Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 121 | 81 | 108 | 166 | 174 | 153 | 104 | 89 |
N.S. |
1 | 1.06 | 0.71 | 0.95 | 1.46 | 1.53 | 1.34 | 0.91 | 0.78 |
time (sec) |
N/A | 0.231 | 0.163 | 0.036 | 0.277 | 0.288 | 10.783 | 0.316 | 6.101 |
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 | 90 | 91 | 70 | 97 | 135 | 151 | 124 | 91 | 72 |
N.S. |
1 | 1.01 | 0.78 | 1.08 | 1.50 | 1.68 | 1.38 | 1.01 | 0.80 |
time (sec) |
N/A | 0.205 | 0.137 | 0.032 | 0.263 | 0.283 | 3.470 | 0.297 | 6.055 |
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 | 66 | 65 | 54 | 83 | 98 | 130 | 75 | 77 | 52 |
N.S. |
1 | 0.98 | 0.82 | 1.26 | 1.48 | 1.97 | 1.14 | 1.17 | 0.79 |
time (sec) |
N/A | 0.204 | 0.135 | 0.031 | 0.272 | 0.293 | 1.616 | 0.305 | 5.824 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F(-2) | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 58 | 46 | 78 | 63 | 100 | 92 | 0 | 34 |
N.S. |
1 | 1.07 | 0.85 | 1.44 | 1.17 | 1.85 | 1.70 | 0.00 | 0.63 |
time (sec) |
N/A | 0.174 | 0.072 | 0.035 | 0.269 | 0.318 | 1.365 | 0.000 | 5.945 |
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 | 55 | 58 | 50 | 79 | 61 | 110 | 71 | 0 | 43 |
N.S. |
1 | 1.05 | 0.91 | 1.44 | 1.11 | 2.00 | 1.29 | 0.00 | 0.78 |
time (sec) |
N/A | 0.182 | 0.104 | 0.036 | 0.285 | 0.287 | 1.212 | 0.000 | 6.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 15 | 14 | 35 | 65 | 145 | 24 |
N.S. |
1 | 1.00 | 1.11 | 0.83 | 0.78 | 1.94 | 3.61 | 8.06 | 1.33 |
time (sec) |
N/A | 0.140 | 0.033 | 0.046 | 0.189 | 0.272 | 0.573 | 0.304 | 6.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 33 | 30 | 49 | 360 | 177 | 68 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.79 | 1.29 | 9.47 | 4.66 | 1.79 |
time (sec) |
N/A | 0.175 | 0.049 | 0.036 | 0.182 | 0.288 | 0.779 | 0.312 | 6.255 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 49 | 44 | 47 | 60 | 986 | 208 | 88 |
N.S. |
1 | 1.00 | 0.83 | 0.75 | 0.80 | 1.02 | 16.71 | 3.53 | 1.49 |
time (sec) |
N/A | 0.189 | 0.053 | 0.034 | 0.188 | 0.297 | 1.108 | 0.312 | 6.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 60 | 55 | 64 | 71 | 2297 | 239 | 108 |
N.S. |
1 | 1.00 | 0.75 | 0.69 | 0.80 | 0.89 | 28.71 | 2.99 | 1.35 |
time (sec) |
N/A | 0.205 | 0.060 | 0.039 | 0.191 | 0.285 | 1.585 | 0.318 | 6.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 71 | 66 | 81 | 82 | 5289 | 270 | 128 |
N.S. |
1 | 1.00 | 0.70 | 0.65 | 0.80 | 0.81 | 52.37 | 2.67 | 1.27 |
time (sec) |
N/A | 0.217 | 0.067 | 0.038 | 0.198 | 0.307 | 2.654 | 0.364 | 6.866 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 82 | 77 | 98 | 93 | 10344 | 301 | 148 |
N.S. |
1 | 1.00 | 0.67 | 0.63 | 0.80 | 0.76 | 84.79 | 2.47 | 1.21 |
time (sec) |
N/A | 0.243 | 0.075 | 0.045 | 0.194 | 0.272 | 6.594 | 0.329 | 6.968 |
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 | 111 | 115 | 81 | 108 | 164 | 173 | 155 | 105 | 89 |
N.S. |
1 | 1.04 | 0.73 | 0.97 | 1.48 | 1.56 | 1.40 | 0.95 | 0.80 |
time (sec) |
N/A | 0.212 | 0.169 | 0.046 | 0.273 | 0.288 | 7.020 | 0.300 | 5.811 |
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 | 87 | 89 | 66 | 94 | 131 | 152 | 102 | 91 | 72 |
N.S. |
1 | 1.02 | 0.76 | 1.08 | 1.51 | 1.75 | 1.17 | 1.05 | 0.83 |
time (sec) |
N/A | 0.194 | 0.156 | 0.040 | 0.274 | 0.301 | 2.724 | 0.304 | 6.000 |
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 | 84 | 83 | 64 | 93 | 115 | 130 | 126 | 0 | 72 |
N.S. |
1 | 0.99 | 0.76 | 1.11 | 1.37 | 1.55 | 1.50 | 0.00 | 0.86 |
time (sec) |
N/A | 0.192 | 0.138 | 0.043 | 0.288 | 0.394 | 2.435 | 0.000 | 5.917 |
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 | 71 | 76 | 64 | 94 | 78 | 139 | 99 | 0 | 34 |
N.S. |
1 | 1.07 | 0.90 | 1.32 | 1.10 | 1.96 | 1.39 | 0.00 | 0.48 |
time (sec) |
N/A | 0.187 | 0.129 | 0.043 | 0.301 | 0.276 | 2.130 | 0.000 | 6.030 |
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 | 73 | 76 | 63 | 92 | 75 | 142 | 97 | 0 | 60 |
N.S. |
1 | 1.04 | 0.86 | 1.26 | 1.03 | 1.95 | 1.33 | 0.00 | 0.82 |
time (sec) |
N/A | 0.191 | 0.131 | 0.042 | 0.282 | 0.302 | 2.288 | 0.000 | 6.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 15 | 14 | 46 | 80 | 207 | 68 |
N.S. |
1 | 1.00 | 1.11 | 0.83 | 0.78 | 2.56 | 4.44 | 11.50 | 3.78 |
time (sec) |
N/A | 0.142 | 0.036 | 0.055 | 0.194 | 0.291 | 0.395 | 0.307 | 6.680 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 33 | 30 | 60 | 416 | 239 | 88 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.79 | 1.58 | 10.95 | 6.29 | 2.32 |
time (sec) |
N/A | 0.176 | 0.054 | 0.043 | 0.198 | 0.286 | 0.887 | 0.313 | 6.880 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 49 | 44 | 47 | 71 | 1073 | 270 | 108 |
N.S. |
1 | 1.00 | 0.83 | 0.75 | 0.80 | 1.20 | 18.19 | 4.58 | 1.83 |
time (sec) |
N/A | 0.187 | 0.065 | 0.046 | 0.194 | 0.309 | 1.213 | 0.340 | 7.137 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 60 | 55 | 64 | 82 | 2562 | 301 | 128 |
N.S. |
1 | 1.00 | 0.75 | 0.69 | 0.80 | 1.02 | 32.02 | 3.76 | 1.60 |
time (sec) |
N/A | 0.203 | 0.070 | 0.053 | 0.196 | 0.284 | 1.648 | 0.321 | 7.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 71 | 66 | 81 | 93 | 5482 | 332 | 148 |
N.S. |
1 | 1.00 | 0.70 | 0.65 | 0.80 | 0.92 | 54.28 | 3.29 | 1.47 |
time (sec) |
N/A | 0.213 | 0.078 | 0.063 | 0.196 | 0.283 | 2.806 | 0.314 | 7.844 |
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 | 120 | 133 | 81 | 108 | 166 | 174 | 155 | 120 | 94 |
N.S. |
1 | 1.11 | 0.68 | 0.90 | 1.38 | 1.45 | 1.29 | 1.00 | 0.78 |
time (sec) |
N/A | 0.217 | 0.182 | 0.057 | 0.284 | 0.288 | 34.221 | 0.301 | 6.228 |
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 | 96 | 103 | 69 | 97 | 137 | 151 | 128 | 104 | 77 |
N.S. |
1 | 1.07 | 0.72 | 1.01 | 1.43 | 1.57 | 1.33 | 1.08 | 0.80 |
time (sec) |
N/A | 0.203 | 0.150 | 0.050 | 0.298 | 0.309 | 6.987 | 0.290 | 6.126 |
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 | 72 | 73 | 59 | 86 | 104 | 130 | 100 | 88 | 57 |
N.S. |
1 | 1.01 | 0.82 | 1.19 | 1.44 | 1.81 | 1.39 | 1.22 | 0.79 |
time (sec) |
N/A | 0.187 | 0.116 | 0.048 | 0.278 | 0.301 | 2.431 | 0.287 | 6.007 |
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 | 43 | 43 | 43 | 70 | 67 | 98 | 44 | 69 | 66 |
N.S. |
1 | 1.00 | 1.00 | 1.63 | 1.56 | 2.28 | 1.02 | 1.60 | 1.53 |
time (sec) |
N/A | 0.165 | 0.077 | 0.042 | 0.271 | 0.295 | 1.150 | 0.318 | 5.962 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 27 | 119 | 37 | 60 | 22 | 47 | 19 |
N.S. |
1 | 1.00 | 1.08 | 4.76 | 1.48 | 2.40 | 0.88 | 1.88 | 0.76 |
time (sec) |
N/A | 0.161 | 0.034 | 0.043 | 0.265 | 0.287 | 0.555 | 0.287 | 6.057 |
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 | 18 | 15 | 14 | 16 | 22 | 27 | 14 |
N.S. |
1 | 1.00 | 1.12 | 0.94 | 0.88 | 1.00 | 1.38 | 1.69 | 0.88 |
time (sec) |
N/A | 0.142 | 0.025 | 0.054 | 0.192 | 0.298 | 0.212 | 0.280 | 5.694 |
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 | 36 | 36 | 31 | 32 | 30 | 27 | 248 | 53 | 23 |
N.S. |
1 | 1.00 | 0.86 | 0.89 | 0.83 | 0.75 | 6.89 | 1.47 | 0.64 |
time (sec) |
N/A | 0.174 | 0.037 | 0.048 | 0.200 | 0.302 | 0.692 | 0.272 | 5.750 |
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 | 57 | 57 | 42 | 43 | 47 | 38 | 813 | 82 | 54 |
N.S. |
1 | 1.00 | 0.74 | 0.75 | 0.82 | 0.67 | 14.26 | 1.44 | 0.95 |
time (sec) |
N/A | 0.188 | 0.049 | 0.049 | 0.188 | 0.270 | 1.035 | 0.297 | 5.731 |
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 | 76 | 76 | 53 | 54 | 64 | 49 | 2164 | 111 | 73 |
N.S. |
1 | 1.00 | 0.70 | 0.71 | 0.84 | 0.64 | 28.47 | 1.46 | 0.96 |
time (sec) |
N/A | 0.200 | 0.053 | 0.049 | 0.194 | 0.277 | 1.544 | 0.284 | 5.822 |
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 | 99 | 99 | 64 | 65 | 81 | 60 | 4901 | 140 | 93 |
N.S. |
1 | 1.00 | 0.65 | 0.66 | 0.82 | 0.61 | 49.51 | 1.41 | 0.94 |
time (sec) |
N/A | 0.214 | 0.057 | 0.052 | 0.196 | 0.288 | 2.477 | 0.287 | 5.704 |
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 | 117 | 128 | 87 | 140 | 154 | 207 | 133 | 151 | 93 |
N.S. |
1 | 1.09 | 0.74 | 1.20 | 1.32 | 1.77 | 1.14 | 1.29 | 0.79 |
time (sec) |
N/A | 0.216 | 0.213 | 0.064 | 0.273 | 0.314 | 12.629 | 0.309 | 6.099 |
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 | 93 | 98 | 76 | 129 | 122 | 186 | 105 | 135 | 73 |
N.S. |
1 | 1.05 | 0.82 | 1.39 | 1.31 | 2.00 | 1.13 | 1.45 | 0.78 |
time (sec) |
N/A | 0.214 | 0.168 | 0.061 | 0.285 | 0.311 | 3.636 | 0.294 | 5.959 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 67 | 57 | 116 | 85 | 156 | 71 | 114 | 34 |
N.S. |
1 | 1.12 | 0.95 | 1.93 | 1.42 | 2.60 | 1.18 | 1.90 | 0.57 |
time (sec) |
N/A | 0.184 | 0.145 | 0.057 | 0.278 | 0.305 | 1.750 | 0.310 | 5.859 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 50 | 198 | 52 | 128 | 148 | 86 | 34 |
N.S. |
1 | 1.00 | 1.19 | 4.71 | 1.24 | 3.05 | 3.52 | 2.05 | 0.81 |
time (sec) |
N/A | 0.173 | 0.098 | 0.046 | 0.281 | 0.289 | 0.941 | 0.303 | 5.857 |
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 | 16 | 16 | 26 | 15 | 14 | 24 | 20 | 47 | 14 |
N.S. |
1 | 1.00 | 1.62 | 0.94 | 0.88 | 1.50 | 1.25 | 2.94 | 0.88 |
time (sec) |
N/A | 0.142 | 0.035 | 0.067 | 0.192 | 0.269 | 0.284 | 0.282 | 5.748 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 31 | 31 | 30 | 31 | 42 | 33 | 36 |
N.S. |
1 | 1.00 | 0.91 | 0.91 | 0.88 | 0.91 | 1.24 | 0.97 | 1.06 |
time (sec) |
N/A | 0.178 | 0.045 | 0.098 | 0.222 | 0.272 | 0.331 | 0.278 | 5.781 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 49 | 44 | 47 | 48 | 457 | 0 | 43 |
N.S. |
1 | 1.00 | 0.89 | 0.80 | 0.85 | 0.87 | 8.31 | 0.00 | 0.78 |
time (sec) |
N/A | 0.192 | 0.055 | 0.058 | 0.208 | 0.285 | 1.038 | 0.000 | 5.765 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 58 | 53 | 64 | 59 | 2032 | 0 | 52 |
N.S. |
1 | 1.00 | 0.78 | 0.72 | 0.86 | 0.80 | 27.46 | 0.00 | 0.70 |
time (sec) |
N/A | 0.208 | 0.063 | 0.064 | 0.202 | 0.300 | 1.650 | 0.000 | 5.917 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 71 | 66 | 81 | 72 | 4707 | 0 | 91 |
N.S. |
1 | 1.00 | 0.75 | 0.69 | 0.85 | 0.76 | 49.55 | 0.00 | 0.96 |
time (sec) |
N/A | 0.214 | 0.074 | 0.063 | 0.188 | 0.282 | 2.560 | 0.000 | 5.866 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 82 | 77 | 98 | 83 | 9534 | 0 | 112 |
N.S. |
1 | 1.00 | 0.71 | 0.66 | 0.84 | 0.72 | 82.19 | 0.00 | 0.97 |
time (sec) |
N/A | 0.228 | 0.073 | 0.071 | 0.179 | 0.288 | 5.594 | 0.000 | 5.942 |
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 | 138 | 151 | 98 | 181 | 171 | 273 | 532 | 208 | 113 |
N.S. |
1 | 1.09 | 0.71 | 1.31 | 1.24 | 1.98 | 3.86 | 1.51 | 0.82 |
time (sec) |
N/A | 0.237 | 0.189 | 0.079 | 0.276 | 0.330 | 87.595 | 0.313 | 6.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 121 | 87 | 170 | 139 | 252 | 464 | 192 | 93 |
N.S. |
1 | 1.06 | 0.76 | 1.49 | 1.22 | 2.21 | 4.07 | 1.68 | 0.82 |
time (sec) |
N/A | 0.227 | 0.148 | 0.081 | 0.276 | 0.291 | 8.029 | 0.319 | 6.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 90 | 72 | 157 | 101 | 225 | 774 | 171 | 34 |
N.S. |
1 | 1.14 | 0.91 | 1.99 | 1.28 | 2.85 | 9.80 | 2.16 | 0.43 |
time (sec) |
N/A | 0.200 | 0.136 | 0.074 | 0.279 | 0.300 | 2.632 | 0.309 | 5.825 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 66 | 60 | 274 | 62 | 197 | 700 | 146 | 49 |
N.S. |
1 | 1.10 | 1.00 | 4.57 | 1.03 | 3.28 | 11.67 | 2.43 | 0.82 |
time (sec) |
N/A | 0.185 | 0.114 | 0.053 | 0.272 | 0.292 | 1.493 | 0.292 | 6.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 15 | 14 | 37 | 39 | 100 | 14 |
N.S. |
1 | 1.00 | 1.11 | 0.83 | 0.78 | 2.06 | 2.17 | 5.56 | 0.78 |
time (sec) |
N/A | 0.142 | 0.035 | 0.065 | 0.203 | 0.304 | 0.490 | 0.284 | 5.925 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 33 | 30 | 47 | 82 | 75 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 1.31 | 2.28 | 2.08 | 0.69 |
time (sec) |
N/A | 0.173 | 0.056 | 0.052 | 0.194 | 0.275 | 0.539 | 0.284 | 5.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 46 | 44 | 47 | 55 | 136 | 0 | 40 |
N.S. |
1 | 1.00 | 0.84 | 0.80 | 0.85 | 1.00 | 2.47 | 0.00 | 0.73 |
time (sec) |
N/A | 0.191 | 0.056 | 0.063 | 0.192 | 0.283 | 0.607 | 0.000 | 5.764 |
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 | 76 | 76 | 60 | 55 | 64 | 70 | 187 | 66 | 54 |
N.S. |
1 | 1.00 | 0.79 | 0.72 | 0.84 | 0.92 | 2.46 | 0.87 | 0.71 |
time (sec) |
N/A | 0.198 | 0.068 | 0.067 | 0.194 | 0.293 | 0.673 | 0.300 | 5.658 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 71 | 66 | 81 | 83 | 2032 | 0 | 65 |
N.S. |
1 | 1.00 | 0.73 | 0.68 | 0.84 | 0.86 | 20.95 | 0.00 | 0.67 |
time (sec) |
N/A | 0.216 | 0.074 | 0.069 | 0.194 | 0.274 | 2.440 | 0.000 | 5.709 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 82 | 77 | 98 | 94 | 9263 | 0 | 110 |
N.S. |
1 | 1.00 | 0.71 | 0.66 | 0.84 | 0.81 | 79.85 | 0.00 | 0.95 |
time (sec) |
N/A | 0.230 | 0.078 | 0.077 | 0.190 | 0.275 | 5.202 | 0.000 | 5.794 |
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 | 100 | 112 | 64 | 55 | 69 | 60 | 518 | 61 | 58 |
N.S. |
1 | 1.12 | 0.64 | 0.55 | 0.69 | 0.60 | 5.18 | 0.61 | 0.58 |
time (sec) |
N/A | 0.225 | 5.230 | 0.043 | 0.197 | 0.290 | 17.340 | 0.282 | 6.265 |
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 | 74 | 80 | 53 | 44 | 52 | 49 | 314 | 50 | 47 |
N.S. |
1 | 1.08 | 0.72 | 0.59 | 0.70 | 0.66 | 4.24 | 0.68 | 0.64 |
time (sec) |
N/A | 0.203 | 5.267 | 0.041 | 0.194 | 0.286 | 6.061 | 0.278 | 6.117 |
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 | 48 | 48 | 41 | 33 | 35 | 37 | 65 | 37 | 36 |
N.S. |
1 | 1.00 | 0.85 | 0.69 | 0.73 | 0.77 | 1.35 | 0.77 | 0.75 |
time (sec) |
N/A | 0.170 | 5.572 | 0.037 | 0.211 | 0.268 | 1.980 | 0.291 | 5.995 |
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 | 23 | 28 | 25 | 17 | 24 | 39 | 24 | 22 |
N.S. |
1 | 1.00 | 1.22 | 1.09 | 0.74 | 1.04 | 1.70 | 1.04 | 0.96 |
time (sec) |
N/A | 0.142 | 5.517 | 0.017 | 0.189 | 0.296 | 0.705 | 0.277 | 6.071 |
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 | 49 | 50 | 61 | 50 | 59 | 101 | 68 | 62 | 0 |
N.S. |
1 | 1.02 | 1.24 | 1.02 | 1.20 | 2.06 | 1.39 | 1.27 | 0.00 |
time (sec) |
N/A | 0.172 | 5.303 | 0.039 | 0.279 | 0.293 | 0.983 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 56 | 61 | 54 | 77 | 121 | 44 | 43 | 0 |
N.S. |
1 | 1.12 | 1.22 | 1.08 | 1.54 | 2.42 | 0.88 | 0.86 | 0.00 |
time (sec) |
N/A | 0.170 | 5.319 | 0.046 | 0.272 | 0.284 | 1.433 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 85 | 82 | 69 | 118 | 147 | 97 | 68 | 0 |
N.S. |
1 | 1.06 | 1.02 | 0.86 | 1.48 | 1.84 | 1.21 | 0.85 | 0.00 |
time (sec) |
N/A | 0.194 | 5.778 | 0.047 | 0.273 | 0.294 | 3.501 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 117 | 89 | 81 | 161 | 173 | 122 | 86 | 0 |
N.S. |
1 | 1.10 | 0.84 | 0.76 | 1.52 | 1.63 | 1.15 | 0.81 | 0.00 |
time (sec) |
N/A | 0.216 | 10.172 | 0.051 | 0.282 | 0.314 | 10.164 | 0.329 | 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 | 100 | 112 | 60 | 55 | 69 | 71 | 585 | 138 | 67 |
N.S. |
1 | 1.12 | 0.60 | 0.55 | 0.69 | 0.71 | 5.85 | 1.38 | 0.67 |
time (sec) |
N/A | 0.225 | 6.342 | 0.043 | 0.195 | 0.288 | 80.647 | 0.290 | 6.392 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 80 | 49 | 44 | 52 | 60 | 369 | 114 | 56 |
N.S. |
1 | 1.08 | 0.66 | 0.59 | 0.70 | 0.81 | 4.99 | 1.54 | 0.76 |
time (sec) |
N/A | 0.202 | 6.231 | 0.041 | 0.193 | 0.430 | 28.015 | 0.289 | 6.338 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 38 | 33 | 35 | 48 | 88 | 90 | 45 |
N.S. |
1 | 1.00 | 0.79 | 0.69 | 0.73 | 1.00 | 1.83 | 1.88 | 0.94 |
time (sec) |
N/A | 0.173 | 6.234 | 0.039 | 0.194 | 0.280 | 9.981 | 0.289 | 6.325 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 30 | 25 | 17 | 35 | 63 | 64 | 34 |
N.S. |
1 | 1.00 | 1.30 | 1.09 | 0.74 | 1.52 | 2.74 | 2.78 | 1.48 |
time (sec) |
N/A | 0.145 | 6.212 | 0.016 | 0.193 | 0.270 | 3.361 | 0.278 | 6.376 |
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 | 70 | 73 | 70 | 63 | 74 | 116 | 71 | 44 | 0 |
N.S. |
1 | 1.04 | 1.00 | 0.90 | 1.06 | 1.66 | 1.01 | 0.63 | 0.00 |
time (sec) |
N/A | 0.195 | 6.247 | 0.038 | 0.280 | 0.342 | 2.723 | 0.304 | 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 | 69 | 78 | 69 | 70 | 93 | 130 | 92 | 56 | 0 |
N.S. |
1 | 1.13 | 1.00 | 1.01 | 1.35 | 1.88 | 1.33 | 0.81 | 0.00 |
time (sec) |
N/A | 0.185 | 6.295 | 0.051 | 0.267 | 0.269 | 2.437 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 82 | 79 | 67 | 117 | 152 | 76 | 64 | 0 |
N.S. |
1 | 1.06 | 1.03 | 0.87 | 1.52 | 1.97 | 0.99 | 0.83 | 0.00 |
time (sec) |
N/A | 0.188 | 6.394 | 0.046 | 0.271 | 0.365 | 2.645 | 0.321 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 111 | 93 | 81 | 159 | 173 | 124 | 84 | 0 |
N.S. |
1 | 1.08 | 0.90 | 0.79 | 1.54 | 1.68 | 1.20 | 0.82 | 0.00 |
time (sec) |
N/A | 0.209 | 6.366 | 0.058 | 0.276 | 0.283 | 5.521 | 0.322 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 112 | 60 | 55 | 69 | 82 | 0 | 229 | 78 |
N.S. |
1 | 1.12 | 0.60 | 0.55 | 0.69 | 0.82 | 0.00 | 2.29 | 0.78 |
time (sec) |
N/A | 0.230 | 6.872 | 0.066 | 0.191 | 0.270 | 0.000 | 0.306 | 6.412 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 80 | 49 | 44 | 52 | 71 | 423 | 194 | 67 |
N.S. |
1 | 1.08 | 0.66 | 0.59 | 0.70 | 0.96 | 5.72 | 2.62 | 0.91 |
time (sec) |
N/A | 0.197 | 6.865 | 0.063 | 0.187 | 0.318 | 131.377 | 0.298 | 6.598 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 38 | 33 | 35 | 59 | 114 | 157 | 56 |
N.S. |
1 | 1.00 | 0.79 | 0.69 | 0.73 | 1.23 | 2.38 | 3.27 | 1.17 |
time (sec) |
N/A | 0.170 | 6.820 | 0.061 | 0.182 | 0.276 | 45.163 | 0.280 | 6.729 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 30 | 25 | 17 | 46 | 88 | 120 | 45 |
N.S. |
1 | 1.00 | 1.30 | 1.09 | 0.74 | 2.00 | 3.83 | 5.22 | 1.96 |
time (sec) |
N/A | 0.148 | 6.804 | 0.039 | 0.197 | 0.256 | 16.740 | 0.274 | 6.667 |
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 | 93 | 96 | 82 | 81 | 91 | 142 | 97 | 56 | 0 |
N.S. |
1 | 1.03 | 0.88 | 0.87 | 0.98 | 1.53 | 1.04 | 0.60 | 0.00 |
time (sec) |
N/A | 0.208 | 6.909 | 0.038 | 0.273 | 0.287 | 11.603 | 0.281 | 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 | 94 | 104 | 86 | 82 | 111 | 154 | 99 | 74 | 0 |
N.S. |
1 | 1.11 | 0.91 | 0.87 | 1.18 | 1.64 | 1.05 | 0.79 | 0.00 |
time (sec) |
N/A | 0.201 | 6.901 | 0.051 | 0.268 | 0.297 | 7.346 | 0.334 | 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 | 97 | 104 | 90 | 80 | 137 | 161 | 126 | 80 | 0 |
N.S. |
1 | 1.07 | 0.93 | 0.82 | 1.41 | 1.66 | 1.30 | 0.82 | 0.00 |
time (sec) |
N/A | 0.198 | 6.950 | 0.056 | 0.278 | 0.336 | 6.280 | 0.333 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 108 | 90 | 78 | 156 | 174 | 104 | 79 | 0 |
N.S. |
1 | 1.08 | 0.90 | 0.78 | 1.56 | 1.74 | 1.04 | 0.79 | 0.00 |
time (sec) |
N/A | 0.195 | 7.075 | 0.049 | 0.271 | 0.296 | 6.494 | 0.329 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 126 | 137 | 104 | 92 | 194 | 195 | 155 | 99 | 0 |
N.S. |
1 | 1.09 | 0.83 | 0.73 | 1.54 | 1.55 | 1.23 | 0.79 | 0.00 |
time (sec) |
N/A | 0.232 | 7.090 | 0.056 | 0.273 | 0.367 | 10.874 | 0.343 | 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 | 126 | 144 | 64 | 61 | 86 | 60 | 692 | 78 | 61 |
N.S. |
1 | 1.14 | 0.51 | 0.48 | 0.68 | 0.48 | 5.49 | 0.62 | 0.48 |
time (sec) |
N/A | 0.257 | 4.624 | 0.025 | 0.209 | 0.273 | 14.552 | 0.284 | 6.663 |
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 | 100 | 112 | 53 | 50 | 69 | 49 | 452 | 67 | 50 |
N.S. |
1 | 1.12 | 0.53 | 0.50 | 0.69 | 0.49 | 4.52 | 0.67 | 0.50 |
time (sec) |
N/A | 0.231 | 4.636 | 0.023 | 0.185 | 0.269 | 5.085 | 0.280 | 6.658 |
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 | 74 | 80 | 42 | 39 | 52 | 38 | 260 | 54 | 39 |
N.S. |
1 | 1.08 | 0.57 | 0.53 | 0.70 | 0.51 | 3.51 | 0.73 | 0.53 |
time (sec) |
N/A | 0.192 | 4.606 | 0.023 | 0.223 | 0.296 | 1.665 | 0.299 | 6.489 |
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 | 48 | 48 | 30 | 27 | 34 | 26 | 42 | 39 | 28 |
N.S. |
1 | 1.00 | 0.62 | 0.56 | 0.71 | 0.54 | 0.88 | 0.81 | 0.58 |
time (sec) |
N/A | 0.167 | 4.580 | 0.021 | 0.201 | 0.311 | 0.626 | 0.271 | 6.468 |
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 | 21 | 21 | 20 | 17 | 19 | 17 | 26 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.81 | 0.90 | 0.81 | 1.24 | 0.81 |
time (sec) |
N/A | 0.143 | 4.552 | 0.017 | 0.195 | 0.265 | 0.686 | 0.294 | 6.027 |
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 | 30 | 32 | 39 | 44 | 70 | 24 | 44 | 0 |
N.S. |
1 | 1.00 | 1.07 | 1.30 | 1.47 | 2.33 | 0.80 | 1.47 | 0.00 |
time (sec) |
N/A | 0.160 | 2.725 | 0.043 | 0.278 | 0.436 | 1.319 | 0.305 | 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 | 52 | 59 | 54 | 55 | 80 | 121 | 44 | 51 | 0 |
N.S. |
1 | 1.13 | 1.04 | 1.06 | 1.54 | 2.33 | 0.85 | 0.98 | 0.00 |
time (sec) |
N/A | 0.177 | 4.010 | 0.043 | 0.293 | 0.274 | 3.525 | 0.300 | 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 | 83 | 91 | 93 | 74 | 122 | 151 | 102 | 73 | 0 |
N.S. |
1 | 1.10 | 1.12 | 0.89 | 1.47 | 1.82 | 1.23 | 0.88 | 0.00 |
time (sec) |
N/A | 0.197 | 10.081 | 0.043 | 0.282 | 0.297 | 10.271 | 0.332 | 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 | 109 | 123 | 106 | 86 | 161 | 173 | 129 | 88 | 0 |
N.S. |
1 | 1.13 | 0.97 | 0.79 | 1.48 | 1.59 | 1.18 | 0.81 | 0.00 |
time (sec) |
N/A | 0.219 | 10.076 | 0.050 | 0.272 | 0.342 | 30.505 | 0.321 | 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 | 126 | 140 | 71 | 66 | 90 | 70 | 614 | 77 | 67 |
N.S. |
1 | 1.11 | 0.56 | 0.52 | 0.71 | 0.56 | 4.87 | 0.61 | 0.53 |
time (sec) |
N/A | 0.250 | 5.821 | 0.035 | 0.189 | 0.313 | 5.811 | 0.276 | 6.405 |
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 | 100 | 108 | 59 | 54 | 72 | 58 | 320 | 61 | 59 |
N.S. |
1 | 1.08 | 0.59 | 0.54 | 0.72 | 0.58 | 3.20 | 0.61 | 0.59 |
time (sec) |
N/A | 0.219 | 5.467 | 0.032 | 0.184 | 0.308 | 1.994 | 0.292 | 6.356 |
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 | 74 | 76 | 48 | 43 | 55 | 47 | 206 | 46 | 49 |
N.S. |
1 | 1.03 | 0.65 | 0.58 | 0.74 | 0.64 | 2.78 | 0.62 | 0.66 |
time (sec) |
N/A | 0.192 | 5.435 | 0.032 | 0.195 | 0.254 | 1.106 | 0.275 | 6.348 |
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 | 44 | 44 | 35 | 32 | 36 | 36 | 39 | 29 | 37 |
N.S. |
1 | 1.00 | 0.80 | 0.73 | 0.82 | 0.82 | 0.89 | 0.66 | 0.84 |
time (sec) |
N/A | 0.162 | 5.433 | 0.029 | 0.191 | 0.272 | 1.292 | 0.293 | 6.329 |
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 | 21 | 28 | 25 | 17 | 27 | 19 | 12 | 25 |
N.S. |
1 | 1.00 | 1.33 | 1.19 | 0.81 | 1.29 | 0.90 | 0.57 | 1.19 |
time (sec) |
N/A | 0.138 | 5.421 | 0.023 | 0.205 | 0.297 | 2.150 | 0.286 | 6.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 53 | 64 | 52 | 62 | 138 | 146 | 37 | 0 |
N.S. |
1 | 1.02 | 1.23 | 1.00 | 1.19 | 2.65 | 2.81 | 0.71 | 0.00 |
time (sec) |
N/A | 0.170 | 5.546 | 0.042 | 0.280 | 0.286 | 5.688 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 86 | 56 | 61 | 101 | 179 | 73 | 64 | 0 |
N.S. |
1 | 1.16 | 0.76 | 0.82 | 1.36 | 2.42 | 0.99 | 0.86 | 0.00 |
time (sec) |
N/A | 0.190 | 10.019 | 0.061 | 0.287 | 0.265 | 16.859 | 0.322 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 104 | 118 | 56 | 78 | 143 | 217 | 107 | 80 | 0 |
N.S. |
1 | 1.13 | 0.54 | 0.75 | 1.38 | 2.09 | 1.03 | 0.77 | 0.00 |
time (sec) |
N/A | 0.216 | 10.019 | 0.061 | 0.274 | 0.257 | 45.287 | 0.332 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 130 | 150 | 56 | 89 | 181 | 239 | 134 | 95 | 0 |
N.S. |
1 | 1.15 | 0.43 | 0.68 | 1.39 | 1.84 | 1.03 | 0.73 | 0.00 |
time (sec) |
N/A | 0.239 | 10.022 | 0.063 | 0.312 | 0.288 | 141.836 | 0.348 | 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 | 152 | 168 | 82 | 77 | 106 | 92 | 799 | 90 | 78 |
N.S. |
1 | 1.11 | 0.54 | 0.51 | 0.70 | 0.61 | 5.26 | 0.59 | 0.51 |
time (sec) |
N/A | 0.285 | 6.340 | 0.039 | 0.203 | 0.254 | 6.116 | 0.312 | 6.672 |
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 | 126 | 136 | 71 | 66 | 89 | 81 | 536 | 75 | 81 |
N.S. |
1 | 1.08 | 0.56 | 0.52 | 0.71 | 0.64 | 4.25 | 0.60 | 0.64 |
time (sec) |
N/A | 0.252 | 6.339 | 0.038 | 0.193 | 0.261 | 3.495 | 0.291 | 6.477 |
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 | 96 | 104 | 59 | 54 | 71 | 69 | 320 | 59 | 71 |
N.S. |
1 | 1.08 | 0.61 | 0.56 | 0.74 | 0.72 | 3.33 | 0.61 | 0.74 |
time (sec) |
N/A | 0.223 | 6.340 | 0.037 | 0.190 | 0.329 | 2.520 | 0.278 | 6.388 |
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 | 70 | 74 | 49 | 44 | 52 | 59 | 151 | 39 | 43 |
N.S. |
1 | 1.06 | 0.70 | 0.63 | 0.74 | 0.84 | 2.16 | 0.56 | 0.61 |
time (sec) |
N/A | 0.189 | 6.335 | 0.037 | 0.191 | 0.275 | 3.152 | 0.313 | 6.348 |
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 | 46 | 46 | 38 | 33 | 31 | 48 | 94 | 20 | 49 |
N.S. |
1 | 1.00 | 0.83 | 0.72 | 0.67 | 1.04 | 2.04 | 0.43 | 1.07 |
time (sec) |
N/A | 0.160 | 6.340 | 0.030 | 0.198 | 0.287 | 5.280 | 0.308 | 6.362 |
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 | 23 | 23 | 30 | 25 | 17 | 38 | 42 | 12 | 38 |
N.S. |
1 | 1.00 | 1.30 | 1.09 | 0.74 | 1.65 | 1.83 | 0.52 | 1.65 |
time (sec) |
N/A | 0.142 | 6.344 | 0.026 | 0.202 | 0.302 | 9.035 | 0.300 | 6.319 |