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 | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 21 | 28 | 24 | 26 | 24 | 28 | 22 |
N.S. |
1 | 0.00 | 1.00 | 1.33 | 1.14 | 1.24 | 1.14 | 1.33 | 1.05 |
time (sec) |
N/A | 0.000 | 0.212 | 0.115 | 0.270 | 0.254 | 0.138 | 0.282 | 8.671 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | F | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 130 | 227 | 0 | 169 | 212 | 759 | 269 |
N.S. |
1 | 0.00 | 5.00 | 8.73 | 0.00 | 6.50 | 8.15 | 29.19 | 10.35 |
time (sec) |
N/A | 0.000 | 0.292 | 0.126 | 0.000 | 0.253 | 0.350 | 0.301 | 12.201 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 4 | 4 | 5 | 4 | 4 | 3 | 5 | 4 |
N.S. |
1 | 0.40 | 0.40 | 0.50 | 0.40 | 0.40 | 0.30 | 0.50 | 0.40 |
time (sec) |
N/A | 0.001 | 0.001 | 0.014 | 0.182 | 0.240 | 0.025 | 0.250 | 0.015 |
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 | 19 | 129 | 34 | 32 | 136 | 31 | 27 | 31 | 23 |
N.S. |
1 | 6.79 | 1.79 | 1.68 | 7.16 | 1.63 | 1.42 | 1.63 | 1.21 |
time (sec) |
N/A | 0.386 | 0.103 | 0.163 | 0.702 | 0.257 | 0.069 | 0.306 | 8.609 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 31 | 38 | 77 | 77 | 42 | 49 | 259 |
N.S. |
1 | 0.00 | 1.03 | 1.27 | 2.57 | 2.57 | 1.40 | 1.63 | 8.63 |
time (sec) |
N/A | 0.000 | 0.072 | 1.041 | 0.248 | 0.261 | 0.114 | 0.322 | 8.494 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 23 | 51 | 25 | 36 | 54 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 2.12 | 1.04 | 1.50 | 2.25 | 0.00 |
time (sec) |
N/A | 0.000 | 0.145 | 0.233 | 0.375 | 0.258 | 0.255 | 0.250 | 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 | 29 | 30 | 37 | 28 | 49 | 31 | 24 | 34 | 30 |
N.S. |
1 | 1.03 | 1.28 | 0.97 | 1.69 | 1.07 | 0.83 | 1.17 | 1.03 |
time (sec) |
N/A | 0.035 | 0.013 | 0.083 | 0.187 | 0.243 | 0.133 | 0.255 | 8.396 |
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 | 25 | 23 | 26 | 36 | 27 | 38 | 100 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 1.04 | 1.44 | 1.08 | 1.52 | 4.00 |
time (sec) |
N/A | 0.000 | 0.258 | 0.400 | 0.235 | 0.267 | 0.087 | 0.272 | 9.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 30 | 20 | 43 | 17 | 43 | 20 |
N.S. |
1 | 1.00 | 1.00 | 1.36 | 0.91 | 1.95 | 0.77 | 1.95 | 0.91 |
time (sec) |
N/A | 0.036 | 0.031 | 0.128 | 0.181 | 0.278 | 0.109 | 0.255 | 8.746 |
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 | 28 | 0 | 21 | 20 | 25 | 19 | 17 | 18 | 17 |
N.S. |
1 | 0.00 | 0.75 | 0.71 | 0.89 | 0.68 | 0.61 | 0.64 | 0.61 |
time (sec) |
N/A | 0.000 | 0.249 | 0.280 | 0.210 | 0.259 | 0.174 | 0.253 | 8.579 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 22 | 28 | 60 | 24 | 24 | 0 | 0 |
N.S. |
1 | 0.00 | 0.85 | 1.08 | 2.31 | 0.92 | 0.92 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.684 | 7.020 | 0.270 | 0.258 | 0.161 | 0.000 | 0.000 |
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 | 23 | 30 | 26 | 24 | 25 | 25 | 41 | 25 | 20 |
N.S. |
1 | 1.30 | 1.13 | 1.04 | 1.09 | 1.09 | 1.78 | 1.09 | 0.87 |
time (sec) |
N/A | 0.007 | 0.003 | 0.033 | 0.176 | 0.248 | 0.022 | 0.246 | 8.399 |
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 | 22 | 21 | 21 | 19 | 21 | 59 |
N.S. |
1 | 0.00 | 1.00 | 0.92 | 0.88 | 0.88 | 0.79 | 0.88 | 2.46 |
time (sec) |
N/A | 0.000 | 0.865 | 0.358 | 0.212 | 0.249 | 0.106 | 0.261 | 8.596 |
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 | 31 | 0 | 0 | 129 | 70 | 108 | 110 | 622 | 0 |
N.S. |
1 | 0.00 | 0.00 | 4.16 | 2.26 | 3.48 | 3.55 | 20.06 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.017 | 0.998 | 0.263 | 2.842 | 0.343 | 0.000 |
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 | 18 | 18 | 17 | 0 | 14 | 15 | 27 | 17 |
N.S. |
1 | 0.90 | 0.90 | 0.85 | 0.00 | 0.70 | 0.75 | 1.35 | 0.85 |
time (sec) |
N/A | 0.012 | 0.024 | 0.046 | 0.000 | 0.260 | 0.077 | 0.247 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 90 | 57 | 58 | 147 | 64 | 63 | 57 | 62 |
N.S. |
1 | 2.73 | 1.73 | 1.76 | 4.45 | 1.94 | 1.91 | 1.73 | 1.88 |
time (sec) |
N/A | 0.409 | 0.115 | 0.086 | 0.235 | 0.251 | 0.170 | 0.251 | 8.388 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 38 | 36 | 74 | 40 | 41 | 0 | 138 |
N.S. |
1 | 0.00 | 1.52 | 1.44 | 2.96 | 1.60 | 1.64 | 0.00 | 5.52 |
time (sec) |
N/A | 0.000 | 0.483 | 3.915 | 0.323 | 0.275 | 0.200 | 0.000 | 8.897 |
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 | 29 | 0 | 30 | 31 | 26 | 31 | 24 | 0 | 29 |
N.S. |
1 | 0.00 | 1.03 | 1.07 | 0.90 | 1.07 | 0.83 | 0.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.327 | 51.421 | 0.323 | 0.255 | 9.272 | 0.000 | 9.160 |
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 | 6 | 6 | 5 | 6 | 6 | 5 | 7 | 4 |
N.S. |
1 | 0.75 | 0.75 | 0.62 | 0.75 | 0.75 | 0.62 | 0.88 | 0.50 |
time (sec) |
N/A | 0.001 | 0.001 | 0.121 | 0.192 | 0.242 | 0.023 | 0.254 | 0.100 |
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 | 29 | 0 | 31 | 47 | 43 | 40 | 56 | 46 | 0 |
N.S. |
1 | 0.00 | 1.07 | 1.62 | 1.48 | 1.38 | 1.93 | 1.59 | 0.00 |
time (sec) |
N/A | 0.000 | 0.538 | 16.319 | 0.323 | 0.265 | 0.396 | 5.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | C | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 26 | 22 | 42 | 48 | 19 | 65 | 39 |
N.S. |
1 | 0.00 | 1.04 | 0.88 | 1.68 | 1.92 | 0.76 | 2.60 | 1.56 |
time (sec) |
N/A | 0.000 | 2.238 | 0.087 | 0.224 | 0.273 | 0.128 | 0.281 | 8.582 |
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 | 29 | 32 | 28 | 25 | 24 | 24 | 27 | 28 | 0 |
N.S. |
1 | 1.10 | 0.97 | 0.86 | 0.83 | 0.83 | 0.93 | 0.97 | 0.00 |
time (sec) |
N/A | 0.423 | 0.273 | 0.439 | 0.230 | 0.268 | 0.164 | 0.321 | 0.000 |
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 | 28 | 31 | 33 | 30 | 30 | 32 | 24 | 34 | 0 |
N.S. |
1 | 1.11 | 1.18 | 1.07 | 1.07 | 1.14 | 0.86 | 1.21 | 0.00 |
time (sec) |
N/A | 0.338 | 0.229 | 0.257 | 0.221 | 0.273 | 0.111 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 26 | 27 | 31 | 31 | 27 | 26 | 30 |
N.S. |
1 | 0.00 | 0.96 | 1.00 | 1.15 | 1.15 | 1.00 | 0.96 | 1.11 |
time (sec) |
N/A | 0.000 | 0.240 | 0.261 | 0.206 | 0.264 | 0.117 | 0.247 | 8.700 |
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 | 21 | 25 | 52 | 17 | 15 | 15 | 63 | 19 | 19 |
N.S. |
1 | 1.19 | 2.48 | 0.81 | 0.71 | 0.71 | 3.00 | 0.90 | 0.90 |
time (sec) |
N/A | 0.039 | 0.035 | 0.183 | 0.191 | 0.266 | 4.038 | 0.252 | 8.577 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F(-1) | A | C | B | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 74 | 83 | 23 | 0 | 0 | 42 |
N.S. |
1 | 0.00 | 1.00 | 2.96 | 3.32 | 0.92 | 0.00 | 0.00 | 1.68 |
time (sec) |
N/A | 0.000 | 0.442 | 0.331 | 0.391 | 0.261 | 0.000 | 0.000 | 9.505 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | F(-1) | B | A | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 173 | 46 | 0 | 74 | 42 | 42 | 0 | 87 |
N.S. |
1 | 6.65 | 1.77 | 0.00 | 2.85 | 1.62 | 1.62 | 0.00 | 3.35 |
time (sec) |
N/A | 0.373 | 2.194 | 0.000 | 0.403 | 0.269 | 16.753 | 0.000 | 9.009 |
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 | 15 | 17 | 14 | 13 | 13 | 12 | 15 | 15 |
N.S. |
1 | 0.56 | 0.63 | 0.52 | 0.48 | 0.48 | 0.44 | 0.56 | 0.56 |
time (sec) |
N/A | 0.223 | 0.059 | 0.205 | 0.224 | 0.248 | 0.065 | 0.248 | 8.443 |
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 | 29 | 31 | 39 | 30 | 27 | 29 | 50 |
N.S. |
1 | 0.00 | 1.21 | 1.29 | 1.62 | 1.25 | 1.12 | 1.21 | 2.08 |
time (sec) |
N/A | 0.000 | 1.498 | 4.713 | 0.284 | 0.264 | 0.424 | 0.462 | 9.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 49 | 22 | 18 | 69 | 31 | 22 | 27 | 21 |
N.S. |
1 | 2.23 | 1.00 | 0.82 | 3.14 | 1.41 | 1.00 | 1.23 | 0.95 |
time (sec) |
N/A | 0.157 | 0.330 | 0.045 | 0.244 | 0.260 | 0.059 | 0.254 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | F(-2) | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 43 | 59 | 63 | 49 | 0 | 53 | 87 |
N.S. |
1 | 0.00 | 1.48 | 2.03 | 2.17 | 1.69 | 0.00 | 1.83 | 3.00 |
time (sec) |
N/A | 0.000 | 0.132 | 0.278 | 0.221 | 0.257 | 0.000 | 0.310 | 8.571 |
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 | 23 | 36 | 36 | 17 | 22 | 22 |
N.S. |
1 | 0.00 | 0.96 | 0.85 | 1.33 | 1.33 | 0.63 | 0.81 | 0.81 |
time (sec) |
N/A | 0.000 | 0.180 | 0.253 | 0.213 | 0.253 | 0.054 | 0.250 | 8.950 |
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 | 27 | 1209 | 115 | 100 | 1976 | 94 | 107 | 141 | 107 |
N.S. |
1 | 44.78 | 4.26 | 3.70 | 73.19 | 3.48 | 3.96 | 5.22 | 3.96 |
time (sec) |
N/A | 1.370 | 0.101 | 0.353 | 0.313 | 0.260 | 0.221 | 0.284 | 8.963 |
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 | 27 | 21 | 42 | 36 | 15 | 42 | 22 |
N.S. |
1 | 0.00 | 1.12 | 0.88 | 1.75 | 1.50 | 0.62 | 1.75 | 0.92 |
time (sec) |
N/A | 0.000 | 3.725 | 0.185 | 0.230 | 0.264 | 0.081 | 0.256 | 8.932 |
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 | 31 | 43 | 37 | 42 | 37 | 42 | 160 |
N.S. |
1 | 0.00 | 1.29 | 1.79 | 1.54 | 1.75 | 1.54 | 1.75 | 6.67 |
time (sec) |
N/A | 0.000 | 0.525 | 0.403 | 0.216 | 0.258 | 0.154 | 0.244 | 9.172 |
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 | 108 | 108 | 94 | 360 | 100 | 112 | 381 | 93 |
N.S. |
1 | 4.50 | 4.50 | 3.92 | 15.00 | 4.17 | 4.67 | 15.88 | 3.88 |
time (sec) |
N/A | 1.339 | 0.723 | 0.129 | 0.208 | 0.260 | 0.193 | 0.266 | 0.467 |
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 | 28 | 0 | 40 | 41 | 46 | 46 | 36 | 50 | 32 |
N.S. |
1 | 0.00 | 1.43 | 1.46 | 1.64 | 1.64 | 1.29 | 1.79 | 1.14 |
time (sec) |
N/A | 0.000 | 4.504 | 0.296 | 0.286 | 0.276 | 0.188 | 0.333 | 9.024 |
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 | 21 | 60 | 30 | 28 | 40 | 27 | 29 | 27 | 24 |
N.S. |
1 | 2.86 | 1.43 | 1.33 | 1.90 | 1.29 | 1.38 | 1.29 | 1.14 |
time (sec) |
N/A | 0.021 | 0.045 | 0.041 | 0.198 | 0.266 | 0.090 | 0.240 | 8.913 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 15 | 14 | 14 | 12 | 14 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.93 | 0.93 | 0.80 | 0.93 | 1.00 |
time (sec) |
N/A | 0.175 | 0.064 | 0.156 | 0.231 | 0.261 | 0.069 | 0.256 | 0.215 |
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 | 21 | 22 | 41 | 27 | 24 | 31 | 32 |
N.S. |
1 | 0.00 | 0.91 | 0.96 | 1.78 | 1.17 | 1.04 | 1.35 | 1.39 |
time (sec) |
N/A | 0.000 | 10.641 | 0.160 | 0.230 | 0.254 | 0.103 | 0.346 | 9.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 17 | 17 | 16 | 15 | 15 | 12 | 18 | 15 |
N.S. |
1 | 0.52 | 0.52 | 0.48 | 0.45 | 0.45 | 0.36 | 0.55 | 0.45 |
time (sec) |
N/A | 0.025 | 0.015 | 0.196 | 0.186 | 0.253 | 0.096 | 0.260 | 9.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 11 | 15 | 12 | 11 | 17 | 7 | 11 | 11 |
N.S. |
1 | 0.55 | 0.75 | 0.60 | 0.55 | 0.85 | 0.35 | 0.55 | 0.55 |
time (sec) |
N/A | 0.006 | 0.009 | 0.223 | 0.189 | 0.250 | 0.033 | 0.246 | 0.039 |
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 | 14 | 13 | 13 | 14 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.81 | 0.81 | 0.88 | 0.81 | 0.81 |
time (sec) |
N/A | 0.045 | 0.044 | 0.050 | 0.231 | 0.275 | 0.109 | 0.248 | 9.271 |
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 | 17 | 16 | 16 | 17 | 16 | 16 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.94 | 0.94 | 1.00 | 0.94 | 0.94 |
time (sec) |
N/A | 0.000 | 0.129 | 0.049 | 0.217 | 0.254 | 0.115 | 0.245 | 8.970 |
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 | 30 | 34 | 34 | 35 | 47 | 45 | 34 | 35 | 0 |
N.S. |
1 | 1.13 | 1.13 | 1.17 | 1.57 | 1.50 | 1.13 | 1.17 | 0.00 |
time (sec) |
N/A | 0.286 | 0.072 | 1.233 | 0.316 | 0.271 | 0.591 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 28 | 20 | 18 | 19 | 19 | 17 | 24 | 17 |
N.S. |
1 | 1.17 | 0.83 | 0.75 | 0.79 | 0.79 | 0.71 | 1.00 | 0.71 |
time (sec) |
N/A | 0.036 | 0.058 | 0.122 | 0.203 | 0.248 | 0.087 | 0.242 | 0.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 25 | 25 | 21 | 20 | 20 | 17 | 20 | 17 |
N.S. |
1 | 0.89 | 0.89 | 0.75 | 0.71 | 0.71 | 0.61 | 0.71 | 0.61 |
time (sec) |
N/A | 0.033 | 0.017 | 0.139 | 0.193 | 0.248 | 0.058 | 0.243 | 9.182 |
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 | 38 | 0 | 55 | 52 | 60 | 68 | 54 | 62 | 191 |
N.S. |
1 | 0.00 | 1.45 | 1.37 | 1.58 | 1.79 | 1.42 | 1.63 | 5.03 |
time (sec) |
N/A | 0.000 | 0.187 | 3.391 | 0.284 | 0.272 | 0.206 | 0.373 | 9.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 7 | 7 | 7 | 6 | 6 | 3 | 6 | 6 |
N.S. |
1 | 0.78 | 0.78 | 0.78 | 0.67 | 0.67 | 0.33 | 0.67 | 0.67 |
time (sec) |
N/A | 0.002 | 0.001 | 0.040 | 0.183 | 0.250 | 0.028 | 0.244 | 0.017 |
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 | 27 | 1088 | 1529 | 380 | 1957 | 362 | 1402 | 508 | 0 |
N.S. |
1 | 40.30 | 56.63 | 14.07 | 72.48 | 13.41 | 51.93 | 18.81 | 0.00 |
time (sec) |
N/A | 3.145 | 4.351 | 0.471 | 0.408 | 0.283 | 2.958 | 0.293 | 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 | 25 | 32 | 34 | 27 | 36 | 36 | 29 | 36 | 27 |
N.S. |
1 | 1.28 | 1.36 | 1.08 | 1.44 | 1.44 | 1.16 | 1.44 | 1.08 |
time (sec) |
N/A | 0.006 | 0.005 | 0.030 | 0.188 | 0.259 | 0.022 | 0.242 | 0.087 |
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 | 16 | 39 | 13 | 13 | 12 | 12 | 15 | 32 | 11 |
N.S. |
1 | 2.44 | 0.81 | 0.81 | 0.75 | 0.75 | 0.94 | 2.00 | 0.69 |
time (sec) |
N/A | 0.008 | 0.029 | 0.105 | 0.202 | 0.272 | 0.095 | 0.241 | 9.388 |
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 | 27 | 23 | 23 | 23 | 37 | 27 | 37 | 54 | 20 |
N.S. |
1 | 0.85 | 0.85 | 0.85 | 1.37 | 1.00 | 1.37 | 2.00 | 0.74 |
time (sec) |
N/A | 0.035 | 0.023 | 0.139 | 0.210 | 0.263 | 0.081 | 0.251 | 9.207 |
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 | 28 | 0 | 0 | 68 | 75 | 72 | 68 | 70 | 0 |
N.S. |
1 | 0.00 | 0.00 | 2.43 | 2.68 | 2.57 | 2.43 | 2.50 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.308 | 0.322 | 0.282 | 0.501 | 0.576 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 31 | 136 | 153 | 132 | 134 | 165 | 8404 |
N.S. |
1 | 0.00 | 1.29 | 5.67 | 6.38 | 5.50 | 5.58 | 6.88 | 350.17 |
time (sec) |
N/A | 0.000 | 5.070 | 10.388 | 0.410 | 0.261 | 0.302 | 0.296 | 16.871 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 13 | 13 | 14 | 13 | 13 | 10 | 13 | 13 |
N.S. |
1 | 0.68 | 0.68 | 0.74 | 0.68 | 0.68 | 0.53 | 0.68 | 0.68 |
time (sec) |
N/A | 0.064 | 0.008 | 0.072 | 0.189 | 0.267 | 0.198 | 0.252 | 0.132 |
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 | 31 | 0 | 33 | 33 | 56 | 53 | 51 | 150 | 56 |
N.S. |
1 | 0.00 | 1.06 | 1.06 | 1.81 | 1.71 | 1.65 | 4.84 | 1.81 |
time (sec) |
N/A | 0.000 | 0.201 | 5.016 | 0.300 | 0.286 | 0.597 | 0.531 | 9.817 |
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 | 25 | 22 | 25 | 27 | 17 | 27 | 23 |
N.S. |
1 | 0.00 | 1.25 | 1.10 | 1.25 | 1.35 | 0.85 | 1.35 | 1.15 |
time (sec) |
N/A | 0.000 | 2.172 | 0.150 | 0.220 | 0.256 | 0.058 | 0.249 | 0.117 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 0 | 24 | 26 | 21 | 24 | 0 | 29 |
N.S. |
1 | 0.00 | 0.00 | 1.33 | 1.44 | 1.17 | 1.33 | 0.00 | 1.61 |
time (sec) |
N/A | 0.000 | 0.000 | 3.977 | 0.314 | 0.261 | 0.670 | 0.000 | 10.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 45 | 58 | 873 | 60 | 60 | 0 | 217 |
N.S. |
1 | 0.00 | 1.67 | 2.15 | 32.33 | 2.22 | 2.22 | 0.00 | 8.04 |
time (sec) |
N/A | 0.000 | 0.318 | 1.502 | 0.954 | 0.260 | 0.776 | 0.000 | 9.908 |
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 | 33 | 333 | 35 | 32 | 67 | 34 | 27 | 34 | 31 |
N.S. |
1 | 10.09 | 1.06 | 0.97 | 2.03 | 1.03 | 0.82 | 1.03 | 0.94 |
time (sec) |
N/A | 0.623 | 0.158 | 0.161 | 0.340 | 0.266 | 0.100 | 0.275 | 9.453 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | A | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 0 | 29 | 49 | 28 | 29 | 51 | 28 |
N.S. |
1 | 0.00 | 0.00 | 1.32 | 2.23 | 1.27 | 1.32 | 2.32 | 1.27 |
time (sec) |
N/A | 0.000 | 0.000 | 1.103 | 0.300 | 0.263 | 0.253 | 0.383 | 10.214 |
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 | 48 | 43 | 37 | 36 | 36 | 39 | 36 | 36 |
N.S. |
1 | 1.85 | 1.65 | 1.42 | 1.38 | 1.38 | 1.50 | 1.38 | 1.38 |
time (sec) |
N/A | 0.033 | 0.114 | 0.125 | 0.213 | 0.259 | 0.149 | 0.256 | 9.164 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 27 | 21 | 18 | 20 | 22 | 20 | 22 | 21 |
N.S. |
1 | 1.12 | 0.88 | 0.75 | 0.83 | 0.92 | 0.83 | 0.92 | 0.88 |
time (sec) |
N/A | 0.183 | 0.854 | 0.135 | 0.284 | 0.253 | 0.199 | 0.254 | 9.515 |
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 | 20 | 16 | 16 | 15 | 16 | 16 | 17 | 16 | 14 |
N.S. |
1 | 0.80 | 0.80 | 0.75 | 0.80 | 0.80 | 0.85 | 0.80 | 0.70 |
time (sec) |
N/A | 0.138 | 0.152 | 0.152 | 0.222 | 0.261 | 0.097 | 0.245 | 9.493 |
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 | 24 | 41 | 37 | 27 | 36 | 37 | 37 | 38 | 31 |
N.S. |
1 | 1.71 | 1.54 | 1.12 | 1.50 | 1.54 | 1.54 | 1.58 | 1.29 |
time (sec) |
N/A | 0.048 | 0.029 | 0.124 | 0.186 | 0.264 | 0.329 | 0.254 | 0.209 |
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 | 28 | 0 | 20 | 28 | 21 | 23 | 24 | 27 | 19 |
N.S. |
1 | 0.00 | 0.71 | 1.00 | 0.75 | 0.82 | 0.86 | 0.96 | 0.68 |
time (sec) |
N/A | 0.000 | 0.388 | 0.372 | 0.236 | 0.265 | 0.078 | 0.270 | 9.565 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | B | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 38 | 0 | 67 | 36 | 0 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.46 | 0.00 | 2.58 | 1.38 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.345 | 0.376 | 0.000 | 0.259 | 0.187 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 81 | 91 | 77 | 297 | 76 | 65 | 76 | 101 |
N.S. |
1 | 2.79 | 3.14 | 2.66 | 10.24 | 2.62 | 2.24 | 2.62 | 3.48 |
time (sec) |
N/A | 1.893 | 0.050 | 0.624 | 0.274 | 0.254 | 0.119 | 0.270 | 9.500 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | F(-1) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 72 | 133 | 180 | 130 | 133 | 0 | 135 |
N.S. |
1 | 0.00 | 2.18 | 4.03 | 5.45 | 3.94 | 4.03 | 0.00 | 4.09 |
time (sec) |
N/A | 0.000 | 0.267 | 1.517 | 0.292 | 0.274 | 0.392 | 0.000 | 12.012 |
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 | 31 | 15 | 13 | 250 | 17 | 19 | 22 | 14 |
N.S. |
1 | 1.63 | 0.79 | 0.68 | 13.16 | 0.89 | 1.00 | 1.16 | 0.74 |
time (sec) |
N/A | 0.144 | 0.154 | 0.066 | 0.243 | 0.275 | 0.097 | 0.275 | 9.015 |
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 | 22 | 54 | 42 | 39 | 54 | 32 | 34 | 35 | 26 |
N.S. |
1 | 2.45 | 1.91 | 1.77 | 2.45 | 1.45 | 1.55 | 1.59 | 1.18 |
time (sec) |
N/A | 0.070 | 0.034 | 0.065 | 0.192 | 0.251 | 0.103 | 0.266 | 9.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 30 | 36 | 32 | 210 | 33 | 31 | 29 | 1340 | 0 |
N.S. |
1 | 1.20 | 1.07 | 7.00 | 1.10 | 1.03 | 0.97 | 44.67 | 0.00 |
time (sec) |
N/A | 1.021 | 0.182 | 0.079 | 1.029 | 0.254 | 1.297 | 4.020 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 23 | 37 | 37 | 34 | 31 | 37 | 22 |
N.S. |
1 | 0.00 | 0.96 | 1.54 | 1.54 | 1.42 | 1.29 | 1.54 | 0.92 |
time (sec) |
N/A | 0.000 | 0.155 | 8.479 | 0.224 | 0.258 | 0.485 | 0.329 | 8.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 40 | 103 | 74 | 412 | 83 | 0 | 87 |
N.S. |
1 | 0.00 | 1.29 | 3.32 | 2.39 | 13.29 | 2.68 | 0.00 | 2.81 |
time (sec) |
N/A | 0.000 | 0.671 | 99.124 | 2.096 | 0.270 | 4.033 | 0.000 | 9.804 |
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 | 12 | 11 | 11 | 10 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.92 | 0.92 | 0.83 | 0.92 | 0.92 |
time (sec) |
N/A | 0.003 | 0.000 | 0.049 | 0.190 | 0.255 | 0.018 | 0.260 | 0.041 |
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 | 32 | 30 | 32 | 29 | 31 | 29 | 31 | 33 |
N.S. |
1 | 1.19 | 1.11 | 1.19 | 1.07 | 1.15 | 1.07 | 1.15 | 1.22 |
time (sec) |
N/A | 0.318 | 0.612 | 0.329 | 0.388 | 0.243 | 0.109 | 0.296 | 8.417 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | A | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 33 | 75 | 42 | 73 | 71 | 97 | 74 |
N.S. |
1 | 0.00 | 1.22 | 2.78 | 1.56 | 2.70 | 2.63 | 3.59 | 2.74 |
time (sec) |
N/A | 0.000 | 0.177 | 0.734 | 7.161 | 0.257 | 0.629 | 5.629 | 10.028 |
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 | 23 | 46 | 29 | 29 | 32 | 41 | 41 |
N.S. |
1 | 0.00 | 0.88 | 1.77 | 1.12 | 1.12 | 1.23 | 1.58 | 1.58 |
time (sec) |
N/A | 0.000 | 0.222 | 0.102 | 0.436 | 0.257 | 16.393 | 0.267 | 10.610 |
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 | 37 | 0 | 36 | 40 | 35 | 57 | 27 | 32 | 33 |
N.S. |
1 | 0.00 | 0.97 | 1.08 | 0.95 | 1.54 | 0.73 | 0.86 | 0.89 |
time (sec) |
N/A | 0.000 | 1.048 | 0.280 | 0.346 | 0.252 | 0.327 | 0.289 | 8.240 |
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 | 9 | 9 | 9 | 8 | 8 | 7 | 8 | 8 |
N.S. |
1 | 0.64 | 0.64 | 0.64 | 0.57 | 0.57 | 0.50 | 0.57 | 0.57 |
time (sec) |
N/A | 0.003 | 0.003 | 0.057 | 0.175 | 0.235 | 0.038 | 0.253 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 56 | 67 | 65 | 72 | 75 | 80 | 201 |
N.S. |
1 | 0.00 | 2.33 | 2.79 | 2.71 | 3.00 | 3.12 | 3.33 | 8.38 |
time (sec) |
N/A | 0.000 | 0.121 | 141.997 | 0.817 | 0.243 | 0.278 | 0.552 | 8.572 |
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 | 30 | 973 | 30 | 29 | 191 | 29 | 24 | 37 | 33 |
N.S. |
1 | 32.43 | 1.00 | 0.97 | 6.37 | 0.97 | 0.80 | 1.23 | 1.10 |
time (sec) |
N/A | 4.049 | 1.267 | 0.324 | 1.103 | 0.253 | 0.120 | 0.269 | 8.817 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 54 | 44 | 188 | 57 | 53 | 73 | 59 |
N.S. |
1 | 0.00 | 2.45 | 2.00 | 8.55 | 2.59 | 2.41 | 3.32 | 2.68 |
time (sec) |
N/A | 0.000 | 0.135 | 0.459 | 0.289 | 0.249 | 0.137 | 0.293 | 8.901 |
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 | 38 | 33 | 34 | 48 | 25 | 26 | 26 | 28 |
N.S. |
1 | 1.31 | 1.14 | 1.17 | 1.66 | 0.86 | 0.90 | 0.90 | 0.97 |
time (sec) |
N/A | 0.229 | 0.075 | 0.237 | 0.228 | 0.260 | 0.140 | 0.260 | 8.562 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 18 | 22 | 16 | 70 | 17 | 0 | 18 |
N.S. |
1 | 0.00 | 0.78 | 0.96 | 0.70 | 3.04 | 0.74 | 0.00 | 0.78 |
time (sec) |
N/A | 0.000 | 0.288 | 0.243 | 0.304 | 0.247 | 0.107 | 0.000 | 8.616 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 25 | 30 | 30 | 31 | 0 | 50 | 68 |
N.S. |
1 | 0.00 | 0.93 | 1.11 | 1.11 | 1.15 | 0.00 | 1.85 | 2.52 |
time (sec) |
N/A | 0.000 | 0.452 | 129.774 | 0.323 | 0.245 | 0.000 | 0.267 | 8.759 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | B | B | A | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 43 | 44 | 52 | 54 | 45 | 42 |
N.S. |
1 | 0.00 | 0.00 | 1.59 | 1.63 | 1.93 | 2.00 | 1.67 | 1.56 |
time (sec) |
N/A | 0.000 | 0.000 | 0.119 | 0.221 | 0.247 | 0.170 | 0.273 | 8.603 |
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 | 28 | 22 | 22 | 30 | 19 | 29 | 27 | 53 | 63 |
N.S. |
1 | 0.79 | 0.79 | 1.07 | 0.68 | 1.04 | 0.96 | 1.89 | 2.25 |
time (sec) |
N/A | 0.480 | 0.424 | 1.650 | 0.235 | 0.254 | 0.320 | 0.409 | 8.813 |
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 | 36 | 23 | 23 | 0 | 23 | 31 | 23 | 19 |
N.S. |
1 | 1.80 | 1.15 | 1.15 | 0.00 | 1.15 | 1.55 | 1.15 | 0.95 |
time (sec) |
N/A | 0.138 | 0.644 | 0.344 | 0.000 | 0.242 | 0.123 | 0.266 | 0.151 |
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 | 9 | 9 | 8 | 7 | 7 | 5 | 7 | 7 |
N.S. |
1 | 0.60 | 0.60 | 0.53 | 0.47 | 0.47 | 0.33 | 0.47 | 0.47 |
time (sec) |
N/A | 0.001 | 0.001 | 0.016 | 0.179 | 0.238 | 0.017 | 0.247 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 49 | 28 | 21 | 20 | 21 | 24 | 0 | 21 |
N.S. |
1 | 1.69 | 0.97 | 0.72 | 0.69 | 0.72 | 0.83 | 0.00 | 0.72 |
time (sec) |
N/A | 0.398 | 0.042 | 0.128 | 0.378 | 0.248 | 0.142 | 0.000 | 0.132 |
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 | 23 | 20 | 18 | 19 | 19 | 15 | 20 | 16 |
N.S. |
1 | 1.44 | 1.25 | 1.12 | 1.19 | 1.19 | 0.94 | 1.25 | 1.00 |
time (sec) |
N/A | 0.014 | 0.012 | 0.095 | 0.176 | 0.232 | 0.177 | 0.257 | 7.745 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 76 | 25 | 24 | 23 | 23 | 19 | 48 | 23 |
N.S. |
1 | 2.53 | 0.83 | 0.80 | 0.77 | 0.77 | 0.63 | 1.60 | 0.77 |
time (sec) |
N/A | 0.189 | 5.106 | 0.517 | 0.219 | 0.258 | 132.558 | 0.290 | 0.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 0 | 36 | 36 | 36 | 31 | 36 | 32 |
N.S. |
1 | 0.00 | 0.00 | 1.12 | 1.12 | 1.12 | 0.97 | 1.12 | 1.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.861 | 0.264 | 0.249 | 0.179 | 0.273 | 7.525 |
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 | 30 | 26 | 32 | 34 | 31 | 32 | 34 | 121 |
N.S. |
1 | 1.25 | 1.08 | 1.33 | 1.42 | 1.29 | 1.33 | 1.42 | 5.04 |
time (sec) |
N/A | 0.201 | 0.397 | 1.349 | 0.230 | 0.242 | 0.169 | 0.316 | 8.664 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F(-1) | B | B | B | B | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 0 | 50 | 81 | 50 | 44 | 0 | 44 |
N.S. |
1 | 0.00 | 0.00 | 2.27 | 3.68 | 2.27 | 2.00 | 0.00 | 2.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.267 | 0.439 | 0.249 | 0.243 | 0.000 | 8.185 |
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 | 20 | 20 | 18 | 18 | 19 | 18 | 17 | 36 | 21 |
N.S. |
1 | 1.00 | 0.90 | 0.90 | 0.95 | 0.90 | 0.85 | 1.80 | 1.05 |
time (sec) |
N/A | 0.026 | 0.036 | 0.082 | 0.182 | 0.249 | 0.107 | 0.256 | 7.595 |
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 | 33 | 51 | 36 | 25 | 0 | 25 | 29 | 36 | 35 |
N.S. |
1 | 1.55 | 1.09 | 0.76 | 0.00 | 0.76 | 0.88 | 1.09 | 1.06 |
time (sec) |
N/A | 0.219 | 0.863 | 0.227 | 0.000 | 0.260 | 0.145 | 0.261 | 7.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-2) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 42 | 62 | 58 | 50 | 24 | 0 | 33 |
N.S. |
1 | 0.00 | 1.17 | 1.72 | 1.61 | 1.39 | 0.67 | 0.00 | 0.92 |
time (sec) |
N/A | 0.000 | 0.330 | 0.370 | 0.252 | 0.247 | 0.143 | 0.000 | 7.689 |