0.37 | 0.37 | 0.37 |
time (sec) |
N/A | 0.003 | 0.003 | 0.238 | 0.216 | 0.239 | 0.036 | 0.247 | 0.039 |
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 | 32 | 31 | 29 | 30 | 31 | 35 | 36 |
N.S. |
1 | 0.00 | 1.23 | 1.19 | 1.12 | 1.15 | 1.19 | 1.35 | 1.38 |
time (sec) |
N/A | 0.000 | 0.086 | 0.765 | 0.254 | 0.254 | 0.110 | 0.299 | 10.477 |
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 | 30 | 0 | 26 | 25 | 0 | 43 | 42 | 71 | 50 |
N.S. |
1 | 0.00 | 0.87 | 0.83 | 0.00 | 1.43 | 1.40 | 2.37 | 1.67 |
time (sec) |
N/A | 0.000 | 0.139 | 7.092 | 0.000 | 0.257 | 32.253 | 1.038 | 11.097 |
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 | 22 | 19 | 26 | 26 | 22 | 22 | 18 |
N.S. |
1 | 0.00 | 0.92 | 0.79 | 1.08 | 1.08 | 0.92 | 0.92 | 0.75 |
time (sec) |
N/A | 0.000 | 0.359 | 0.397 | 0.227 | 0.248 | 0.139 | 0.257 | 10.673 |
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 | 13 | 12 | 12 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.119 | 0.094 | 2.392 | 0.241 | 0.242 | 0.151 | 0.270 | 10.848 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 20 | 43 | 44 | 44 | 44 | 50 |
N.S. |
1 | 0.00 | 1.00 | 0.91 | 1.95 | 2.00 | 2.00 | 2.00 | 2.27 |
time (sec) |
N/A | 0.000 | 0.444 | 2.366 | 0.240 | 0.237 | 0.106 | 0.263 | 10.826 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 36 | 40 | 40 | 44 | 58 | 53 | 97 | 58 |
N.S. |
1 | 1.89 | 2.11 | 2.11 | 2.32 | 3.05 | 2.79 | 5.11 | 3.05 |
time (sec) |
N/A | 0.017 | 0.026 | 0.994 | 0.191 | 0.227 | 0.084 | 0.245 | 10.324 |
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 | 13 | 11 | 14 | 13 | 13 | 14 | 15 | 9 |
N.S. |
1 | 0.87 | 0.73 | 0.93 | 0.87 | 0.87 | 0.93 | 1.00 | 0.60 |
time (sec) |
N/A | 0.007 | 0.029 | 1.329 | 0.282 | 0.238 | 0.072 | 0.245 | 10.484 |
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 | 20 | 60 | 25 | 26 | 32 | 23 | 29 | 34 | 21 |
N.S. |
1 | 3.00 | 1.25 | 1.30 | 1.60 | 1.15 | 1.45 | 1.70 | 1.05 |
time (sec) |
N/A | 0.067 | 0.114 | 2.397 | 0.268 | 0.254 | 0.113 | 0.261 | 0.142 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | C | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 1101 | 552 | 25 | 77 | 23 | 20 | 23 | 23 |
N.S. |
1 | 55.05 | 27.60 | 1.25 | 3.85 | 1.15 | 1.00 | 1.15 | 1.15 |
time (sec) |
N/A | 1.413 | 0.439 | 1.624 | 0.626 | 0.237 | 0.087 | 0.332 | 10.664 |
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 | 17 | 58 | 17 | 18 | 18 | 17 | 20 | 18 | 18 |
N.S. |
1 | 3.41 | 1.00 | 1.06 | 1.06 | 1.00 | 1.18 | 1.06 | 1.06 |
time (sec) |
N/A | 0.221 | 0.082 | 2.198 | 0.223 | 0.247 | 0.143 | 0.257 | 10.834 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 21 | 14 | 14 | 24 | 13 | 14 | 13 | 20 |
N.S. |
1 | 0.95 | 0.64 | 0.64 | 1.09 | 0.59 | 0.64 | 0.59 | 0.91 |
time (sec) |
N/A | 0.183 | 0.041 | 0.425 | 0.227 | 0.242 | 0.040 | 0.246 | 10.594 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | F(-1) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 31 | 31 | 0 | 31 | 27 | 0 | 27 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.00 | 1.00 | 0.87 | 0.00 | 0.87 |
time (sec) |
N/A | 0.000 | 0.317 | 95.398 | 0.000 | 0.248 | 9.219 | 0.000 | 11.586 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 26 | 25 | 60 | 29 | 26 | 102 | 50 |
N.S. |
1 | 0.00 | 0.84 | 0.81 | 1.94 | 0.94 | 0.84 | 3.29 | 1.61 |
time (sec) |
N/A | 0.000 | 0.310 | 23.286 | 0.269 | 0.233 | 0.111 | 0.292 | 0.506 |
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 | 22 | 87 | 22 | 70 | 59 | 59 | 78 | 59 | 63 |
N.S. |
1 | 3.95 | 1.00 | 3.18 | 2.68 | 2.68 | 3.55 | 2.68 | 2.86 |
time (sec) |
N/A | 0.015 | 0.014 | 0.903 | 0.189 | 0.252 | 0.033 | 0.262 | 11.014 |
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 | 20 | 8 | 8 | 16 | 7 | 7 | 7 | 7 |
N.S. |
1 | 1.33 | 0.53 | 0.53 | 1.07 | 0.47 | 0.47 | 0.47 | 0.47 |
time (sec) |
N/A | 0.006 | 0.002 | 0.088 | 0.192 | 0.248 | 0.050 | 0.258 | 0.024 |
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 | 29 | 0 | 33 | 29 | 33 | 28 | 0 | 33 | 38 |
N.S. |
1 | 0.00 | 1.14 | 1.00 | 1.14 | 0.97 | 0.00 | 1.14 | 1.31 |
time (sec) |
N/A | 0.000 | 3.121 | 1.586 | 0.310 | 0.258 | 0.000 | 0.315 | 11.969 |
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 | 31 | 49 | 49 | 47 | 47 | 47 | 44 | 59 | 61 |
N.S. |
1 | 1.58 | 1.58 | 1.52 | 1.52 | 1.52 | 1.42 | 1.90 | 1.97 |
time (sec) |
N/A | 0.028 | 0.149 | 0.663 | 0.204 | 0.285 | 0.098 | 0.264 | 0.117 |
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 | 20 | 25 | 23 | 22 | 0 | 22 | 22 | 21 | 30 |
N.S. |
1 | 1.25 | 1.15 | 1.10 | 0.00 | 1.10 | 1.10 | 1.05 | 1.50 |
time (sec) |
N/A | 0.326 | 0.050 | 1.857 | 0.000 | 0.261 | 0.212 | 0.288 | 11.406 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 18 | 18 | 17 | 18 | 20 | 19 | 18 | 16 |
N.S. |
1 | 0.78 | 0.78 | 0.74 | 0.78 | 0.87 | 0.83 | 0.78 | 0.70 |
time (sec) |
N/A | 0.187 | 0.164 | 0.532 | 0.248 | 0.246 | 0.100 | 0.264 | 10.874 |
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 | 22 | 27 | 24 | 50 | 86 | 49 | 54 | 53 | 49 |
N.S. |
1 | 1.23 | 1.09 | 2.27 | 3.91 | 2.23 | 2.45 | 2.41 | 2.23 |
time (sec) |
N/A | 0.275 | 0.024 | 3.302 | 0.323 | 0.246 | 0.160 | 0.281 | 11.545 |
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 | 17 | 13 | 16 | 16 | 12 | 12 | 12 |
N.S. |
1 | 0.00 | 0.81 | 0.62 | 0.76 | 0.76 | 0.57 | 0.57 | 0.57 |
time (sec) |
N/A | 0.000 | 0.215 | 0.360 | 0.228 | 0.274 | 0.074 | 0.261 | 9.970 |
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 | 24 | 160 | 152 | 82 | 135 | 77 | 87 | 94 | 35 |
N.S. |
1 | 6.67 | 6.33 | 3.42 | 5.62 | 3.21 | 3.62 | 3.92 | 1.46 |
time (sec) |
N/A | 0.128 | 0.167 | 0.959 | 0.195 | 0.265 | 0.158 | 0.261 | 10.262 |
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 | 18 | 0 | 19 | 36 | 44 | 44 | 42 | 87 | 50 |
N.S. |
1 | 0.00 | 1.06 | 2.00 | 2.44 | 2.44 | 2.33 | 4.83 | 2.78 |
time (sec) |
N/A | 0.000 | 0.090 | 0.454 | 0.253 | 0.267 | 0.093 | 0.264 | 10.335 |
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 | 19 | 19 | 19 | 19 | 19 | 19 | 19 | 19 |
N.S. |
1 | 0.66 | 0.66 | 0.66 | 0.66 | 0.66 | 0.66 | 0.66 | 0.66 |
time (sec) |
N/A | 0.002 | 0.000 | 0.487 | 0.184 | 0.271 | 0.019 | 0.256 | 0.035 |
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 | 19 | 62 | 21 | 48 | 45 | 45 | 54 | 62 | 43 |
N.S. |
1 | 3.26 | 1.11 | 2.53 | 2.37 | 2.37 | 2.84 | 3.26 | 2.26 |
time (sec) |
N/A | 0.139 | 0.033 | 1.172 | 0.273 | 0.257 | 0.103 | 0.247 | 10.341 |
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 | 22 | 21 | 21 | 20 | 19 | 21 | 14 | 54 | 19 |
N.S. |
1 | 0.95 | 0.95 | 0.91 | 0.86 | 0.95 | 0.64 | 2.45 | 0.86 |
time (sec) |
N/A | 0.263 | 0.179 | 3.243 | 0.239 | 0.268 | 0.093 | 0.264 | 10.342 |
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 | 47 | 27 | 44 | 36 | 48 | 39 | 48 | 33 |
N.S. |
1 | 1.81 | 1.04 | 1.69 | 1.38 | 1.85 | 1.50 | 1.85 | 1.27 |
time (sec) |
N/A | 0.019 | 0.074 | 2.101 | 0.201 | 0.246 | 0.114 | 0.241 | 0.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 16 | 34 | 30 | 48 | 44 | 149 | 153 |
N.S. |
1 | 0.00 | 0.84 | 1.79 | 1.58 | 2.53 | 2.32 | 7.84 | 8.05 |
time (sec) |
N/A | 0.000 | 0.887 | 3.044 | 0.386 | 0.247 | 0.138 | 0.263 | 10.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 43 | 41 | 39 | 89 | 46 | 34 | 50 | 46 |
N.S. |
1 | 1.65 | 1.58 | 1.50 | 3.42 | 1.77 | 1.31 | 1.92 | 1.77 |
time (sec) |
N/A | 0.943 | 0.238 | 1.806 | 0.234 | 0.256 | 0.106 | 0.277 | 10.387 |
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 | 21 | 12 | 15 | 15 |
N.S. |
1 | 0.79 | 0.79 | 0.84 | 0.79 | 1.11 | 0.63 | 0.79 | 0.79 |
time (sec) |
N/A | 0.136 | 0.010 | 1.884 | 0.223 | 0.249 | 0.043 | 0.257 | 0.153 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 893 | 535 | 81 | 196 | 172 | 207 | 80 | 0 |
N.S. |
1 | 38.83 | 23.26 | 3.52 | 8.52 | 7.48 | 9.00 | 3.48 | 0.00 |
time (sec) |
N/A | 1.186 | 1.836 | 3.353 | 0.219 | 0.262 | 14.375 | 0.310 | 0.000 |
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 | 26 | 23 | 52 | 56 | 31 | 60 | 54 |
N.S. |
1 | 0.00 | 0.96 | 0.85 | 1.93 | 2.07 | 1.15 | 2.22 | 2.00 |
time (sec) |
N/A | 0.000 | 0.554 | 1.142 | 0.312 | 0.244 | 0.085 | 0.261 | 0.588 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 30 | 40 | 32 | 3007 | 41 | 42 | 32 | 44 | 36 |
N.S. |
1 | 1.33 | 1.07 | 100.23 | 1.37 | 1.40 | 1.07 | 1.47 | 1.20 |
time (sec) |
N/A | 0.202 | 0.119 | 1.506 | 0.270 | 0.272 | 159.821 | 0.688 | 10.835 |
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 | 27 | 21 | 21 | 18 | 23 | 17 | 19 | 0 | 17 |
N.S. |
1 | 0.78 | 0.78 | 0.67 | 0.85 | 0.63 | 0.70 | 0.00 | 0.63 |
time (sec) |
N/A | 0.103 | 0.190 | 19.446 | 0.313 | 0.263 | 0.224 | 0.000 | 9.475 |
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 | 30 | 31 | 22 | 33 | 19 | 20 | 30 | 19 |
N.S. |
1 | 1.11 | 1.15 | 0.81 | 1.22 | 0.70 | 0.74 | 1.11 | 0.70 |
time (sec) |
N/A | 0.270 | 0.058 | 1.463 | 0.315 | 0.248 | 0.150 | 0.267 | 9.352 |
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 | 20 | 13 | 13 | 13 | 38 | 12 | 14 | 12 | 12 |
N.S. |
1 | 0.65 | 0.65 | 0.65 | 1.90 | 0.60 | 0.70 | 0.60 | 0.60 |
time (sec) |
N/A | 1.131 | 0.359 | 0.987 | 0.315 | 0.260 | 0.128 | 0.268 | 9.263 |
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 | 20 | 20 | 20 | 18 | 28 | 24 | 31 | 28 | 40 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 1.40 | 1.20 | 1.55 | 1.40 | 2.00 |
time (sec) |
N/A | 0.113 | 0.018 | 4.263 | 0.219 | 0.258 | 0.070 | 0.254 | 9.651 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 39 | 29 | 40 | 108 | 55 | 65 | 56 | 57 |
N.S. |
1 | 1.44 | 1.07 | 1.48 | 4.00 | 2.04 | 2.41 | 2.07 | 2.11 |
time (sec) |
N/A | 0.618 | 0.190 | 4.655 | 0.225 | 0.252 | 0.068 | 0.250 | 9.125 |
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 | 32 | 22 | 35 | 21 | 19 | 28 | 22 |
N.S. |
1 | 0.00 | 1.07 | 0.73 | 1.17 | 0.70 | 0.63 | 0.93 | 0.73 |
time (sec) |
N/A | 0.000 | 1.532 | 2.310 | 0.229 | 0.256 | 0.083 | 0.265 | 0.106 |
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 | 26 | 27 | 26 | 26 | 24 | 26 | 26 |
N.S. |
1 | 0.00 | 1.53 | 1.59 | 1.53 | 1.53 | 1.41 | 1.53 | 1.53 |
time (sec) |
N/A | 0.000 | 0.692 | 2.268 | 0.215 | 0.245 | 0.093 | 0.252 | 9.368 |
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 | 22 | 0 | 0 | 87 | 111 | 82 | 87 | 111 | 0 |
N.S. |
1 | 0.00 | 0.00 | 3.95 | 5.05 | 3.73 | 3.95 | 5.05 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 42.798 | 0.603 | 0.247 | 0.388 | 0.384 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | F(-2) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 29 | 29 | 50 | 52 | 0 | 29 | 29 |
N.S. |
1 | 0.00 | 0.97 | 0.97 | 1.67 | 1.73 | 0.00 | 0.97 | 0.97 |
time (sec) |
N/A | 0.000 | 3.684 | 2.454 | 0.219 | 0.253 | 0.000 | 0.252 | 9.272 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 18 | 18 | 18 | 22 | 19 | 14 | 19 | 19 |
N.S. |
1 | 0.82 | 0.82 | 0.82 | 1.00 | 0.86 | 0.64 | 0.86 | 0.86 |
time (sec) |
N/A | 0.026 | 0.016 | 0.897 | 0.214 | 0.270 | 0.041 | 0.246 | 0.069 |
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 | 20 | 24 | 30 | 28 | 24 | 28 | 23 |
N.S. |
1 | 0.00 | 0.95 | 1.14 | 1.43 | 1.33 | 1.14 | 1.33 | 1.10 |
time (sec) |
N/A | 0.000 | 0.242 | 2.916 | 0.319 | 0.250 | 0.075 | 0.280 | 9.473 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 23 | 29 | 0 | 77 | 26 | 0 | 40 |
N.S. |
1 | 0.00 | 0.79 | 1.00 | 0.00 | 2.66 | 0.90 | 0.00 | 1.38 |
time (sec) |
N/A | 0.000 | 5.219 | 15.779 | 0.000 | 0.254 | 0.517 | 0.000 | 9.300 |
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 | 26 | 0 | 45 | 56 | 75 | 31 | 66 | 56 | 71 |
N.S. |
1 | 0.00 | 1.73 | 2.15 | 2.88 | 1.19 | 2.54 | 2.15 | 2.73 |
time (sec) |
N/A | 0.000 | 0.963 | 3.943 | 0.320 | 0.254 | 0.420 | 0.300 | 10.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 24 | 25 | 291 | 24 | 0 | 0 | 24 |
N.S. |
1 | 0.00 | 0.92 | 0.96 | 11.19 | 0.92 | 0.00 | 0.00 | 0.92 |
time (sec) |
N/A | 0.000 | 1.689 | 11.396 | 0.393 | 0.248 | 0.000 | 0.000 | 9.089 |
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 | 21 | 20 | 20 | 24 | 20 | 20 |
N.S. |
1 | 0.00 | 0.92 | 0.81 | 0.77 | 0.77 | 0.92 | 0.77 | 0.77 |
time (sec) |
N/A | 0.000 | 0.459 | 90.109 | 0.623 | 0.263 | 0.311 | 0.268 | 8.988 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 36 | 46 | 53 | 56 | 0 | 0 | 50 |
N.S. |
1 | 0.00 | 1.06 | 1.35 | 1.56 | 1.65 | 0.00 | 0.00 | 1.47 |
time (sec) |
N/A | 0.000 | 0.370 | 0.829 | 0.434 | 0.252 | 0.000 | 0.000 | 10.724 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | A | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 318 | 32 | 30 | 32 | 81 | 54 | 0 | 38 |
N.S. |
1 | 12.23 | 1.23 | 1.15 | 1.23 | 3.12 | 2.08 | 0.00 | 1.46 |
time (sec) |
N/A | 0.750 | 0.185 | 5.974 | 0.319 | 0.250 | 0.164 | 0.000 | 12.435 |
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 | 25 | 119 | 15 | 19 | 86 | 30 | 12 | 18 | 18 |
N.S. |
1 | 4.76 | 0.60 | 0.76 | 3.44 | 1.20 | 0.48 | 0.72 | 0.72 |
time (sec) |
N/A | 0.211 | 0.127 | 0.504 | 0.479 | 0.251 | 0.061 | 0.249 | 12.149 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 115 | 53 | 49 | 86 | 34 | 39 | 42 | 47 |
N.S. |
1 | 4.42 | 2.04 | 1.88 | 3.31 | 1.31 | 1.50 | 1.62 | 1.81 |
time (sec) |
N/A | 0.329 | 0.094 | 1.871 | 0.243 | 0.240 | 0.125 | 0.254 | 12.175 |
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 | 34 | 0 | 36 | 31 | 0 | 50 | 51 | 57 | 143 |
N.S. |
1 | 0.00 | 1.06 | 0.91 | 0.00 | 1.47 | 1.50 | 1.68 | 4.21 |
time (sec) |
N/A | 0.000 | 0.286 | 3.323 | 0.000 | 0.246 | 0.380 | 1.108 | 12.428 |
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 | 14 | 14 | 13 | 12 | 12 | 10 | 12 | 12 |
N.S. |
1 | 0.64 | 0.64 | 0.59 | 0.55 | 0.55 | 0.45 | 0.55 | 0.55 |
time (sec) |
N/A | 0.016 | 0.016 | 0.431 | 0.227 | 0.251 | 0.070 | 0.252 | 11.838 |
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 | 32 | 0 | 32 | 33 | 36 | 35 | 29 | 39 | 35 |
N.S. |
1 | 0.00 | 1.00 | 1.03 | 1.12 | 1.09 | 0.91 | 1.22 | 1.09 |
time (sec) |
N/A | 0.000 | 0.086 | 299.454 | 0.374 | 0.241 | 4.179 | 0.665 | 14.069 |
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 | 15 | 17 | 17 | 14 | 17 | 15 |
N.S. |
1 | 0.68 | 0.68 | 0.68 | 0.77 | 0.77 | 0.64 | 0.77 | 0.68 |
time (sec) |
N/A | 0.005 | 0.004 | 0.388 | 0.200 | 0.251 | 0.057 | 0.250 | 11.950 |
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 | 29 | 27 | 26 | 15 | 14 | 14 | 27 | 14 | 14 |
N.S. |
1 | 0.93 | 0.90 | 0.52 | 0.48 | 0.48 | 0.93 | 0.48 | 0.48 |
time (sec) |
N/A | 0.002 | 0.004 | 0.457 | 0.183 | 0.242 | 0.030 | 0.251 | 0.086 |
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 | 22 | 21 | 21 | 19 | 22 | 22 | 14 | 72 | 18 |
N.S. |
1 | 0.95 | 0.95 | 0.86 | 1.00 | 1.00 | 0.64 | 3.27 | 0.82 |
time (sec) |
N/A | 0.029 | 0.085 | 1.798 | 0.220 | 0.248 | 0.046 | 0.240 | 11.926 |
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 | 26 | 26 | 25 | 38 | 33 | 27 | 23 | 23 |
N.S. |
1 | 1.08 | 1.08 | 1.04 | 1.58 | 1.38 | 1.12 | 0.96 | 0.96 |
time (sec) |
N/A | 0.042 | 0.010 | 0.172 | 0.192 | 0.258 | 0.064 | 0.248 | 11.992 |
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 | 85 | 50 | 48 | 44 | 53 | 52 | 68 |
N.S. |
1 | 2.45 | 3.86 | 2.27 | 2.18 | 2.00 | 2.41 | 2.36 | 3.09 |
time (sec) |
N/A | 0.096 | 0.068 | 0.589 | 0.189 | 0.257 | 1.646 | 0.257 | 0.215 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 111 | 28 | 43 | 85 | 31 | 49 | 58 | 61 |
N.S. |
1 | 4.27 | 1.08 | 1.65 | 3.27 | 1.19 | 1.88 | 2.23 | 2.35 |
time (sec) |
N/A | 1.065 | 0.086 | 3.540 | 0.236 | 0.257 | 0.375 | 0.275 | 12.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 14 | 12 | 13 | 12 | 16 | 8 | 13 | 12 |
N.S. |
1 | 0.93 | 0.80 | 0.87 | 0.80 | 1.07 | 0.53 | 0.87 | 0.80 |
time (sec) |
N/A | 0.016 | 0.012 | 0.287 | 0.175 | 0.240 | 0.039 | 0.246 | 0.055 |
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 | 17 | 29 | 16 | 20 | 27 | 14 | 20 | 17 |
N.S. |
1 | 0.65 | 1.12 | 0.62 | 0.77 | 1.04 | 0.54 | 0.77 | 0.65 |
time (sec) |
N/A | 0.013 | 0.014 | 2.204 | 0.184 | 0.236 | 0.068 | 0.243 | 11.957 |
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 | 10 | 10 | 12 | 9 | 14 | 9 | 9 |
N.S. |
1 | 0.00 | 0.71 | 0.71 | 0.86 | 0.64 | 1.00 | 0.64 | 0.64 |
time (sec) |
N/A | 0.000 | 0.026 | 0.829 | 0.235 | 0.246 | 0.097 | 0.259 | 12.241 |
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 | 28 | 15 | 16 | 53 | 16 | 15 | 16 | 14 |
N.S. |
1 | 1.87 | 1.00 | 1.07 | 3.53 | 1.07 | 1.00 | 1.07 | 0.93 |
time (sec) |
N/A | 0.047 | 0.068 | 1.217 | 0.187 | 0.243 | 0.046 | 0.237 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 26 | 27 | 84 | 31 | 29 | 53 | 31 |
N.S. |
1 | 0.00 | 0.87 | 0.90 | 2.80 | 1.03 | 0.97 | 1.77 | 1.03 |
time (sec) |
N/A | 0.000 | 0.159 | 13.167 | 0.339 | 0.251 | 0.487 | 0.595 | 13.367 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | A | A | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 29 | 173 | 55 | 46 | 24 | 67 | 167 |
N.S. |
1 | 0.00 | 0.97 | 5.77 | 1.83 | 1.53 | 0.80 | 2.23 | 5.57 |
time (sec) |
N/A | 0.000 | 0.112 | 36.961 | 0.243 | 0.251 | 0.453 | 0.477 | 13.803 |
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 | 12 | 26 | 12 | 26 | 25 | 25 | 29 | 25 | 25 |
N.S. |
1 | 2.17 | 1.00 | 2.17 | 2.08 | 2.08 | 2.42 | 2.08 | 2.08 |
time (sec) |
N/A | 0.045 | 0.230 | 1.181 | 0.230 | 0.249 | 0.087 | 0.264 | 11.993 |
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 | 19 | 27 | 26 | 25 | 50 | 24 | 22 | 24 | 24 |
N.S. |
1 | 1.42 | 1.37 | 1.32 | 2.63 | 1.26 | 1.16 | 1.26 | 1.26 |
time (sec) |
N/A | 0.276 | 0.041 | 1.797 | 0.188 | 0.262 | 0.077 | 0.268 | 12.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 31 | 37 | 19 | 347 | 18 | 15 | 282 | 0 |
N.S. |
1 | 1.72 | 2.06 | 1.06 | 19.28 | 1.00 | 0.83 | 15.67 | 0.00 |
time (sec) |
N/A | 0.175 | 0.059 | 4.003 | 0.279 | 0.260 | 0.143 | 0.382 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | B | B | B | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 65 | 106 | 61 | 61 | 249 | 81 |
N.S. |
1 | 0.00 | 0.00 | 2.17 | 3.53 | 2.03 | 2.03 | 8.30 | 2.70 |
time (sec) |
N/A | 0.000 | 0.000 | 28.006 | 0.711 | 0.245 | 0.632 | 0.512 | 15.474 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 25 | 28 | 26 | 26 | 28 | 21 |
N.S. |
1 | 0.00 | 1.00 | 1.04 | 1.17 | 1.08 | 1.08 | 1.17 | 0.88 |
time (sec) |
N/A | 0.000 | 0.377 | 1.604 | 0.322 | 0.259 | 0.128 | 0.269 | 13.970 |
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 | 39 | 99 | 54 | 42 | 0 | 47 | 41 | 65 | 57 |
N.S. |
1 | 2.54 | 1.38 | 1.08 | 0.00 | 1.21 | 1.05 | 1.67 | 1.46 |
time (sec) |
N/A | 6.762 | 1.413 | 0.511 | 0.000 | 0.272 | 0.131 | 0.258 | 0.240 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 59 | 45 | 40 | 53 | 43 | 39 | 45 | 41 |
N.S. |
1 | 2.57 | 1.96 | 1.74 | 2.30 | 1.87 | 1.70 | 1.96 | 1.78 |
time (sec) |
N/A | 0.166 | 0.230 | 1.038 | 0.182 | 0.246 | 0.077 | 0.251 | 13.482 |
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 | 29 | 0 | 33 | 38 | 147 | 145 | 219 | 199 | 0 |
N.S. |
1 | 0.00 | 1.14 | 1.31 | 5.07 | 5.00 | 7.55 | 6.86 | 0.00 |
time (sec) |
N/A | 0.000 | 1.003 | 7.930 | 1.249 | 0.259 | 0.553 | 0.717 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 82 | 38 | 170 | 59 | 34 | 0 | 107 |
N.S. |
1 | 0.00 | 2.56 | 1.19 | 5.31 | 1.84 | 1.06 | 0.00 | 3.34 |
time (sec) |
N/A | 0.000 | 0.463 | 41.535 | 0.496 | 0.271 | 0.576 | 0.000 | 13.199 |
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 | 22 | 21 | 18 | 24 | 60 | 16 |
N.S. |
1 | 0.00 | 1.00 | 1.22 | 1.17 | 1.00 | 1.33 | 3.33 | 0.89 |
time (sec) |
N/A | 0.000 | 0.069 | 1.533 | 0.234 | 0.250 | 0.124 | 0.250 | 13.078 |
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 | 20 | 54 | 23 | 47 | 46 | 46 | 48 | 47 | 22 |
N.S. |
1 | 2.70 | 1.15 | 2.35 | 2.30 | 2.30 | 2.40 | 2.35 | 1.10 |
time (sec) |
N/A | 0.036 | 0.073 | 0.363 | 0.192 | 0.255 | 0.052 | 0.249 | 0.090 |
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 | 12 | 12 | 10 | 9 | 9 | 8 | 9 | 8 |
N.S. |
1 | 0.92 | 0.92 | 0.77 | 0.69 | 0.69 | 0.62 | 0.69 | 0.62 |
time (sec) |
N/A | 0.002 | 0.000 | 0.258 | 0.189 | 0.241 | 0.016 | 0.255 | 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 | 19 | 12 | 12 | 13 | 14 | 14 | 15 | 15 | 12 |
N.S. |
1 | 0.63 | 0.63 | 0.68 | 0.74 | 0.74 | 0.79 | 0.79 | 0.63 |
time (sec) |
N/A | 0.003 | 0.002 | 0.461 | 0.187 | 0.236 | 0.037 | 0.249 | 0.053 |
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 | 9 | 8 | 8 | 7 | 8 | 8 |
N.S. |
1 | 0.79 | 0.79 | 0.64 | 0.57 | 0.57 | 0.50 | 0.57 | 0.57 |
time (sec) |
N/A | 0.002 | 0.004 | 0.309 | 0.187 | 0.247 | 0.031 | 0.245 | 12.868 |
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 | 15 | 18 | 17 | 14 | 16 | 12 | 15 | 14 |
N.S. |
1 | 0.60 | 0.72 | 0.68 | 0.56 | 0.64 | 0.48 | 0.60 | 0.56 |
time (sec) |
N/A | 0.005 | 0.006 | 0.571 | 0.181 | 0.244 | 0.055 | 0.253 | 0.042 |
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 | 22 | 55 | 41 | 29 | 38 | 29 | 41 | 37 | 19 |
N.S. |
1 | 2.50 | 1.86 | 1.32 | 1.73 | 1.32 | 1.86 | 1.68 | 0.86 |
time (sec) |
N/A | 0.013 | 0.008 | 0.316 | 0.180 | 0.246 | 0.070 | 0.248 | 12.670 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 33 | 41 | 162 | 91 | 58 | 130 | 44 |
N.S. |
1 | 0.00 | 1.38 | 1.71 | 6.75 | 3.79 | 2.42 | 5.42 | 1.83 |
time (sec) |
N/A | 0.000 | 5.084 | 6.234 | 0.292 | 0.269 | 0.527 | 0.272 | 13.018 |
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 | 27 | 0 | 36 | 34 | 53 | 53 | 0 | 34 | 92 |
N.S. |
1 | 0.00 | 1.33 | 1.26 | 1.96 | 1.96 | 0.00 | 1.26 | 3.41 |
time (sec) |
N/A | 0.000 | 0.053 | 2.813 | 0.305 | 0.262 | 0.000 | 0.267 | 14.569 |
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 | 19 | 20 | 17 | 17 | 14 | 21 | 30 |
N.S. |
1 | 0.00 | 0.86 | 0.91 | 0.77 | 0.77 | 0.64 | 0.95 | 1.36 |
time (sec) |
N/A | 0.000 | 0.162 | 6.986 | 0.311 | 0.243 | 0.054 | 0.261 | 14.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 45 | 19 | 20 | 17 | 26 | 20 | 0 | 17 |
N.S. |
1 | 2.14 | 0.90 | 0.95 | 0.81 | 1.24 | 0.95 | 0.00 | 0.81 |
time (sec) |
N/A | 0.453 | 0.098 | 3.120 | 0.323 | 0.271 | 0.106 | 0.000 | 13.512 |
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 | 17 | 0 | 16 | 15 | 22 | 22 | 22 | 0 | 27 |
N.S. |
1 | 0.00 | 0.94 | 0.88 | 1.29 | 1.29 | 1.29 | 0.00 | 1.59 |
time (sec) |
N/A | 0.000 | 1.927 | 0.987 | 0.698 | 0.243 | 0.099 | 0.000 | 13.374 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 83 | 30 | 42 | 369 | 63 | 60 | 76 | 22 |
N.S. |
1 | 3.19 | 1.15 | 1.62 | 14.19 | 2.42 | 2.31 | 2.92 | 0.85 |
time (sec) |
N/A | 0.329 | 0.073 | 0.891 | 0.206 | 0.245 | 0.173 | 0.257 | 10.203 |
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 | 12 | 12 | 11 | 10 | 12 | 12 | 10 | 10 |
N.S. |
1 | 0.57 | 0.57 | 0.52 | 0.48 | 0.57 | 0.57 | 0.48 | 0.48 |
time (sec) |
N/A | 0.120 | 0.068 | 1.099 | 0.226 | 0.242 | 0.070 | 0.246 | 10.593 |