Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 108 | 91 | 90 | 90 | 97 | 90 | 92 |
N.S. |
1 | 1.00 | 5.68 | 4.79 | 4.74 | 4.74 | 5.11 | 4.74 | 4.84 |
time (sec) |
N/A | 0.142 | 0.010 | 3.615 | 0.200 | 0.312 | 0.555 | 0.288 | 5.514 |
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 | 40 | 44 | 108 | 91 | 92 | 92 | 99 | 92 | 92 |
N.S. |
1 | 1.10 | 2.70 | 2.28 | 2.30 | 2.30 | 2.48 | 2.30 | 2.30 |
time (sec) |
N/A | 0.161 | 0.004 | 3.723 | 0.192 | 0.265 | 0.590 | 0.268 | 5.452 |
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 | 62 | 72 | 108 | 91 | 92 | 92 | 99 | 92 | 92 |
N.S. |
1 | 1.16 | 1.74 | 1.47 | 1.48 | 1.48 | 1.60 | 1.48 | 1.48 |
time (sec) |
N/A | 0.175 | 0.008 | 3.733 | 0.187 | 0.258 | 0.626 | 0.283 | 0.084 |
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 | 84 | 100 | 108 | 91 | 92 | 92 | 99 | 92 | 92 |
N.S. |
1 | 1.19 | 1.29 | 1.08 | 1.10 | 1.10 | 1.18 | 1.10 | 1.10 |
time (sec) |
N/A | 0.193 | 0.004 | 3.572 | 0.188 | 0.260 | 0.656 | 0.290 | 5.467 |
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 | 106 | 128 | 108 | 91 | 92 | 92 | 99 | 92 | 92 |
N.S. |
1 | 1.21 | 1.02 | 0.86 | 0.87 | 0.87 | 0.93 | 0.87 | 0.87 |
time (sec) |
N/A | 0.207 | 0.007 | 3.606 | 0.199 | 0.290 | 0.702 | 0.276 | 0.087 |
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 | 108 | 110 | 108 | 91 | 92 | 92 | 99 | 92 | 92 |
N.S. |
1 | 1.02 | 1.00 | 0.84 | 0.85 | 0.85 | 0.92 | 0.85 | 0.85 |
time (sec) |
N/A | 0.242 | 0.004 | 3.671 | 0.201 | 0.299 | 0.735 | 0.274 | 0.085 |
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 | 108 | 110 | 108 | 91 | 92 | 92 | 99 | 92 | 92 |
N.S. |
1 | 1.02 | 1.00 | 0.84 | 0.85 | 0.85 | 0.92 | 0.85 | 0.85 |
time (sec) |
N/A | 0.235 | 0.008 | 3.625 | 0.195 | 0.266 | 0.756 | 0.279 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 103 | 90 | 89 | 89 | 102 | 89 | 89 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.86 | 0.86 | 0.99 | 0.86 | 0.86 |
time (sec) |
N/A | 0.241 | 0.002 | 3.639 | 0.199 | 0.274 | 0.025 | 0.285 | 0.097 |
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 | 108 | 108 | 108 | 91 | 90 | 90 | 107 | 90 | 90 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.83 | 0.83 | 0.99 | 0.83 | 0.83 |
time (sec) |
N/A | 0.242 | 0.002 | 3.552 | 0.179 | 0.291 | 0.025 | 0.276 | 0.088 |
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 | 106 | 106 | 106 | 91 | 90 | 90 | 105 | 90 | 90 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.85 | 0.85 | 0.99 | 0.85 | 0.85 |
time (sec) |
N/A | 0.239 | 0.002 | 3.646 | 0.316 | 0.255 | 0.024 | 0.274 | 0.060 |
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 | 99 | 99 | 99 | 88 | 87 | 87 | 100 | 87 | 87 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.88 | 0.88 | 1.01 | 0.88 | 0.88 |
time (sec) |
N/A | 0.238 | 0.001 | 3.520 | 0.319 | 0.299 | 0.023 | 0.281 | 0.043 |
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 | 100 | 100 | 100 | 91 | 90 | 92 | 99 | 90 | 90 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.90 | 0.92 | 0.99 | 0.90 | 0.90 |
time (sec) |
N/A | 0.231 | 0.007 | 3.713 | 0.193 | 0.272 | 0.066 | 0.288 | 0.052 |
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 | 98 | 98 | 98 | 89 | 88 | 92 | 99 | 88 | 88 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.90 | 0.94 | 1.01 | 0.90 | 0.90 |
time (sec) |
N/A | 0.228 | 0.003 | 3.783 | 0.186 | 0.268 | 0.071 | 0.271 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 102 | 91 | 91 | 92 | 104 | 91 | 93 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.89 | 0.90 | 1.02 | 0.89 | 0.91 |
time (sec) |
N/A | 0.236 | 0.004 | 3.650 | 0.199 | 0.294 | 0.099 | 0.272 | 5.515 |
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 | 98 | 98 | 98 | 89 | 89 | 92 | 99 | 89 | 91 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.91 | 0.94 | 1.01 | 0.91 | 0.93 |
time (sec) |
N/A | 0.240 | 0.007 | 3.830 | 0.192 | 0.293 | 0.097 | 0.295 | 5.433 |
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 | 98 | 98 | 98 | 91 | 91 | 92 | 100 | 91 | 93 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.93 | 0.94 | 1.02 | 0.93 | 0.95 |
time (sec) |
N/A | 0.234 | 0.005 | 3.682 | 0.191 | 0.282 | 0.137 | 0.283 | 0.052 |
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 | 100 | 100 | 100 | 89 | 91 | 92 | 102 | 91 | 91 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.91 | 0.92 | 1.02 | 0.91 | 0.91 |
time (sec) |
N/A | 0.237 | 0.005 | 3.765 | 0.189 | 0.253 | 0.133 | 0.269 | 0.048 |
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 | 40 | 39 | 40 | 34 | 34 | 33 | 32 | 35 | 33 |
N.S. |
1 | 0.98 | 1.00 | 0.85 | 0.85 | 0.82 | 0.80 | 0.88 | 0.82 |
time (sec) |
N/A | 0.186 | 0.005 | 3.691 | 0.204 | 0.260 | 0.086 | 0.290 | 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 | 27 | 26 | 27 | 23 | 23 | 22 | 20 | 24 | 22 |
N.S. |
1 | 0.96 | 1.00 | 0.85 | 0.85 | 0.81 | 0.74 | 0.89 | 0.81 |
time (sec) |
N/A | 0.177 | 0.008 | 3.712 | 0.207 | 0.256 | 0.082 | 0.298 | 5.503 |
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 | 14 | 13 | 13 | 10 | 14 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 0.67 | 0.93 | 0.87 |
time (sec) |
N/A | 0.144 | 0.003 | 3.648 | 0.188 | 0.249 | 0.061 | 0.277 | 0.033 |
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 | 26 | 22 | 21 | 23 | 18 | 15 | 22 | 18 |
N.S. |
1 | 1.18 | 1.00 | 0.95 | 1.05 | 0.82 | 0.68 | 1.00 | 0.82 |
time (sec) |
N/A | 0.153 | 0.005 | 3.646 | 0.190 | 0.249 | 0.119 | 0.280 | 5.500 |
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 | 35 | 36 | 35 | 32 | 33 | 33 | 31 | 42 | 31 |
N.S. |
1 | 1.03 | 1.00 | 0.91 | 0.94 | 0.94 | 0.89 | 1.20 | 0.89 |
time (sec) |
N/A | 0.176 | 0.006 | 3.716 | 0.196 | 0.260 | 0.163 | 0.283 | 5.446 |
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 | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 133 | 111 | 37 | 109 | 123 | 32 | 114 | 120 |
N.S. |
1 | 1.07 | 0.90 | 0.30 | 0.88 | 0.99 | 0.26 | 0.92 | 0.97 |
time (sec) |
N/A | 0.286 | 0.024 | 3.619 | 0.279 | 0.292 | 0.075 | 0.288 | 0.251 |
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 | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 123 | 108 | 34 | 106 | 106 | 22 | 111 | 114 |
N.S. |
1 | 1.03 | 0.91 | 0.29 | 0.89 | 0.89 | 0.18 | 0.93 | 0.96 |
time (sec) |
N/A | 0.289 | 0.012 | 3.671 | 0.286 | 0.284 | 0.071 | 0.277 | 5.496 |
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 | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 116 | 89 | 27 | 98 | 304 | 24 | 112 | 111 |
N.S. |
1 | 1.01 | 0.77 | 0.23 | 0.85 | 2.64 | 0.21 | 0.97 | 0.97 |
time (sec) |
N/A | 0.265 | 0.008 | 3.715 | 0.289 | 0.267 | 0.059 | 0.280 | 5.716 |
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 | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 111 | 89 | 27 | 98 | 299 | 20 | 112 | 99 |
N.S. |
1 | 0.97 | 0.77 | 0.23 | 0.85 | 2.60 | 0.17 | 0.97 | 0.86 |
time (sec) |
N/A | 0.265 | 0.011 | 3.647 | 0.286 | 0.303 | 0.067 | 0.285 | 0.236 |
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 | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 131 | 114 | 53 | 106 | 103 | 29 | 121 | 102 |
N.S. |
1 | 1.07 | 0.93 | 0.43 | 0.87 | 0.84 | 0.24 | 0.99 | 0.84 |
time (sec) |
N/A | 0.285 | 0.013 | 3.677 | 0.283 | 0.265 | 0.084 | 0.307 | 5.705 |
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 | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 128 | 119 | 54 | 106 | 143 | 32 | 115 | 128 |
N.S. |
1 | 1.03 | 0.96 | 0.44 | 0.85 | 1.15 | 0.26 | 0.93 | 1.03 |
time (sec) |
N/A | 0.289 | 0.014 | 3.655 | 0.282 | 0.255 | 0.103 | 0.285 | 0.229 |
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 | 46 | 43 | 38 | 41 | 43 | 56 | 42 | 49 | 45 |
N.S. |
1 | 0.93 | 0.83 | 0.89 | 0.93 | 1.22 | 0.91 | 1.07 | 0.98 |
time (sec) |
N/A | 0.185 | 0.013 | 3.663 | 0.210 | 0.254 | 0.146 | 0.294 | 0.049 |
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 | 31 | 27 | 30 | 32 | 35 | 29 | 48 | 29 |
N.S. |
1 | 0.94 | 0.82 | 0.91 | 0.97 | 1.06 | 0.88 | 1.45 | 0.88 |
time (sec) |
N/A | 0.178 | 0.008 | 3.676 | 0.191 | 0.266 | 0.124 | 0.284 | 5.473 |
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 | 15 | 14 | 15 | 15 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.94 | 0.94 | 0.88 | 0.88 |
time (sec) |
N/A | 0.143 | 0.004 | 3.580 | 0.217 | 0.262 | 0.086 | 0.276 | 0.030 |
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 | 38 | 39 | 33 | 35 | 37 | 47 | 34 | 45 | 34 |
N.S. |
1 | 1.03 | 0.87 | 0.92 | 0.97 | 1.24 | 0.89 | 1.18 | 0.89 |
time (sec) |
N/A | 0.183 | 0.011 | 3.586 | 0.218 | 0.250 | 0.175 | 0.278 | 5.416 |
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 | 52 | 52 | 41 | 54 | 53 | 73 | 54 | 51 | 53 |
N.S. |
1 | 1.00 | 0.79 | 1.04 | 1.02 | 1.40 | 1.04 | 0.98 | 1.02 |
time (sec) |
N/A | 0.195 | 0.029 | 3.866 | 0.254 | 0.259 | 0.244 | 0.275 | 5.487 |
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 | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 143 | 119 | 45 | 116 | 400 | 44 | 132 | 138 |
N.S. |
1 | 1.05 | 0.88 | 0.33 | 0.85 | 2.94 | 0.32 | 0.97 | 1.01 |
time (sec) |
N/A | 0.296 | 0.054 | 3.674 | 0.304 | 0.297 | 0.123 | 0.295 | 0.245 |
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 | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 136 | 118 | 43 | 114 | 391 | 39 | 130 | 108 |
N.S. |
1 | 1.01 | 0.88 | 0.32 | 0.85 | 2.92 | 0.29 | 0.97 | 0.81 |
time (sec) |
N/A | 0.283 | 0.044 | 3.648 | 0.291 | 0.308 | 0.115 | 0.279 | 5.632 |
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 | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 143 | 119 | 48 | 124 | 402 | 44 | 129 | 138 |
N.S. |
1 | 1.05 | 0.88 | 0.35 | 0.91 | 2.96 | 0.32 | 0.95 | 1.01 |
time (sec) |
N/A | 0.287 | 0.041 | 3.616 | 0.283 | 0.295 | 0.111 | 0.271 | 5.656 |
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 | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 136 | 118 | 46 | 122 | 389 | 39 | 127 | 128 |
N.S. |
1 | 1.01 | 0.88 | 0.34 | 0.91 | 2.90 | 0.29 | 0.95 | 0.96 |
time (sec) |
N/A | 0.288 | 0.039 | 3.617 | 0.285 | 0.299 | 0.124 | 0.285 | 5.592 |
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 | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 158 | 131 | 73 | 126 | 146 | 56 | 139 | 120 |
N.S. |
1 | 1.08 | 0.90 | 0.50 | 0.86 | 1.00 | 0.38 | 0.95 | 0.82 |
time (sec) |
N/A | 0.317 | 0.058 | 3.622 | 0.284 | 0.276 | 0.160 | 0.273 | 5.702 |
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 | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 155 | 129 | 74 | 128 | 187 | 58 | 131 | 146 |
N.S. |
1 | 1.06 | 0.88 | 0.51 | 0.88 | 1.28 | 0.40 | 0.90 | 1.00 |
time (sec) |
N/A | 0.307 | 0.056 | 3.577 | 0.287 | 0.278 | 0.183 | 0.271 | 5.866 |
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 | 61 | 62 | 48 | 54 | 66 | 91 | 65 | 62 | 67 |
N.S. |
1 | 1.02 | 0.79 | 0.89 | 1.08 | 1.49 | 1.07 | 1.02 | 1.10 |
time (sec) |
N/A | 0.211 | 0.039 | 3.602 | 0.192 | 0.246 | 0.241 | 0.293 | 0.129 |
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 | 52 | 51 | 39 | 43 | 55 | 69 | 53 | 42 | 53 |
N.S. |
1 | 0.98 | 0.75 | 0.83 | 1.06 | 1.33 | 1.02 | 0.81 | 1.02 |
time (sec) |
N/A | 0.192 | 0.012 | 3.636 | 0.199 | 0.273 | 0.205 | 0.285 | 0.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 24 | 23 | 36 | 36 | 36 | 22 | 37 |
N.S. |
1 | 1.00 | 1.26 | 1.21 | 1.89 | 1.89 | 1.89 | 1.16 | 1.95 |
time (sec) |
N/A | 0.142 | 0.006 | 3.605 | 0.204 | 0.247 | 0.163 | 0.290 | 0.035 |
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 | 15 | 14 | 26 | 27 | 14 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 1.62 | 1.69 | 0.88 | 1.75 |
time (sec) |
N/A | 0.139 | 0.004 | 3.631 | 0.203 | 0.250 | 0.134 | 0.275 | 5.434 |
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 | 54 | 55 | 43 | 46 | 60 | 90 | 56 | 57 | 56 |
N.S. |
1 | 1.02 | 0.80 | 0.85 | 1.11 | 1.67 | 1.04 | 1.06 | 1.04 |
time (sec) |
N/A | 0.194 | 0.021 | 3.648 | 0.198 | 0.272 | 0.254 | 0.270 | 0.081 |
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 | 66 | 69 | 59 | 64 | 76 | 119 | 76 | 80 | 73 |
N.S. |
1 | 1.05 | 0.89 | 0.97 | 1.15 | 1.80 | 1.15 | 1.21 | 1.11 |
time (sec) |
N/A | 0.220 | 0.035 | 3.636 | 0.207 | 0.288 | 0.297 | 0.282 | 5.610 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 170 | 140 | 56 | 139 | 510 | 70 | 142 | 161 |
N.S. |
1 | 1.10 | 0.90 | 0.36 | 0.90 | 3.29 | 0.45 | 0.92 | 1.04 |
time (sec) |
N/A | 0.333 | 0.048 | 3.644 | 0.288 | 0.298 | 0.202 | 0.295 | 5.574 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 153 | 163 | 136 | 54 | 137 | 503 | 68 | 140 | 127 |
N.S. |
1 | 1.07 | 0.89 | 0.35 | 0.90 | 3.29 | 0.44 | 0.92 | 0.83 |
time (sec) |
N/A | 0.319 | 0.045 | 3.653 | 0.288 | 0.295 | 0.198 | 0.284 | 0.331 |
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 | Yes | TBD | TBD | TBD | TBD | TBD |
size | 158 | 170 | 141 | 58 | 149 | 512 | 70 | 145 | 168 |
N.S. |
1 | 1.08 | 0.89 | 0.37 | 0.94 | 3.24 | 0.44 | 0.92 | 1.06 |
time (sec) |
N/A | 0.320 | 0.070 | 3.753 | 0.302 | 0.268 | 0.183 | 0.295 | 5.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 154 | 161 | 138 | 56 | 146 | 503 | 65 | 142 | 145 |
N.S. |
1 | 1.05 | 0.90 | 0.36 | 0.95 | 3.27 | 0.42 | 0.92 | 0.94 |
time (sec) |
N/A | 0.313 | 0.048 | 3.636 | 0.286 | 0.282 | 0.179 | 0.277 | 5.481 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 155 | 170 | 139 | 59 | 147 | 514 | 70 | 139 | 163 |
N.S. |
1 | 1.10 | 0.90 | 0.38 | 0.95 | 3.32 | 0.45 | 0.90 | 1.05 |
time (sec) |
N/A | 0.327 | 0.045 | 3.622 | 0.282 | 0.300 | 0.175 | 0.284 | 0.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 151 | 161 | 135 | 57 | 145 | 499 | 63 | 137 | 142 |
N.S. |
1 | 1.07 | 0.89 | 0.38 | 0.96 | 3.30 | 0.42 | 0.91 | 0.94 |
time (sec) |
N/A | 0.307 | 0.041 | 3.619 | 0.286 | 0.264 | 0.188 | 0.293 | 5.549 |
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 | 41 | 41 | 41 | 36 | 36 | 35 | 34 | 37 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.88 | 0.85 | 0.83 | 0.90 | 0.85 |
time (sec) |
N/A | 0.194 | 0.006 | 3.581 | 0.204 | 0.245 | 0.087 | 0.282 | 0.068 |
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 | 28 | 28 | 24 | 25 | 23 | 22 | 26 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.89 | 0.82 | 0.79 | 0.93 | 0.82 |
time (sec) |
N/A | 0.183 | 0.004 | 3.629 | 0.212 | 0.243 | 0.086 | 0.271 | 0.038 |
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 | 15 | 15 | 15 | 12 | 16 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.94 | 0.94 | 0.75 | 1.00 | 0.94 |
time (sec) |
N/A | 0.144 | 0.003 | 3.644 | 0.196 | 0.247 | 0.066 | 0.277 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 27 | 23 | 22 | 25 | 20 | 15 | 24 | 21 |
N.S. |
1 | 1.17 | 1.00 | 0.96 | 1.09 | 0.87 | 0.65 | 1.04 | 0.91 |
time (sec) |
N/A | 0.154 | 0.006 | 3.639 | 0.228 | 0.251 | 0.118 | 0.265 | 0.101 |
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 | 35 | 37 | 35 | 32 | 35 | 33 | 31 | 41 | 31 |
N.S. |
1 | 1.06 | 1.00 | 0.91 | 1.00 | 0.94 | 0.89 | 1.17 | 0.89 |
time (sec) |
N/A | 0.187 | 0.007 | 3.653 | 0.200 | 0.253 | 0.165 | 0.266 | 0.074 |
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 | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 131 | 111 | 39 | 108 | 130 | 34 | 106 | 134 |
N.S. |
1 | 1.05 | 0.89 | 0.31 | 0.86 | 1.04 | 0.27 | 0.85 | 1.07 |
time (sec) |
N/A | 0.287 | 0.024 | 3.771 | 0.285 | 0.268 | 0.078 | 0.275 | 5.610 |
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 | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 122 | 108 | 37 | 106 | 103 | 24 | 104 | 116 |
N.S. |
1 | 1.02 | 0.90 | 0.31 | 0.88 | 0.86 | 0.20 | 0.87 | 0.97 |
time (sec) |
N/A | 0.282 | 0.011 | 3.637 | 0.283 | 0.269 | 0.077 | 0.268 | 5.804 |
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 | Yes | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 89 | 29 | 97 | 307 | 26 | 104 | 109 |
N.S. |
1 | 1.00 | 0.77 | 0.25 | 0.84 | 2.67 | 0.23 | 0.90 | 0.95 |
time (sec) |
N/A | 0.259 | 0.008 | 3.632 | 0.288 | 0.280 | 0.060 | 0.278 | 0.221 |
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 | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 110 | 89 | 29 | 97 | 320 | 22 | 104 | 115 |
N.S. |
1 | 0.96 | 0.78 | 0.25 | 0.85 | 2.81 | 0.19 | 0.91 | 1.01 |
time (sec) |
N/A | 0.253 | 0.007 | 3.655 | 0.286 | 0.304 | 0.072 | 0.276 | 5.680 |
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 | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 129 | 114 | 50 | 105 | 111 | 31 | 113 | 127 |
N.S. |
1 | 1.05 | 0.93 | 0.41 | 0.85 | 0.90 | 0.25 | 0.92 | 1.03 |
time (sec) |
N/A | 0.284 | 0.019 | 3.654 | 0.294 | 0.262 | 0.092 | 0.273 | 5.483 |
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 | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 126 | 119 | 54 | 105 | 141 | 34 | 107 | 127 |
N.S. |
1 | 1.02 | 0.96 | 0.44 | 0.85 | 1.14 | 0.27 | 0.86 | 1.02 |
time (sec) |
N/A | 0.280 | 0.021 | 3.651 | 0.295 | 0.277 | 0.108 | 0.262 | 5.416 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 123 | 101 | 28 | 114 | 446 | 32 | 143 | 137 |
N.S. |
1 | 0.98 | 0.81 | 0.22 | 0.91 | 3.57 | 0.26 | 1.14 | 1.10 |
time (sec) |
N/A | 0.312 | 0.023 | 3.688 | 0.283 | 0.282 | 0.132 | 0.275 | 5.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 122 | 124 | 30 | 113 | 467 | 34 | 131 | 165 |
N.S. |
1 | 0.98 | 1.00 | 0.24 | 0.91 | 3.77 | 0.27 | 1.06 | 1.33 |
time (sec) |
N/A | 0.294 | 0.047 | 3.629 | 0.288 | 0.274 | 0.145 | 0.277 | 0.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 134 | 101 | 28 | 0 | 446 | 32 | 142 | 137 |
N.S. |
1 | 0.96 | 0.73 | 0.20 | 0.00 | 3.21 | 0.23 | 1.02 | 0.99 |
time (sec) |
N/A | 0.322 | 0.023 | 3.770 | 0.000 | 0.290 | 0.136 | 0.284 | 5.762 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F(-2) | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 138 | 135 | 124 | 30 | 0 | 467 | 34 | 138 | 165 |
N.S. |
1 | 0.98 | 0.90 | 0.22 | 0.00 | 3.38 | 0.25 | 1.00 | 1.20 |
time (sec) |
N/A | 0.313 | 0.038 | 3.603 | 0.000 | 0.273 | 0.141 | 0.290 | 5.811 |
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 | 10 | 10 | 10 | 7 | 6 | 6 | 42 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.70 | 0.60 | 0.60 | 4.20 | 0.60 | 0.60 |
time (sec) |
N/A | 0.149 | 0.024 | 3.649 | 0.302 | 0.264 | 0.277 | 0.273 | 0.150 |
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 | 80 | 84 | 61 | 47 | 64 | 57 | 114 | 57 | 90 |
N.S. |
1 | 1.05 | 0.76 | 0.59 | 0.80 | 0.71 | 1.42 | 0.71 | 1.12 |
time (sec) |
N/A | 0.205 | 0.031 | 4.252 | 0.196 | 0.276 | 0.375 | 0.266 | 5.482 |
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 | 59 | 63 | 50 | 36 | 47 | 46 | 90 | 43 | 70 |
N.S. |
1 | 1.07 | 0.85 | 0.61 | 0.80 | 0.78 | 1.53 | 0.73 | 1.19 |
time (sec) |
N/A | 0.191 | 0.027 | 3.841 | 0.206 | 0.268 | 0.284 | 0.276 | 5.507 |
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 | 38 | 42 | 38 | 25 | 30 | 34 | 66 | 29 | 29 |
N.S. |
1 | 1.11 | 1.00 | 0.66 | 0.79 | 0.89 | 1.74 | 0.76 | 0.76 |
time (sec) |
N/A | 0.177 | 0.024 | 3.717 | 0.204 | 0.247 | 0.201 | 0.280 | 5.500 |
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 | 18 | 18 | 18 | 15 | 14 | 14 | 42 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 0.78 | 2.33 | 0.78 | 0.78 |
time (sec) |
N/A | 0.141 | 0.012 | 3.731 | 0.197 | 0.249 | 0.084 | 0.277 | 5.548 |
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 | 43 | 43 | 43 | 32 | 49 | 84 | 76 | 36 | 52 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 1.14 | 1.95 | 1.77 | 0.84 | 1.21 |
time (sec) |
N/A | 0.170 | 0.027 | 3.875 | 0.276 | 0.272 | 0.822 | 0.273 | 5.711 |
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 | 47 | 47 | 47 | 36 | 53 | 108 | 49 | 46 | 56 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 1.13 | 2.30 | 1.04 | 0.98 | 1.19 |
time (sec) |
N/A | 0.177 | 0.047 | 4.237 | 0.295 | 0.268 | 1.015 | 0.284 | 5.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 73 | 62 | 50 | 100 | 133 | 100 | 72 | 76 |
N.S. |
1 | 1.03 | 0.87 | 0.70 | 1.41 | 1.87 | 1.41 | 1.01 | 1.07 |
time (sec) |
N/A | 0.184 | 0.089 | 3.760 | 0.287 | 0.283 | 2.019 | 0.279 | 5.920 |
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 | 95 | 103 | 73 | 62 | 137 | 159 | 129 | 92 | 96 |
N.S. |
1 | 1.08 | 0.77 | 0.65 | 1.44 | 1.67 | 1.36 | 0.97 | 1.01 |
time (sec) |
N/A | 0.204 | 0.106 | 3.777 | 0.301 | 0.268 | 4.802 | 0.280 | 5.928 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 275 | 284 | 94 | 323 | 0 | 58 | 39 | 0 | 0 |
N.S. |
1 | 1.03 | 0.34 | 1.17 | 0.00 | 0.21 | 0.14 | 0.00 | 0.00 |
time (sec) |
N/A | 0.330 | 3.913 | 3.881 | 0.000 | 0.075 | 0.528 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 251 | 254 | 62 | 312 | 0 | 48 | 39 | 0 | 0 |
N.S. |
1 | 1.01 | 0.25 | 1.24 | 0.00 | 0.19 | 0.16 | 0.00 | 0.00 |
time (sec) |
N/A | 0.275 | 3.467 | 3.752 | 0.000 | 0.078 | 0.505 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 227 | 227 | 46 | 297 | 0 | 33 | 37 | 0 | 37 |
N.S. |
1 | 1.00 | 0.20 | 1.31 | 0.00 | 0.15 | 0.16 | 0.00 | 0.16 |
time (sec) |
N/A | 0.250 | 3.336 | 3.825 | 0.000 | 0.074 | 0.455 | 0.000 | 5.298 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 228 | 228 | 51 | 295 | 0 | 34 | 42 | 0 | 0 |
N.S. |
1 | 1.00 | 0.22 | 1.29 | 0.00 | 0.15 | 0.18 | 0.00 | 0.00 |
time (sec) |
N/A | 0.260 | 7.986 | 3.732 | 0.000 | 0.078 | 0.500 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 253 | 258 | 51 | 312 | 0 | 46 | 46 | 0 | 0 |
N.S. |
1 | 1.02 | 0.20 | 1.23 | 0.00 | 0.18 | 0.18 | 0.00 | 0.00 |
time (sec) |
N/A | 0.292 | 10.008 | 3.857 | 0.000 | 0.078 | 0.584 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 277 | 288 | 51 | 325 | 0 | 57 | 46 | 0 | 0 |
N.S. |
1 | 1.04 | 0.18 | 1.17 | 0.00 | 0.21 | 0.17 | 0.00 | 0.00 |
time (sec) |
N/A | 0.313 | 10.010 | 4.012 | 0.000 | 0.079 | 0.664 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 535 | 568 | 96 | 477 | 0 | 69 | 39 | 0 | 0 |
N.S. |
1 | 1.06 | 0.18 | 0.89 | 0.00 | 0.13 | 0.07 | 0.00 | 0.00 |
time (sec) |
N/A | 0.569 | 3.632 | 4.009 | 0.000 | 0.108 | 0.564 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 511 | 538 | 64 | 466 | 0 | 57 | 39 | 0 | 0 |
N.S. |
1 | 1.05 | 0.13 | 0.91 | 0.00 | 0.11 | 0.08 | 0.00 | 0.00 |
time (sec) |
N/A | 0.551 | 3.578 | 3.958 | 0.000 | 0.077 | 0.523 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 487 | 508 | 51 | 451 | 0 | 43 | 39 | 0 | 0 |
N.S. |
1 | 1.04 | 0.10 | 0.93 | 0.00 | 0.09 | 0.08 | 0.00 | 0.00 |
time (sec) |
N/A | 0.516 | 3.366 | 3.880 | 0.000 | 0.076 | 0.487 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 479 | 506 | 49 | 447 | 0 | 38 | 41 | 0 | 40 |
N.S. |
1 | 1.06 | 0.10 | 0.93 | 0.00 | 0.08 | 0.09 | 0.00 | 0.08 |
time (sec) |
N/A | 0.507 | 5.204 | 3.774 | 0.000 | 0.088 | 0.490 | 0.000 | 6.213 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 511 | 536 | 51 | 464 | 0 | 54 | 46 | 0 | 0 |
N.S. |
1 | 1.05 | 0.10 | 0.91 | 0.00 | 0.11 | 0.09 | 0.00 | 0.00 |
time (sec) |
N/A | 0.526 | 10.010 | 3.859 | 0.000 | 0.081 | 0.533 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 84 | 50 | 47 | 64 | 68 | 136 | 57 | 108 |
N.S. |
1 | 1.05 | 0.62 | 0.59 | 0.80 | 0.85 | 1.70 | 0.71 | 1.35 |
time (sec) |
N/A | 0.214 | 0.043 | 3.785 | 0.203 | 0.263 | 0.558 | 0.324 | 5.998 |
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 | 59 | 63 | 39 | 36 | 47 | 57 | 112 | 43 | 88 |
N.S. |
1 | 1.07 | 0.66 | 0.61 | 0.80 | 0.97 | 1.90 | 0.73 | 1.49 |
time (sec) |
N/A | 0.198 | 0.100 | 3.837 | 0.203 | 0.258 | 0.408 | 0.269 | 6.172 |
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 | 38 | 42 | 28 | 25 | 30 | 45 | 88 | 29 | 68 |
N.S. |
1 | 1.11 | 0.74 | 0.66 | 0.79 | 1.18 | 2.32 | 0.76 | 1.79 |
time (sec) |
N/A | 0.184 | 0.032 | 3.846 | 0.202 | 0.251 | 0.302 | 0.267 | 6.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 32 | 65 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 1.78 | 3.61 | 0.78 | 0.78 |
time (sec) |
N/A | 0.148 | 0.014 | 3.784 | 0.191 | 0.260 | 0.145 | 0.282 | 5.891 |
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 | 59 | 61 | 52 | 41 | 61 | 103 | 83 | 50 | 68 |
N.S. |
1 | 1.03 | 0.88 | 0.69 | 1.03 | 1.75 | 1.41 | 0.85 | 1.15 |
time (sec) |
N/A | 0.185 | 0.044 | 3.860 | 0.285 | 0.254 | 1.183 | 0.266 | 6.197 |
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 | 58 | 65 | 55 | 49 | 66 | 121 | 100 | 63 | 69 |
N.S. |
1 | 1.12 | 0.95 | 0.84 | 1.14 | 2.09 | 1.72 | 1.09 | 1.19 |
time (sec) |
N/A | 0.187 | 0.060 | 3.777 | 0.312 | 0.270 | 1.401 | 0.285 | 6.326 |
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 | 68 | 71 | 59 | 48 | 98 | 138 | 78 | 70 | 74 |
N.S. |
1 | 1.04 | 0.87 | 0.71 | 1.44 | 2.03 | 1.15 | 1.03 | 1.09 |
time (sec) |
N/A | 0.193 | 0.097 | 3.906 | 0.284 | 0.291 | 1.629 | 0.284 | 6.230 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 296 | 308 | 79 | 334 | 0 | 69 | 39 | 0 | 0 |
N.S. |
1 | 1.04 | 0.27 | 1.13 | 0.00 | 0.23 | 0.13 | 0.00 | 0.00 |
time (sec) |
N/A | 0.348 | 5.133 | 3.831 | 0.000 | 0.086 | 0.649 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 272 | 278 | 67 | 323 | 0 | 59 | 39 | 0 | 0 |
N.S. |
1 | 1.02 | 0.25 | 1.19 | 0.00 | 0.22 | 0.14 | 0.00 | 0.00 |
time (sec) |
N/A | 0.304 | 4.777 | 3.847 | 0.000 | 0.075 | 0.543 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 246 | 249 | 47 | 309 | 0 | 47 | 37 | 0 | 37 |
N.S. |
1 | 1.01 | 0.19 | 1.26 | 0.00 | 0.19 | 0.15 | 0.00 | 0.15 |
time (sec) |
N/A | 0.270 | 4.335 | 3.765 | 0.000 | 0.088 | 0.491 | 0.000 | 5.798 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 246 | 251 | 52 | 306 | 0 | 44 | 42 | 0 | 0 |
N.S. |
1 | 1.02 | 0.21 | 1.24 | 0.00 | 0.18 | 0.17 | 0.00 | 0.00 |
time (sec) |
N/A | 0.274 | 9.834 | 3.860 | 0.000 | 0.089 | 0.536 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 247 | 252 | 52 | 306 | 0 | 44 | 46 | 0 | 0 |
N.S. |
1 | 1.02 | 0.21 | 1.24 | 0.00 | 0.18 | 0.19 | 0.00 | 0.00 |
time (sec) |
N/A | 0.272 | 10.011 | 3.886 | 0.000 | 0.076 | 0.595 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 556 | 592 | 81 | 488 | 0 | 80 | 39 | 0 | 0 |
N.S. |
1 | 1.06 | 0.15 | 0.88 | 0.00 | 0.14 | 0.07 | 0.00 | 0.00 |
time (sec) |
N/A | 0.579 | 5.236 | 3.882 | 0.000 | 0.080 | 0.657 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 532 | 562 | 69 | 477 | 0 | 68 | 39 | 0 | 0 |
N.S. |
1 | 1.06 | 0.13 | 0.90 | 0.00 | 0.13 | 0.07 | 0.00 | 0.00 |
time (sec) |
N/A | 0.569 | 5.054 | 3.896 | 0.000 | 0.077 | 0.576 | 0.000 | 0.000 |