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 | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 177 | 133 | 116 | 116 | 116 | 177 | 104 | 176 | 0 |
N.S. |
1 | 1.26 | 0.94 | 0.82 | 0.82 | 0.82 | 1.26 | 0.74 | 1.25 | 0.00 |
time (sec) |
N/A | 0.418 | 0.390 | 0.204 | 0.106 | 0.101 | 0.553 | 0.143 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 180 | 164 | 286 | 164 | 129 | 651 | 137 | 162 | 0 |
N.S. |
1 | 0.95 | 0.86 | 1.51 | 0.86 | 0.68 | 3.43 | 0.72 | 0.85 | 0.00 |
time (sec) |
N/A | 0.741 | 0.613 | 0.202 | 0.116 | 0.106 | 6.955 | 0.140 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 175 | 171 | 215 | 174 | 146 | 615 | 200 | 174 | 0 |
N.S. |
1 | 0.90 | 0.88 | 1.11 | 0.90 | 0.75 | 3.17 | 1.03 | 0.90 | 0.00 |
time (sec) |
N/A | 0.759 | 0.533 | 0.233 | 0.112 | 0.133 | 2.851 | 0.143 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 208 | 183 | 177 | 200 | 184 | 158 | 643 | 268 | 186 | 0 |
N.S. |
1 | 0.88 | 0.85 | 0.96 | 0.88 | 0.76 | 3.09 | 1.29 | 0.89 | 0.00 |
time (sec) |
N/A | 0.783 | 0.554 | 0.233 | 0.123 | 0.109 | 3.595 | 0.132 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 216 | 174 | 173 | 188 | 181 | 158 | 624 | 322 | 186 | 0 |
N.S. |
1 | 0.81 | 0.80 | 0.87 | 0.84 | 0.73 | 2.89 | 1.49 | 0.86 | 0.00 |
time (sec) |
N/A | 0.761 | 0.574 | 0.239 | 0.113 | 0.119 | 3.788 | 0.136 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 180 | 175 | 174 | 204 | 157 | 767 | 385 | 186 | 0 |
N.S. |
1 | 0.85 | 0.83 | 0.82 | 0.97 | 0.74 | 3.64 | 1.82 | 0.88 | 0.00 |
time (sec) |
N/A | 0.765 | 0.596 | 0.250 | 0.130 | 0.106 | 5.694 | 0.145 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 209 | 184 | 171 | 160 | 231 | 151 | 1022 | 415 | 180 | 0 |
N.S. |
1 | 0.88 | 0.82 | 0.77 | 1.11 | 0.72 | 4.89 | 1.99 | 0.86 | 0.00 |
time (sec) |
N/A | 0.794 | 0.508 | 0.304 | 0.125 | 0.108 | 5.893 | 0.143 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 191 | 173 | 147 | 255 | 141 | 1161 | 455 | 169 | 0 |
N.S. |
1 | 0.89 | 0.81 | 0.69 | 1.19 | 0.66 | 5.43 | 2.13 | 0.79 | 0.00 |
time (sec) |
N/A | 0.810 | 0.485 | 0.264 | 0.110 | 0.115 | 9.767 | 0.143 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 183 | 144 | 129 | 200 | 120 | 1272 | 518 | 181 | 0 |
N.S. |
1 | 1.10 | 0.86 | 0.77 | 1.20 | 0.72 | 7.62 | 3.10 | 1.08 | 0.00 |
time (sec) |
N/A | 0.688 | 0.470 | 0.319 | 0.111 | 0.118 | 10.126 | 0.132 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 218 | 164 | 143 | 225 | 131 | 1482 | 597 | 205 | 0 |
N.S. |
1 | 1.11 | 0.84 | 0.73 | 1.15 | 0.67 | 7.56 | 3.05 | 1.05 | 0.00 |
time (sec) |
N/A | 0.785 | 0.485 | 0.342 | 0.122 | 0.125 | 28.521 | 0.147 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 253 | 175 | 154 | 250 | 142 | 1661 | 648 | 229 | 0 |
N.S. |
1 | 1.12 | 0.78 | 0.68 | 1.11 | 0.63 | 7.38 | 2.88 | 1.02 | 0.00 |
time (sec) |
N/A | 0.828 | 0.513 | 0.414 | 0.126 | 0.160 | 31.685 | 0.150 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 288 | 186 | 165 | 275 | 153 | 1843 | 731 | 253 | 0 |
N.S. |
1 | 1.13 | 0.73 | 0.65 | 1.08 | 0.60 | 7.26 | 2.88 | 1.00 | 0.00 |
time (sec) |
N/A | 0.885 | 0.515 | 0.463 | 0.111 | 0.151 | 133.210 | 0.144 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 182 | 114 | 108 | 198 | 106 | 178 | 94 | 152 | 0 |
N.S. |
1 | 1.12 | 0.70 | 0.66 | 1.21 | 0.65 | 1.09 | 0.58 | 0.93 | 0.00 |
time (sec) |
N/A | 0.541 | 0.292 | 0.250 | 0.126 | 0.105 | 1.377 | 0.136 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 147 | 103 | 97 | 174 | 94 | 167 | 83 | 128 | 0 |
N.S. |
1 | 1.10 | 0.77 | 0.72 | 1.30 | 0.70 | 1.25 | 0.62 | 0.96 | 0.00 |
time (sec) |
N/A | 0.478 | 0.262 | 0.237 | 0.121 | 0.095 | 1.356 | 0.135 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 111 | 92 | 86 | 153 | 84 | 153 | 71 | 104 | 0 |
N.S. |
1 | 1.05 | 0.87 | 0.81 | 1.44 | 0.79 | 1.44 | 0.67 | 0.98 | 0.00 |
time (sec) |
N/A | 0.389 | 0.227 | 0.225 | 0.118 | 0.105 | 1.317 | 0.136 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 78 | 89 | 72 | 88 | 72 | 134 | 56 | 80 | 0 |
N.S. |
1 | 1.03 | 1.17 | 0.95 | 1.16 | 0.95 | 1.76 | 0.74 | 1.05 | 0.00 |
time (sec) |
N/A | 0.305 | 0.173 | 0.231 | 0.130 | 0.099 | 1.269 | 0.131 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 113 | 220 | 84 | 83 | 207 | 89 | 65 | 0 |
N.S. |
1 | 1.00 | 1.38 | 2.68 | 1.02 | 1.01 | 2.52 | 1.09 | 0.79 | 0.00 |
time (sec) |
N/A | 0.422 | 0.223 | 0.233 | 0.120 | 0.137 | 4.067 | 0.142 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 113 | 114 | 84 | 92 | 230 | 147 | 102 | 0 |
N.S. |
1 | 1.00 | 1.51 | 1.52 | 1.12 | 1.23 | 3.07 | 1.96 | 1.36 | 0.00 |
time (sec) |
N/A | 0.417 | 0.206 | 0.263 | 0.115 | 0.100 | 2.856 | 0.135 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 83 | 127 | 101 | 112 | 96 | 224 | 197 | 73 | 0 |
N.S. |
1 | 1.01 | 1.55 | 1.23 | 1.37 | 1.17 | 2.73 | 2.40 | 0.89 | 0.00 |
time (sec) |
N/A | 0.432 | 0.206 | 0.234 | 0.155 | 0.110 | 2.988 | 0.140 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 82 | 100 | 85 | 108 | 75 | 216 | 256 | 85 | 0 |
N.S. |
1 | 1.00 | 1.22 | 1.04 | 1.32 | 0.91 | 2.63 | 3.12 | 1.04 | 0.00 |
time (sec) |
N/A | 0.349 | 0.208 | 0.227 | 0.114 | 0.096 | 2.591 | 0.145 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 117 | 120 | 99 | 133 | 86 | 304 | 264 | 109 | 0 |
N.S. |
1 | 1.04 | 1.07 | 0.88 | 1.19 | 0.77 | 2.71 | 2.36 | 0.97 | 0.00 |
time (sec) |
N/A | 0.397 | 0.178 | 0.257 | 0.111 | 0.097 | 3.665 | 0.135 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 152 | 131 | 110 | 158 | 97 | 546 | 326 | 133 | 0 |
N.S. |
1 | 1.09 | 0.94 | 0.79 | 1.13 | 0.69 | 3.90 | 2.33 | 0.95 | 0.00 |
time (sec) |
N/A | 0.469 | 0.193 | 0.283 | 0.106 | 0.133 | 3.849 | 0.144 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 187 | 142 | 121 | 183 | 108 | 602 | 463 | 157 | 0 |
N.S. |
1 | 1.10 | 0.84 | 0.71 | 1.08 | 0.64 | 3.54 | 2.72 | 0.92 | 0.00 |
time (sec) |
N/A | 0.548 | 0.225 | 0.274 | 0.115 | 0.144 | 6.690 | 0.142 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 176 | 111 | 97 | 228 | 95 | 0 | 217 | 128 | 0 |
N.S. |
1 | 1.14 | 0.72 | 0.63 | 1.47 | 0.61 | 0.00 | 1.40 | 0.83 | 0.00 |
time (sec) |
N/A | 0.547 | 0.026 | 0.263 | 0.127 | 0.093 | 0.000 | 0.151 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 145 | 92 | 86 | 207 | 83 | 0 | 185 | 104 | 0 |
N.S. |
1 | 1.12 | 0.71 | 0.67 | 1.60 | 0.64 | 0.00 | 1.43 | 0.81 | 0.00 |
time (sec) |
N/A | 0.489 | 0.021 | 0.208 | 0.114 | 0.088 | 0.000 | 0.159 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 112 | 88 | 74 | 158 | 72 | 0 | 153 | 80 | 0 |
N.S. |
1 | 1.12 | 0.88 | 0.74 | 1.58 | 0.72 | 0.00 | 1.53 | 0.80 | 0.00 |
time (sec) |
N/A | 0.358 | 0.200 | 0.218 | 0.125 | 0.107 | 0.000 | 0.149 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 82 | 72 | 61 | 63 | 60 | 0 | 121 | 56 | 0 |
N.S. |
1 | 1.32 | 1.16 | 0.98 | 1.02 | 0.97 | 0.00 | 1.95 | 0.90 | 0.00 |
time (sec) |
N/A | 0.307 | 0.014 | 0.215 | 0.120 | 0.094 | 0.000 | 0.143 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 67 | 100 | 410 | 0 | 73 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.02 | 1.52 | 6.21 | 0.00 | 1.11 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.434 | 0.220 | 0.217 | 0.000 | 0.096 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 71 | 112 | 93 | 0 | 79 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.04 | 1.65 | 1.37 | 0.00 | 1.16 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.430 | 0.213 | 0.233 | 0.000 | 0.131 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 81 | 88 | 72 | 0 | 64 | 0 | 172 | 61 | 0 |
N.S. |
1 | 1.01 | 1.10 | 0.90 | 0.00 | 0.80 | 0.00 | 2.15 | 0.76 | 0.00 |
time (sec) |
N/A | 0.409 | 0.210 | 0.237 | 0.000 | 0.087 | 0.000 | 0.153 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 112 | 99 | 85 | 0 | 73 | 0 | 216 | 85 | 0 |
N.S. |
1 | 1.07 | 0.94 | 0.81 | 0.00 | 0.70 | 0.00 | 2.06 | 0.81 | 0.00 |
time (sec) |
N/A | 0.462 | 0.275 | 0.296 | 0.000 | 0.087 | 0.000 | 0.157 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 151 | 101 | 99 | 0 | 86 | 0 | 245 | 109 | 0 |
N.S. |
1 | 1.08 | 0.72 | 0.71 | 0.00 | 0.61 | 0.00 | 1.75 | 0.78 | 0.00 |
time (sec) |
N/A | 0.529 | 0.328 | 0.279 | 0.000 | 0.102 | 0.000 | 0.156 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 182 | 131 | 110 | 0 | 97 | 0 | 274 | 133 | 0 |
N.S. |
1 | 1.08 | 0.78 | 0.65 | 0.00 | 0.57 | 0.00 | 1.62 | 0.79 | 0.00 |
time (sec) |
N/A | 0.611 | 0.293 | 0.305 | 0.000 | 0.088 | 0.000 | 0.157 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 186 | 110 | 131 | 282 | 124 | 0 | 119 | 236 | 0 |
N.S. |
1 | 1.16 | 0.68 | 0.81 | 1.75 | 0.77 | 0.00 | 0.74 | 1.47 | 0.00 |
time (sec) |
N/A | 0.887 | 0.403 | 0.243 | 0.127 | 0.097 | 0.000 | 0.142 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 153 | 101 | 120 | 232 | 112 | 0 | 108 | 201 | 0 |
N.S. |
1 | 1.14 | 0.75 | 0.90 | 1.73 | 0.84 | 0.00 | 0.81 | 1.50 | 0.00 |
time (sec) |
N/A | 0.681 | 0.351 | 0.277 | 0.112 | 0.099 | 0.000 | 0.142 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 111 | 90 | 109 | 138 | 101 | 0 | 96 | 164 | 0 |
N.S. |
1 | 1.03 | 0.83 | 1.01 | 1.28 | 0.94 | 0.00 | 0.89 | 1.52 | 0.00 |
time (sec) |
N/A | 0.482 | 0.305 | 0.237 | 0.116 | 0.096 | 0.000 | 0.142 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 78 | 94 | 79 | 83 | 0 | 77 | 123 | 0 |
N.S. |
1 | 1.00 | 1.01 | 1.22 | 1.03 | 1.08 | 0.00 | 1.00 | 1.60 | 0.00 |
time (sec) |
N/A | 0.329 | 0.268 | 0.239 | 0.108 | 0.097 | 0.000 | 0.130 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 112 | 652 | 0 | 96 | 0 | 98 | 86 | 0 |
N.S. |
1 | 1.00 | 1.62 | 9.45 | 0.00 | 1.39 | 0.00 | 1.42 | 1.25 | 0.00 |
time (sec) |
N/A | 0.412 | 0.309 | 0.234 | 0.000 | 0.122 | 0.000 | 0.148 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 88 | 106 | 0 | 89 | 0 | 178 | 108 | 0 |
N.S. |
1 | 1.00 | 1.09 | 1.31 | 0.00 | 1.10 | 0.00 | 2.20 | 1.33 | 0.00 |
time (sec) |
N/A | 0.386 | 0.320 | 0.287 | 0.000 | 0.086 | 0.000 | 0.142 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 118 | 108 | 118 | 0 | 114 | 0 | 256 | 138 | 0 |
N.S. |
1 | 1.04 | 0.95 | 1.04 | 0.00 | 1.00 | 0.00 | 2.25 | 1.21 | 0.00 |
time (sec) |
N/A | 0.581 | 0.319 | 0.303 | 0.000 | 0.095 | 0.000 | 0.143 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 149 | 119 | 133 | 0 | 125 | 0 | 318 | 166 | 0 |
N.S. |
1 | 1.03 | 0.82 | 0.92 | 0.00 | 0.86 | 0.00 | 2.19 | 1.14 | 0.00 |
time (sec) |
N/A | 0.805 | 0.393 | 0.319 | 0.000 | 0.105 | 0.000 | 0.139 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 181 | 130 | 144 | 0 | 136 | 0 | 390 | 194 | 0 |
N.S. |
1 | 1.07 | 0.77 | 0.85 | 0.00 | 0.80 | 0.00 | 2.31 | 1.15 | 0.00 |
time (sec) |
N/A | 1.116 | 0.387 | 0.339 | 0.000 | 0.138 | 0.000 | 0.145 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 194 | 119 | 164 | 330 | 155 | 0 | 176 | 308 | 0 |
N.S. |
1 | 1.17 | 0.72 | 0.99 | 1.99 | 0.93 | 0.00 | 1.06 | 1.86 | 0.00 |
time (sec) |
N/A | 0.839 | 0.430 | 0.271 | 0.118 | 0.104 | 0.000 | 0.138 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 153 | 101 | 154 | 235 | 146 | 0 | 165 | 275 | 0 |
N.S. |
1 | 1.06 | 0.70 | 1.07 | 1.63 | 1.01 | 0.00 | 1.15 | 1.91 | 0.00 |
time (sec) |
N/A | 0.617 | 0.381 | 0.283 | 0.115 | 0.105 | 0.000 | 0.144 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 115 | 95 | 142 | 178 | 130 | 0 | 148 | 236 | 0 |
N.S. |
1 | 1.04 | 0.86 | 1.28 | 1.60 | 1.17 | 0.00 | 1.33 | 2.13 | 0.00 |
time (sec) |
N/A | 0.383 | 0.332 | 0.251 | 0.118 | 0.092 | 0.000 | 0.141 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 74 | 291 | 127 | 110 | 0 | 86 | 131 | 0 |
N.S. |
1 | 1.00 | 0.89 | 3.51 | 1.53 | 1.33 | 0.00 | 1.04 | 1.58 | 0.00 |
time (sec) |
N/A | 0.316 | 0.370 | 0.267 | 0.111 | 0.110 | 0.000 | 0.136 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 81 | 84 | 946 | 0 | 107 | 0 | 150 | 195 | 0 |
N.S. |
1 | 1.01 | 1.05 | 11.82 | 0.00 | 1.34 | 0.00 | 1.88 | 2.44 | 0.00 |
time (sec) |
N/A | 0.555 | 0.372 | 0.263 | 0.000 | 0.092 | 0.000 | 0.140 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 118 | 104 | 154 | 0 | 137 | 0 | 242 | 214 | 0 |
N.S. |
1 | 1.02 | 0.90 | 1.33 | 0.00 | 1.18 | 0.00 | 2.09 | 1.84 | 0.00 |
time (sec) |
N/A | 0.649 | 0.446 | 0.306 | 0.000 | 0.097 | 0.000 | 0.156 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 165 | 105 | 160 | 0 | 158 | 0 | 320 | 266 | 0 |
N.S. |
1 | 1.10 | 0.70 | 1.07 | 0.00 | 1.05 | 0.00 | 2.13 | 1.77 | 0.00 |
time (sec) |
N/A | 0.903 | 0.479 | 0.312 | 0.000 | 0.112 | 0.000 | 0.146 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 198 | 128 | 174 | 0 | 167 | 0 | 380 | 272 | 0 |
N.S. |
1 | 1.12 | 0.72 | 0.98 | 0.00 | 0.94 | 0.00 | 2.15 | 1.54 | 0.00 |
time (sec) |
N/A | 1.181 | 0.511 | 0.343 | 0.000 | 0.101 | 0.000 | 0.156 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 150 | 99 | 187 | 297 | 174 | 0 | 175 | 384 | 0 |
N.S. |
1 | 1.02 | 0.67 | 1.27 | 2.02 | 1.18 | 0.00 | 1.19 | 2.61 | 0.00 |
time (sec) |
N/A | 0.494 | 0.440 | 0.300 | 0.126 | 0.102 | 0.000 | 0.153 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 149 | 85 | 96 | 150 | 81 | 122 | 70 | 117 | 133 |
N.S. |
1 | 1.20 | 0.69 | 0.77 | 1.21 | 0.65 | 0.98 | 0.56 | 0.94 | 1.07 |
time (sec) |
N/A | 0.478 | 0.267 | 0.227 | 0.113 | 0.104 | 1.454 | 0.139 | 0.198 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 117 | 77 | 88 | 132 | 73 | 114 | 0 | 98 | 113 |
N.S. |
1 | 1.17 | 0.77 | 0.88 | 1.32 | 0.73 | 1.14 | 0.00 | 0.98 | 1.13 |
time (sec) |
N/A | 0.391 | 0.179 | 0.221 | 0.114 | 0.113 | 1.495 | 0.000 | 0.201 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 82 | 69 | 80 | 115 | 65 | 105 | 53 | 79 | 75 |
N.S. |
1 | 1.06 | 0.90 | 1.04 | 1.49 | 0.84 | 1.36 | 0.69 | 1.03 | 0.97 |
time (sec) |
N/A | 0.330 | 0.175 | 0.208 | 0.122 | 0.092 | 1.430 | 0.127 | 0.206 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 62 | 69 | 67 | 57 | 90 | 41 | 60 | 70 |
N.S. |
1 | 1.00 | 1.19 | 1.33 | 1.29 | 1.10 | 1.73 | 0.79 | 1.15 | 1.35 |
time (sec) |
N/A | 0.272 | 0.147 | 0.215 | 0.111 | 0.101 | 1.384 | 0.140 | 0.185 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 50 | 67 | 165 | 63 | 63 | 141 | 71 | 42 | 64 |
N.S. |
1 | 1.02 | 1.37 | 3.37 | 1.29 | 1.29 | 2.88 | 1.45 | 0.86 | 1.31 |
time (sec) |
N/A | 0.342 | 0.138 | 0.207 | 0.113 | 0.101 | 4.063 | 0.142 | 0.181 | 6.935 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 73 | 87 | 68 | 74 | 170 | 125 | 77 | 74 |
N.S. |
1 | 1.00 | 1.43 | 1.71 | 1.33 | 1.45 | 3.33 | 2.45 | 1.51 | 1.45 |
time (sec) |
N/A | 0.354 | 0.143 | 0.240 | 0.110 | 0.113 | 2.726 | 0.131 | 0.184 | 7.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 85 | 88 | 93 | 83 | 185 | 173 | 62 | 80 |
N.S. |
1 | 1.00 | 1.44 | 1.49 | 1.58 | 1.41 | 3.14 | 2.93 | 1.05 | 1.36 |
time (sec) |
N/A | 0.383 | 0.150 | 0.195 | 0.110 | 0.130 | 2.698 | 0.137 | 0.201 | 7.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 66 | 67 | 84 | 61 | 187 | 211 | 69 | 78 |
N.S. |
1 | 1.00 | 1.00 | 1.02 | 1.27 | 0.92 | 2.83 | 3.20 | 1.05 | 1.18 |
time (sec) |
N/A | 0.327 | 0.127 | 0.221 | 0.141 | 0.087 | 2.391 | 0.134 | 0.240 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 93 | 74 | 75 | 104 | 69 | 257 | 219 | 88 | 98 |
N.S. |
1 | 1.03 | 0.82 | 0.83 | 1.16 | 0.77 | 2.86 | 2.43 | 0.98 | 1.09 |
time (sec) |
N/A | 0.390 | 0.134 | 0.225 | 0.118 | 0.084 | 3.487 | 0.137 | 0.257 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 120 | 82 | 83 | 124 | 77 | 294 | 270 | 107 | 118 |
N.S. |
1 | 1.05 | 0.72 | 0.73 | 1.09 | 0.68 | 2.58 | 2.37 | 0.94 | 1.04 |
time (sec) |
N/A | 0.439 | 0.136 | 0.213 | 0.108 | 0.099 | 3.866 | 0.135 | 0.205 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 147 | 90 | 91 | 144 | 85 | 340 | 385 | 126 | 138 |
N.S. |
1 | 1.07 | 0.65 | 0.66 | 1.04 | 0.62 | 2.46 | 2.79 | 0.91 | 1.00 |
time (sec) |
N/A | 0.510 | 0.153 | 0.233 | 0.105 | 0.086 | 6.585 | 0.134 | 0.193 | 6.864 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 345 | 191 | 185 | 245 | 183 | 286 | 177 | 320 | 0 |
N.S. |
1 | 1.20 | 0.67 | 0.64 | 0.85 | 0.64 | 1.00 | 0.62 | 1.11 | 0.00 |
time (sec) |
N/A | 1.015 | 0.811 | 0.304 | 0.118 | 0.104 | 0.732 | 0.162 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 310 | 180 | 174 | 220 | 172 | 274 | 165 | 296 | 0 |
N.S. |
1 | 1.16 | 0.67 | 0.65 | 0.82 | 0.64 | 1.02 | 0.62 | 1.10 | 0.00 |
time (sec) |
N/A | 0.915 | 0.782 | 0.290 | 0.124 | 0.098 | 0.689 | 0.156 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 232 | 275 | 169 | 163 | 195 | 161 | 262 | 154 | 272 | 0 |
N.S. |
1 | 1.19 | 0.73 | 0.70 | 0.84 | 0.69 | 1.13 | 0.66 | 1.17 | 0.00 |
time (sec) |
N/A | 0.840 | 0.748 | 0.262 | 0.120 | 0.101 | 0.679 | 0.151 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 240 | 158 | 152 | 170 | 150 | 241 | 142 | 248 | 0 |
N.S. |
1 | 1.16 | 0.76 | 0.73 | 0.82 | 0.72 | 1.16 | 0.69 | 1.20 | 0.00 |
time (sec) |
N/A | 0.720 | 0.730 | 0.240 | 0.116 | 0.084 | 0.656 | 0.144 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 206 | 155 | 138 | 136 | 139 | 206 | 127 | 224 | 0 |
N.S. |
1 | 1.25 | 0.94 | 0.84 | 0.82 | 0.84 | 1.25 | 0.77 | 1.36 | 0.00 |
time (sec) |
N/A | 0.464 | 0.451 | 0.236 | 0.109 | 0.114 | 0.684 | 0.140 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 238 | 216 | 186 | 353 | 204 | 151 | 954 | 161 | 210 | 0 |
N.S. |
1 | 0.91 | 0.78 | 1.48 | 0.86 | 0.63 | 4.01 | 0.68 | 0.88 | 0.00 |
time (sec) |
N/A | 0.819 | 0.678 | 0.214 | 0.120 | 0.109 | 9.093 | 0.147 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 245 | 212 | 193 | 265 | 217 | 167 | 887 | 224 | 222 | 0 |
N.S. |
1 | 0.87 | 0.79 | 1.08 | 0.89 | 0.68 | 3.62 | 0.91 | 0.91 | 0.00 |
time (sec) |
N/A | 0.795 | 0.708 | 0.270 | 0.121 | 0.126 | 3.275 | 0.150 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 219 | 203 | 175 | 229 | 179 | 887 | 293 | 234 | 0 |
N.S. |
1 | 0.83 | 0.77 | 0.66 | 0.87 | 0.68 | 3.36 | 1.11 | 0.89 | 0.00 |
time (sec) |
N/A | 0.856 | 0.678 | 0.262 | 0.118 | 0.122 | 4.125 | 0.152 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 222 | 189 | 238 | 226 | 179 | 843 | 346 | 234 | 0 |
N.S. |
1 | 0.82 | 0.70 | 0.88 | 0.83 | 0.66 | 3.11 | 1.28 | 0.86 | 0.00 |
time (sec) |
N/A | 0.853 | 0.624 | 0.260 | 0.115 | 0.118 | 4.206 | 0.145 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 208 | 198 | 223 | 250 | 180 | 959 | 409 | 234 | 0 |
N.S. |
1 | 0.78 | 0.74 | 0.84 | 0.94 | 0.67 | 3.59 | 1.53 | 0.88 | 0.00 |
time (sec) |
N/A | 0.840 | 0.700 | 0.281 | 0.116 | 0.146 | 6.450 | 0.146 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 274 | 219 | 195 | 210 | 278 | 180 | 1182 | 460 | 234 | 0 |
N.S. |
1 | 0.80 | 0.71 | 0.77 | 1.01 | 0.66 | 4.31 | 1.68 | 0.85 | 0.00 |
time (sec) |
N/A | 0.897 | 0.591 | 0.306 | 0.116 | 0.118 | 6.510 | 0.137 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 274 | 224 | 196 | 196 | 303 | 179 | 1380 | 526 | 234 | 0 |
N.S. |
1 | 0.82 | 0.72 | 0.72 | 1.11 | 0.65 | 5.04 | 1.92 | 0.85 | 0.00 |
time (sec) |
N/A | 0.897 | 0.581 | 0.313 | 0.125 | 0.113 | 11.665 | 0.151 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 270 | 224 | 193 | 173 | 326 | 173 | 1513 | 542 | 228 | 0 |
N.S. |
1 | 0.83 | 0.71 | 0.64 | 1.21 | 0.64 | 5.60 | 2.01 | 0.84 | 0.00 |
time (sec) |
N/A | 0.873 | 0.557 | 0.351 | 0.116 | 0.126 | 12.643 | 0.144 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 230 | 198 | 170 | 352 | 163 | 1719 | 584 | 217 | 0 |
N.S. |
1 | 0.84 | 0.73 | 0.62 | 1.29 | 0.60 | 6.30 | 2.14 | 0.79 | 0.00 |
time (sec) |
N/A | 0.929 | 0.590 | 0.343 | 0.124 | 0.144 | 30.827 | 0.154 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 214 | 169 | 151 | 247 | 142 | 1889 | 648 | 229 | 0 |
N.S. |
1 | 1.09 | 0.86 | 0.77 | 1.26 | 0.72 | 9.64 | 3.31 | 1.17 | 0.00 |
time (sec) |
N/A | 0.715 | 0.526 | 0.495 | 0.121 | 0.118 | 32.825 | 0.149 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 249 | 186 | 165 | 272 | 153 | 2159 | 731 | 253 | 0 |
N.S. |
1 | 1.11 | 0.83 | 0.73 | 1.21 | 0.68 | 9.60 | 3.25 | 1.12 | 0.00 |
time (sec) |
N/A | 0.781 | 0.572 | 0.546 | 0.111 | 0.160 | 139.053 | 0.174 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 284 | 189 | 176 | 297 | 164 | 2397 | 778 | 277 | 0 |
N.S. |
1 | 1.12 | 0.74 | 0.69 | 1.17 | 0.65 | 9.44 | 3.06 | 1.09 | 0.00 |
time (sec) |
N/A | 0.847 | 0.594 | 0.790 | 0.133 | 0.220 | 157.531 | 0.152 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 283 | 319 | 200 | 187 | 322 | 175 | 0 | 865 | 301 | 0 |
N.S. |
1 | 1.13 | 0.71 | 0.66 | 1.14 | 0.62 | 0.00 | 3.06 | 1.06 | 0.00 |
time (sec) |
N/A | 0.930 | 0.641 | 0.978 | 0.115 | 0.291 | 0.000 | 0.161 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 211 | 136 | 130 | 221 | 127 | 400 | 120 | 200 | 0 |
N.S. |
1 | 1.10 | 0.71 | 0.68 | 1.15 | 0.66 | 2.08 | 0.62 | 1.04 | 0.00 |
time (sec) |
N/A | 0.599 | 0.438 | 0.257 | 0.131 | 0.110 | 1.574 | 0.146 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 176 | 125 | 119 | 198 | 117 | 371 | 107 | 176 | 0 |
N.S. |
1 | 1.10 | 0.78 | 0.74 | 1.24 | 0.73 | 2.32 | 0.67 | 1.10 | 0.00 |
time (sec) |
N/A | 0.512 | 0.407 | 0.233 | 0.125 | 0.095 | 1.405 | 0.144 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 140 | 114 | 108 | 176 | 105 | 343 | 96 | 152 | 0 |
N.S. |
1 | 1.05 | 0.86 | 0.81 | 1.32 | 0.79 | 2.58 | 0.72 | 1.14 | 0.00 |
time (sec) |
N/A | 0.418 | 0.352 | 0.204 | 0.128 | 0.107 | 1.387 | 0.143 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 107 | 111 | 94 | 109 | 95 | 313 | 80 | 128 | 0 |
N.S. |
1 | 1.07 | 1.11 | 0.94 | 1.09 | 0.95 | 3.13 | 0.80 | 1.28 | 0.00 |
time (sec) |
N/A | 0.338 | 0.238 | 0.215 | 0.118 | 0.107 | 1.375 | 0.149 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 118 | 142 | 297 | 124 | 107 | 400 | 114 | 114 | 0 |
N.S. |
1 | 1.04 | 1.26 | 2.63 | 1.10 | 0.95 | 3.54 | 1.01 | 1.01 | 0.00 |
time (sec) |
N/A | 0.468 | 0.389 | 0.216 | 0.120 | 0.114 | 6.069 | 0.140 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 115 | 140 | 164 | 131 | 123 | 389 | 177 | 126 | 0 |
N.S. |
1 | 1.00 | 1.22 | 1.43 | 1.14 | 1.07 | 3.38 | 1.54 | 1.10 | 0.00 |
time (sec) |
N/A | 0.484 | 0.416 | 0.259 | 0.113 | 0.099 | 3.314 | 0.143 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 111 | 149 | 150 | 138 | 135 | 444 | 245 | 138 | 0 |
N.S. |
1 | 0.92 | 1.24 | 1.25 | 1.15 | 1.12 | 3.70 | 2.04 | 1.15 | 0.00 |
time (sec) |
N/A | 0.485 | 0.424 | 0.286 | 0.120 | 0.130 | 4.191 | 0.143 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 118 | 146 | 136 | 132 | 130 | 457 | 284 | 163 | 0 |
N.S. |
1 | 0.98 | 1.22 | 1.13 | 1.10 | 1.08 | 3.81 | 2.37 | 1.36 | 0.00 |
time (sec) |
N/A | 0.483 | 0.424 | 0.287 | 0.115 | 0.117 | 4.349 | 0.145 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 124 | 151 | 126 | 159 | 119 | 541 | 328 | 121 | 0 |
N.S. |
1 | 1.04 | 1.27 | 1.06 | 1.34 | 1.00 | 4.55 | 2.76 | 1.02 | 0.00 |
time (sec) |
N/A | 0.497 | 0.371 | 0.322 | 0.115 | 0.113 | 5.595 | 0.152 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 113 | 122 | 107 | 153 | 97 | 774 | 388 | 133 | 0 |
N.S. |
1 | 1.02 | 1.10 | 0.96 | 1.38 | 0.87 | 6.97 | 3.50 | 1.20 | 0.00 |
time (sec) |
N/A | 0.396 | 0.435 | 0.348 | 0.107 | 0.116 | 5.254 | 0.139 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 148 | 142 | 121 | 178 | 108 | 918 | 463 | 157 | 0 |
N.S. |
1 | 1.05 | 1.01 | 0.86 | 1.26 | 0.77 | 6.51 | 3.28 | 1.11 | 0.00 |
time (sec) |
N/A | 0.449 | 0.409 | 0.373 | 0.115 | 0.125 | 9.606 | 0.145 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 183 | 153 | 132 | 203 | 119 | 1037 | 518 | 181 | 0 |
N.S. |
1 | 1.08 | 0.91 | 0.78 | 1.20 | 0.70 | 6.14 | 3.07 | 1.07 | 0.00 |
time (sec) |
N/A | 0.508 | 0.448 | 0.440 | 0.118 | 0.103 | 10.163 | 0.142 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 218 | 164 | 143 | 228 | 130 | 1159 | 463 | 205 | 0 |
N.S. |
1 | 1.10 | 0.82 | 0.72 | 1.15 | 0.65 | 5.82 | 2.33 | 1.03 | 0.00 |
time (sec) |
N/A | 0.596 | 0.418 | 0.556 | 0.109 | 0.125 | 27.790 | 0.152 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 246 | 136 | 130 | 275 | 128 | 340 | 312 | 200 | 0 |
N.S. |
1 | 1.16 | 0.64 | 0.61 | 1.30 | 0.60 | 1.60 | 1.47 | 0.94 | 0.00 |
time (sec) |
N/A | 0.692 | 0.452 | 0.286 | 0.125 | 0.125 | 2.137 | 0.175 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 209 | 133 | 119 | 251 | 116 | 255 | 280 | 176 | 0 |
N.S. |
1 | 1.12 | 0.71 | 0.64 | 1.34 | 0.62 | 1.36 | 1.50 | 0.94 | 0.00 |
time (sec) |
N/A | 0.628 | 0.283 | 0.228 | 0.129 | 0.098 | 2.005 | 0.163 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 176 | 114 | 108 | 230 | 106 | 298 | 248 | 152 | 0 |
N.S. |
1 | 1.12 | 0.73 | 0.69 | 1.46 | 0.68 | 1.90 | 1.58 | 0.97 | 0.00 |
time (sec) |
N/A | 0.556 | 0.382 | 0.244 | 0.143 | 0.101 | 1.883 | 0.164 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 141 | 111 | 97 | 167 | 94 | 216 | 216 | 128 | 0 |
N.S. |
1 | 1.03 | 0.81 | 0.71 | 1.22 | 0.69 | 1.58 | 1.58 | 0.93 | 0.00 |
time (sec) |
N/A | 0.464 | 0.204 | 0.234 | 0.113 | 0.120 | 1.796 | 0.157 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 113 | 92 | 83 | 119 | 84 | 253 | 184 | 104 | 0 |
N.S. |
1 | 1.31 | 1.07 | 0.97 | 1.38 | 0.98 | 2.94 | 2.14 | 1.21 | 0.00 |
time (sec) |
N/A | 0.377 | 0.319 | 0.365 | 0.113 | 0.101 | 1.727 | 0.156 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | C | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 97 | 125 | 544 | 103 | 95 | 270 | 0 | 90 | 0 |
N.S. |
1 | 0.86 | 1.11 | 4.81 | 0.91 | 0.84 | 2.39 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.500 | 0.339 | 0.256 | 0.116 | 0.118 | 4.831 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 104 | 130 | 140 | 112 | 111 | 330 | 0 | 101 | 0 |
N.S. |
1 | 0.99 | 1.24 | 1.33 | 1.07 | 1.06 | 3.14 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.481 | 0.334 | 0.266 | 0.119 | 0.119 | 3.517 | 0.000 | 0.209 | 0.000 |