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 | C | C | F | A | F(-2) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 301 | 122 | 96 | 0 | 281 | 0 | 0 | 257 | 1021 |
N.S. |
1 | 1.31 | 0.53 | 0.42 | 0.00 | 1.23 | 0.00 | 0.00 | 1.12 | 4.46 |
time (sec) |
N/A | 0.809 | 0.109 | 0.544 | 0.000 | 0.090 | 0.000 | 0.000 | 0.168 | 0.555 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 111 | 95 | 129 | 102 | 0 | 287 | 84 | 781 | 116 |
N.S. |
1 | 1.28 | 1.09 | 1.48 | 1.17 | 0.00 | 3.30 | 0.97 | 8.98 | 1.33 |
time (sec) |
N/A | 0.341 | 0.044 | 1.253 | 0.121 | 0.000 | 0.522 | 0.143 | 0.180 | 10.674 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | F(-1) | F(-2) | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 0 | 228 | 151 | 0 | 0 | 0 | 2319 | 0 | 4129 |
N.S. |
1 | 0.00 | 1.58 | 1.05 | 0.00 | 0.00 | 0.00 | 16.10 | 0.00 | 28.67 |
time (sec) |
N/A | 0.000 | 0.122 | 2.265 | 0.000 | 0.000 | 0.000 | 1.664 | 1.041 | 45.930 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 50 | 50 | 52 | 53 | 56 | 46 | 54 | 52 | 56 |
N.S. |
1 | 0.91 | 0.91 | 0.95 | 0.96 | 1.02 | 0.84 | 0.98 | 0.95 | 1.02 |
time (sec) |
N/A | 0.333 | 0.039 | 0.133 | 0.030 | 0.067 | 0.977 | 0.150 | 0.164 | 0.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F(-1) | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 104 | 84 | 612 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 0.83 | 6.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.710 | 0.303 | 1.444 | 0.134 | 0.000 | 0.000 | 0.000 | 6.035 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 59 | 71 | 61 | 64 | 112 | 66 | 64 | 118 | 50 |
N.S. |
1 | 0.83 | 1.00 | 0.86 | 0.90 | 1.58 | 0.93 | 0.90 | 1.66 | 0.70 |
time (sec) |
N/A | 0.531 | 0.393 | 4.592 | 0.867 | 0.075 | 1.301 | 0.203 | 0.164 | 14.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | F(-1) | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 216 | 474 | 43 | 554 | 0 | 63 | 0 | 95 | 0 |
N.S. |
1 | 2.84 | 6.24 | 0.57 | 7.29 | 0.00 | 0.83 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 3.617 | 1.844 | 0.679 | 0.282 | 0.000 | 18.356 | 0.000 | 0.389 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | F(-1) | F(-2) | F(-2) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 0 | 174 | 122 | 0 | 0 | 0 | 0 | 0 | 1698 |
N.S. |
1 | 0.00 | 0.89 | 0.63 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 8.71 |
time (sec) |
N/A | 0.000 | 0.104 | 0.556 | 0.000 | 0.000 | 0.000 | 0.000 | 0.226 | 14.344 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | F(-2) | F(-2) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 0 | 131 | 89 | 0 | 113 | 0 | 0 | 518 | 224 |
N.S. |
1 | 0.00 | 0.71 | 0.48 | 0.00 | 0.61 | 0.00 | 0.00 | 2.80 | 1.21 |
time (sec) |
N/A | 0.000 | 0.065 | 0.255 | 0.000 | 0.079 | 0.000 | 0.000 | 0.170 | 1.344 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | B | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 595 | 0 | 211 | 48 | 0 | 456 | 4038 | 0 | 741 | 266 |
N.S. |
1 | 0.00 | 0.35 | 0.08 | 0.00 | 0.77 | 6.79 | 0.00 | 1.25 | 0.45 |
time (sec) |
N/A | 0.000 | 0.094 | 0.473 | 0.000 | 0.096 | 3.730 | 0.000 | 0.182 | 10.833 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 0 | 129 | 70 | 0 | 253 | 80 | 66 | 303 | 166 |
N.S. |
1 | 0.00 | 0.55 | 0.30 | 0.00 | 1.09 | 0.34 | 0.28 | 1.30 | 0.71 |
time (sec) |
N/A | 0.000 | 0.048 | 0.068 | 0.000 | 0.094 | 0.550 | 0.151 | 0.166 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 141 | 127 | 87 | 108 | 129 | 607 | 116 | 125 | 110 |
N.S. |
1 | 1.04 | 0.93 | 0.64 | 0.79 | 0.95 | 4.46 | 0.85 | 0.92 | 0.81 |
time (sec) |
N/A | 0.501 | 0.104 | 0.077 | 0.104 | 0.079 | 1.463 | 0.134 | 0.164 | 0.341 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | B | B | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 0 | 199 | 92 | 0 | 7957 | 150 | 0 | 145 | 771 |
N.S. |
1 | 0.00 | 0.71 | 0.33 | 0.00 | 28.32 | 0.53 | 0.00 | 0.52 | 2.74 |
time (sec) |
N/A | 0.000 | 0.038 | 0.110 | 0.000 | 0.908 | 2.759 | 0.000 | 0.162 | 9.900 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | B | B | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 0 | 192 | 121 | 0 | 7153 | 614 | 0 | 139 | 294 |
N.S. |
1 | 0.00 | 1.00 | 0.63 | 0.00 | 37.26 | 3.20 | 0.00 | 0.72 | 1.53 |
time (sec) |
N/A | 0.000 | 0.088 | 0.212 | 0.000 | 0.903 | 3.645 | 0.000 | 0.173 | 9.806 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 144 | 86 | 61 | 0 | 471 | 41 | 25 | 85 | 146 |
N.S. |
1 | 0.83 | 0.50 | 0.35 | 0.00 | 2.72 | 0.24 | 0.14 | 0.49 | 0.84 |
time (sec) |
N/A | 0.490 | 0.015 | 0.037 | 0.000 | 0.083 | 0.263 | 0.115 | 0.188 | 10.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | A | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 238 | 79 | 43 | 0 | 295 | 46 | 0 | 65 | 151 |
N.S. |
1 | 1.23 | 0.41 | 0.22 | 0.00 | 1.52 | 0.24 | 0.00 | 0.34 | 0.78 |
time (sec) |
N/A | 0.829 | 0.017 | 0.038 | 0.000 | 0.699 | 0.651 | 0.000 | 0.173 | 9.785 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 0 | 85 | 59 | 0 | 155 | 41 | 0 | 83 | 146 |
N.S. |
1 | 0.00 | 0.47 | 0.32 | 0.00 | 0.85 | 0.23 | 0.00 | 0.46 | 0.80 |
time (sec) |
N/A | 0.000 | 0.013 | 0.036 | 0.000 | 0.079 | 0.213 | 0.000 | 0.164 | 9.922 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 264 | 216 | 45 | 192 | 1208573 | 41 | 260 | 21 | 283 |
N.S. |
1 | 1.08 | 0.89 | 0.18 | 0.79 | 4953.17 | 0.17 | 1.07 | 0.09 | 1.16 |
time (sec) |
N/A | 0.560 | 0.164 | 0.350 | 0.104 | 7.066 | 0.102 | 0.146 | 0.162 | 10.852 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 159 | 262 | 122 | 141 | 432 | 0 | 133 | 2054 | 251 |
N.S. |
1 | 1.13 | 1.86 | 0.87 | 1.00 | 3.06 | 0.00 | 0.94 | 14.57 | 1.78 |
time (sec) |
N/A | 0.456 | 0.180 | 0.463 | 0.105 | 0.334 | 0.000 | 0.128 | 0.421 | 10.822 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F(-1) | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 58 | 65 | 58 | 133 | 0 | 0 | 56 | 72 | 358 |
N.S. |
1 | 0.85 | 0.96 | 0.85 | 1.96 | 0.00 | 0.00 | 0.82 | 1.06 | 5.26 |
time (sec) |
N/A | 0.391 | 0.063 | 1.520 | 0.103 | 0.000 | 0.000 | 0.137 | 0.446 | 11.271 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 40 | 29 | 32 | 28 | 35 | 36 | 31 | 28 | 28 |
N.S. |
1 | 0.98 | 0.71 | 0.78 | 0.68 | 0.85 | 0.88 | 0.76 | 0.68 | 0.68 |
time (sec) |
N/A | 0.233 | 0.050 | 0.315 | 0.102 | 0.063 | 0.170 | 0.149 | 0.168 | 11.881 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 354 | 323 | 50 | 46 | 0 | 537 | 31 | 0 | 22 | 674 |
N.S. |
1 | 0.91 | 0.14 | 0.13 | 0.00 | 1.52 | 0.09 | 0.00 | 0.06 | 1.90 |
time (sec) |
N/A | 0.748 | 0.023 | 0.157 | 0.000 | 0.078 | 0.138 | 0.000 | 0.204 | 13.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 153 | 134 | 134 | 167 | 443 | 751 | 170 | 404 | 266 |
N.S. |
1 | 0.87 | 0.76 | 0.76 | 0.95 | 2.52 | 4.27 | 0.97 | 2.30 | 1.51 |
time (sec) |
N/A | 0.488 | 0.165 | 0.137 | 0.100 | 0.084 | 1.294 | 0.140 | 0.162 | 10.365 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 118 | 135 | 139 | 0 | 407 | 0 | 131 | 396 | 7097 |
N.S. |
1 | 1.01 | 1.15 | 1.19 | 0.00 | 3.48 | 0.00 | 1.12 | 3.38 | 60.66 |
time (sec) |
N/A | 0.385 | 0.052 | 0.089 | 0.000 | 0.266 | 0.000 | 0.191 | 0.164 | 19.634 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 186 | 106 | 144 | 17307 | 95 | 268 | 154 | 196 |
N.S. |
1 | 1.00 | 1.59 | 0.91 | 1.23 | 147.92 | 0.81 | 2.29 | 1.32 | 1.68 |
time (sec) |
N/A | 0.372 | 0.102 | 0.104 | 0.104 | 0.816 | 0.384 | 0.130 | 0.166 | 0.263 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 115 | 85 | 131 | 170 | 162 | 222 | 118 | 306 |
N.S. |
1 | 1.00 | 1.35 | 1.00 | 1.54 | 2.00 | 1.91 | 2.61 | 1.39 | 3.60 |
time (sec) |
N/A | 0.305 | 0.029 | 0.102 | 0.104 | 0.080 | 1.216 | 0.157 | 0.168 | 0.994 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 251 | 279 | 277 | 166 | 187 | 3389 | 0 | 301 | 1145 | 3037 |
N.S. |
1 | 1.11 | 1.10 | 0.66 | 0.75 | 13.50 | 0.00 | 1.20 | 4.56 | 12.10 |
time (sec) |
N/A | 0.507 | 0.602 | 1.098 | 0.105 | 0.198 | 0.000 | 0.151 | 0.193 | 68.702 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 165 | 103 | 101 | 109 | 379 | 989 | 102 | 359 | 425 |
N.S. |
1 | 1.45 | 0.90 | 0.89 | 0.96 | 3.32 | 8.68 | 0.89 | 3.15 | 3.73 |
time (sec) |
N/A | 0.481 | 0.063 | 0.150 | 0.101 | 0.085 | 1.339 | 0.131 | 0.157 | 9.773 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 257 | 262 | 226 | 226 | 1179 | 0 | 299 | 561 | 6231 |
N.S. |
1 | 1.00 | 1.02 | 0.88 | 0.88 | 4.59 | 0.00 | 1.16 | 2.18 | 24.25 |
time (sec) |
N/A | 0.465 | 0.088 | 0.117 | 0.103 | 0.116 | 0.000 | 0.132 | 0.173 | 1.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 110 | 104 | 103 | 104 | 151 | 0 | 119 | 212 | 97 |
N.S. |
1 | 0.99 | 0.94 | 0.93 | 0.94 | 1.36 | 0.00 | 1.07 | 1.91 | 0.87 |
time (sec) |
N/A | 0.414 | 0.058 | 0.126 | 0.023 | 0.517 | 0.000 | 0.142 | 0.158 | 9.993 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F(-1) | C | A | B | A | A | B | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 265 | 249 | 0 | 116 | 280 | 476 | 168 | 297 | 1056 | 795 |
N.S. |
1 | 0.94 | 0.00 | 0.44 | 1.06 | 1.80 | 0.63 | 1.12 | 3.98 | 3.00 |
time (sec) |
N/A | 0.531 | 0.000 | 0.173 | 0.106 | 0.080 | 0.554 | 0.113 | 0.179 | 0.346 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 54 | 54 | 73 | 69 | 58 | 394 | 75 | 77 | 167 |
N.S. |
1 | 0.98 | 0.98 | 1.33 | 1.25 | 1.05 | 7.16 | 1.36 | 1.40 | 3.04 |
time (sec) |
N/A | 0.227 | 0.027 | 0.141 | 0.102 | 0.077 | 0.301 | 0.133 | 0.182 | 0.223 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 83 | 75 | 34 | 0 | 96 | 26 | 79 | 795 | 137 |
N.S. |
1 | 1.05 | 0.95 | 0.43 | 0.00 | 1.22 | 0.33 | 1.00 | 10.06 | 1.73 |
time (sec) |
N/A | 0.258 | 0.046 | 0.060 | 0.000 | 0.073 | 0.182 | 0.130 | 0.265 | 9.707 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | A | F(-1) | F(-2) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 0 | 176 | 60 | 0 | 117 | 0 | 0 | 687 | 761 |
N.S. |
1 | 0.00 | 2.02 | 0.69 | 0.00 | 1.34 | 0.00 | 0.00 | 7.90 | 8.75 |
time (sec) |
N/A | 0.000 | 0.183 | 0.447 | 0.000 | 0.090 | 0.000 | 0.000 | 0.197 | 11.708 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | A | F(-1) | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 0 | 171 | 60 | 0 | 114 | 0 | 0 | 687 | 761 |
N.S. |
1 | 0.00 | 2.09 | 0.73 | 0.00 | 1.39 | 0.00 | 0.00 | 8.38 | 9.28 |
time (sec) |
N/A | 0.000 | 0.182 | 0.431 | 0.000 | 0.086 | 0.000 | 0.000 | 0.184 | 11.622 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 334 | 32 | 29 | 53 | 51 | 51 | 58 | 29 |
N.S. |
1 | 1.00 | 9.28 | 0.89 | 0.81 | 1.47 | 1.42 | 1.42 | 1.61 | 0.81 |
time (sec) |
N/A | 0.206 | 0.500 | 0.207 | 0.100 | 0.066 | 0.799 | 0.315 | 0.149 | 0.316 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 54 | 42 | 54 | 66 | 56 | 0 | 66 | 39 |
N.S. |
1 | 1.00 | 1.26 | 0.98 | 1.26 | 1.53 | 1.30 | 0.00 | 1.53 | 0.91 |
time (sec) |
N/A | 0.281 | 0.069 | 0.265 | 0.098 | 0.069 | 0.760 | 0.000 | 0.145 | 0.511 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 515 | 46 | 43 | 63 | 72 | 44 | 45 | 73 | 42 |
N.S. |
1 | 10.10 | 0.90 | 0.84 | 1.24 | 1.41 | 0.86 | 0.88 | 1.43 | 0.82 |
time (sec) |
N/A | 1.867 | 0.034 | 0.697 | 0.101 | 0.068 | 0.377 | 0.150 | 0.181 | 0.651 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 54 | 42 | 54 | 66 | 56 | 0 | 66 | 39 |
N.S. |
1 | 1.00 | 1.26 | 0.98 | 1.26 | 1.53 | 1.30 | 0.00 | 1.53 | 0.91 |
time (sec) |
N/A | 0.465 | 0.026 | 0.000 | 0.101 | 0.065 | 0.764 | 0.000 | 0.160 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 127 | 83 | 44 | 179 | 65 | 90 | 0 | 78 | 40 |
N.S. |
1 | 1.27 | 0.83 | 0.44 | 1.79 | 0.65 | 0.90 | 0.00 | 0.78 | 0.40 |
time (sec) |
N/A | 1.399 | 0.201 | 0.432 | 0.136 | 0.069 | 3.403 | 0.000 | 0.152 | 1.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | B | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 288 | 20 | 91 | 33 | 42 | 19 | 34 | 19 |
N.S. |
1 | 1.00 | 14.40 | 1.00 | 4.55 | 1.65 | 2.10 | 0.95 | 1.70 | 0.95 |
time (sec) |
N/A | 0.390 | 0.218 | 0.279 | 0.100 | 0.072 | 0.765 | 0.184 | 0.156 | 9.402 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 107 | 79 | 61 | 103 | 122 | 102 | 74 | 129 | 76 |
N.S. |
1 | 1.35 | 1.00 | 0.77 | 1.30 | 1.54 | 1.29 | 0.94 | 1.63 | 0.96 |
time (sec) |
N/A | 0.986 | 0.134 | 0.564 | 0.102 | 0.066 | 3.714 | 0.156 | 0.158 | 10.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 0 | 36 | 28 | 0 | 55 | 0 | 37 | 53 | 27 |
N.S. |
1 | 0.00 | 1.00 | 0.78 | 0.00 | 1.53 | 0.00 | 1.03 | 1.47 | 0.75 |
time (sec) |
N/A | 0.000 | 0.083 | 0.574 | 0.000 | 0.072 | 0.000 | 0.437 | 0.178 | 0.695 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 63 | 71 | 39 | 0 | 59 | 49 | 0 | 61 | 42 |
N.S. |
1 | 1.09 | 1.22 | 0.67 | 0.00 | 1.02 | 0.84 | 0.00 | 1.05 | 0.72 |
time (sec) |
N/A | 0.869 | 0.171 | 0.359 | 0.000 | 0.074 | 0.830 | 0.000 | 0.159 | 9.950 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 46 | 36 | 35 | 45 | 45 | 41 | 35 | 45 | 34 |
N.S. |
1 | 1.24 | 0.97 | 0.95 | 1.22 | 1.22 | 1.11 | 0.95 | 1.22 | 0.92 |
time (sec) |
N/A | 0.784 | 0.014 | 0.077 | 0.026 | 0.058 | 0.161 | 0.149 | 2.903 | 9.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | B | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 239 | 143 | 106 | 0 | 225 | 296 | 0 | 43 | 120 |
N.S. |
1 | 1.76 | 1.05 | 0.78 | 0.00 | 1.65 | 2.18 | 0.00 | 0.32 | 0.88 |
time (sec) |
N/A | 1.266 | 0.190 | 0.114 | 0.000 | 0.090 | 0.292 | 0.000 | 200.010 | 9.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | F | A | F(-2) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 103 | 139 | 34 | 0 | 33 | 0 | 35 | 207 | 34 |
N.S. |
1 | 2.51 | 3.39 | 0.83 | 0.00 | 0.80 | 0.00 | 0.85 | 5.05 | 0.83 |
time (sec) |
N/A | 0.857 | 0.100 | 0.243 | 0.000 | 0.066 | 0.000 | 0.174 | 0.163 | 10.976 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | F(-1) | F(-2) | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 0 | 191 | 52 | 0 | 0 | 0 | 66 | 65 | 1659 |
N.S. |
1 | 0.00 | 1.00 | 0.27 | 0.00 | 0.00 | 0.00 | 0.35 | 0.34 | 8.69 |
time (sec) |
N/A | 0.000 | 0.168 | 0.605 | 0.000 | 0.000 | 0.000 | 0.166 | 191.015 | 13.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | A | F | F(-1) | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 291 | 194 | 60 | 0 | 0 | 0 | 0 | 687 | 1086 |
N.S. |
1 | 3.46 | 2.31 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 8.18 | 12.93 |
time (sec) |
N/A | 3.209 | 0.187 | 0.705 | 0.000 | 0.000 | 0.000 | 0.000 | 0.272 | 12.586 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | F | F(-2) | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 153 | 118 | 192 | 0 | 0 | 0 | 0 | 107 | 1889 |
N.S. |
1 | 1.31 | 1.01 | 1.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.91 | 16.15 |
time (sec) |
N/A | 0.536 | 0.121 | 0.623 | 0.000 | 0.000 | 0.000 | 0.000 | 0.268 | 18.533 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | F(-1) | F(-2) | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 0 | 208 | 52 | 0 | 0 | 0 | 0 | 439 | 850 |
N.S. |
1 | 0.00 | 2.77 | 0.69 | 0.00 | 0.00 | 0.00 | 0.00 | 5.85 | 11.33 |
time (sec) |
N/A | 0.000 | 0.226 | 0.558 | 0.000 | 0.000 | 0.000 | 0.000 | 0.480 | 53.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | F(-1) | F(-1) | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 0 | 321 | 71 | 0 | 0 | 0 | 0 | 685 | 761 |
N.S. |
1 | 0.00 | 1.57 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 3.36 | 3.73 |
time (sec) |
N/A | 0.000 | 0.182 | 0.785 | 0.000 | 0.000 | 0.000 | 0.000 | 0.276 | 14.824 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | A | F(-1) | F(-2) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 0 | 178 | 48 | 0 | 104 | 0 | 0 | 687 | 761 |
N.S. |
1 | 0.00 | 2.51 | 0.68 | 0.00 | 1.46 | 0.00 | 0.00 | 9.68 | 10.72 |
time (sec) |
N/A | 0.000 | 0.120 | 0.390 | 0.000 | 0.086 | 0.000 | 0.000 | 0.201 | 10.972 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 33 | 51 | 40 | 39 | 23 | 0 | 39 | 138 | 47 |
N.S. |
1 | 0.97 | 1.50 | 1.18 | 1.15 | 0.68 | 0.00 | 1.15 | 4.06 | 1.38 |
time (sec) |
N/A | 0.380 | 0.043 | 0.122 | 0.103 | 0.071 | 0.000 | 0.307 | 0.173 | 9.579 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | B | F(-1) | F(-2) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 0 | 174 | 46 | 0 | 104 | 0 | 0 | 687 | 761 |
N.S. |
1 | 0.00 | 2.60 | 0.69 | 0.00 | 1.55 | 0.00 | 0.00 | 10.25 | 11.36 |
time (sec) |
N/A | 0.000 | 0.093 | 0.286 | 0.000 | 0.088 | 0.000 | 0.000 | 0.196 | 11.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | F(-1) | F(-2) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 0 | 377 | 173 | 0 | 197 | 0 | 0 | 0 | 841 |
N.S. |
1 | 0.00 | 1.94 | 0.89 | 0.00 | 1.02 | 0.00 | 0.00 | 0.00 | 4.34 |
time (sec) |
N/A | 0.000 | 0.849 | 1.202 | 0.000 | 0.410 | 0.000 | 0.000 | 0.363 | 20.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | F(-1) | F(-2) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 0 | 377 | 173 | 0 | 198 | 0 | 0 | 0 | 837 |
N.S. |
1 | 0.00 | 2.13 | 0.98 | 0.00 | 1.12 | 0.00 | 0.00 | 0.00 | 4.73 |
time (sec) |
N/A | 0.000 | 0.862 | 1.174 | 0.000 | 0.391 | 0.000 | 0.000 | 0.334 | 20.519 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 101 | 163 | 47 | 0 | 200 | 0 | 0 | 687 | 1086 |
N.S. |
1 | 1.36 | 2.20 | 0.64 | 0.00 | 2.70 | 0.00 | 0.00 | 9.28 | 14.68 |
time (sec) |
N/A | 1.901 | 0.116 | 0.417 | 0.000 | 0.088 | 0.000 | 0.000 | 0.253 | 12.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | F(-2) | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 208 | 134 | 87 | 0 | 291 | 0 | 816 | 596 | 160 |
N.S. |
1 | 1.68 | 1.08 | 0.70 | 0.00 | 2.35 | 0.00 | 6.58 | 4.81 | 1.29 |
time (sec) |
N/A | 1.196 | 0.066 | 0.233 | 0.000 | 0.083 | 0.000 | 0.173 | 0.220 | 10.691 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 131 | 84 | 59 | 0 | 129 | 26 | 25 | 79 | 265 |
N.S. |
1 | 1.30 | 0.83 | 0.58 | 0.00 | 1.28 | 0.26 | 0.25 | 0.78 | 2.62 |
time (sec) |
N/A | 0.846 | 0.013 | 0.054 | 0.000 | 0.072 | 0.163 | 0.149 | 0.171 | 0.201 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F(-2) | F | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 105 | 89 | 28 | 0 | 78 | 87 | 0 | 116 | 201 |
N.S. |
1 | 0.97 | 0.82 | 0.26 | 0.00 | 0.72 | 0.81 | 0.00 | 1.07 | 1.86 |
time (sec) |
N/A | 0.784 | 0.019 | 0.070 | 0.000 | 0.065 | 0.116 | 0.000 | 0.184 | 11.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 58 | 55 | 47 | 0 | 74 | 99 | 86 | 70 | 49 |
N.S. |
1 | 0.50 | 0.48 | 0.41 | 0.00 | 0.64 | 0.86 | 0.75 | 0.61 | 0.43 |
time (sec) |
N/A | 0.517 | 0.009 | 0.033 | 0.000 | 0.065 | 0.076 | 0.114 | 0.170 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 31 | 57 | 25 | 0 | 24 | 22 | 55 | 47 | 24 |
N.S. |
1 | 1.82 | 3.35 | 1.47 | 0.00 | 1.41 | 1.29 | 3.24 | 2.76 | 1.41 |
time (sec) |
N/A | 0.418 | 0.015 | 0.084 | 0.000 | 0.067 | 0.063 | 0.138 | 0.202 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 158 | 202 | 38 | 0 | 126 | 148 | 267 | 267 | 69 |
N.S. |
1 | 1.00 | 1.28 | 0.24 | 0.00 | 0.80 | 0.94 | 1.69 | 1.69 | 0.44 |
time (sec) |
N/A | 0.613 | 0.084 | 0.075 | 0.000 | 0.074 | 0.096 | 0.228 | 0.176 | 9.947 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | B | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 179 | 151 | 136 | 0 | 157 | 457 | 0 | 76 | 2153 |
N.S. |
1 | 1.27 | 1.07 | 0.96 | 0.00 | 1.11 | 3.24 | 0.00 | 0.54 | 15.27 |
time (sec) |
N/A | 1.000 | 0.069 | 0.283 | 0.000 | 0.128 | 0.388 | 0.000 | 200.031 | 11.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 0 | 155 | 58 | 0 | 196 | 117 | 84 | 365 | 629 |
N.S. |
1 | 0.00 | 0.86 | 0.32 | 0.00 | 1.08 | 0.65 | 0.46 | 2.02 | 3.48 |
time (sec) |
N/A | 0.000 | 0.080 | 0.254 | 0.000 | 0.214 | 0.985 | 0.188 | 0.202 | 10.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 128 | 115 | 29 | 0 | 88 | 104 | 144 | 26 | 118 |
N.S. |
1 | 1.03 | 0.93 | 0.23 | 0.00 | 0.71 | 0.84 | 1.16 | 0.21 | 0.95 |
time (sec) |
N/A | 0.733 | 0.172 | 0.091 | 0.000 | 0.068 | 0.100 | 0.221 | 200.010 | 0.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 0 | 78 | 30 | 0 | 69 | 90 | 1 | 63 | 321 |
N.S. |
1 | 0.00 | 0.79 | 0.30 | 0.00 | 0.70 | 0.91 | 0.01 | 0.64 | 3.24 |
time (sec) |
N/A | 0.000 | 0.016 | 0.097 | 0.000 | 0.098 | 0.185 | 0.202 | 0.215 | 10.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | B | B | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 0 | 178 | 54 | 0 | 211 | 473 | 0 | 455 | 951 |
N.S. |
1 | 0.00 | 1.23 | 0.37 | 0.00 | 1.46 | 3.26 | 0.00 | 3.14 | 6.56 |
time (sec) |
N/A | 0.000 | 0.097 | 0.179 | 0.000 | 0.112 | 0.381 | 0.000 | 0.259 | 10.535 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 69 | 99 | 54 | 53 | 53 | 70 | 53 | 51 | 83 |
N.S. |
1 | 0.81 | 1.16 | 0.64 | 0.62 | 0.62 | 0.82 | 0.62 | 0.60 | 0.98 |
time (sec) |
N/A | 0.421 | 0.147 | 0.050 | 0.100 | 0.068 | 0.085 | 0.124 | 0.178 | 0.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 0 | 136 | 92 | 0 | 162 | 228 | 48 | 372 | 384 |
N.S. |
1 | 0.00 | 0.89 | 0.60 | 0.00 | 1.06 | 1.49 | 0.31 | 2.43 | 2.51 |
time (sec) |
N/A | 0.000 | 0.044 | 0.149 | 0.000 | 0.096 | 0.506 | 0.541 | 0.310 | 0.685 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 0 | 131 | 54 | 0 | 158 | 109 | 115 | 271 | 629 |
N.S. |
1 | 0.00 | 0.87 | 0.36 | 0.00 | 1.05 | 0.72 | 0.76 | 1.79 | 4.17 |
time (sec) |
N/A | 0.000 | 0.042 | 0.148 | 0.000 | 0.087 | 0.638 | 0.160 | 0.175 | 10.299 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 0 | 75 | 31 | 0 | 87 | 29 | 1 | 74 | 305 |
N.S. |
1 | 0.00 | 0.77 | 0.32 | 0.00 | 0.90 | 0.30 | 0.01 | 0.76 | 3.14 |
time (sec) |
N/A | 0.000 | 0.014 | 0.050 | 0.000 | 0.073 | 0.160 | 0.137 | 0.171 | 0.151 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 129 | 153 | 33 | 0 | 91 | 141 | 1 | 57 | 305 |
N.S. |
1 | 0.77 | 0.92 | 0.20 | 0.00 | 0.54 | 0.84 | 0.01 | 0.34 | 1.83 |
time (sec) |
N/A | 0.791 | 0.023 | 0.057 | 0.000 | 0.072 | 0.208 | 0.164 | 0.180 | 10.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | C | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 209 | 133 | 45 | 0 | 109 | 51 | 22 | 205 | 131 |
N.S. |
1 | 1.12 | 0.72 | 0.24 | 0.00 | 0.59 | 0.27 | 0.12 | 1.10 | 0.70 |
time (sec) |
N/A | 1.083 | 0.053 | 0.241 | 0.000 | 0.077 | 1.349 | 0.167 | 0.183 | 10.471 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 0 | 45 | 38 | 0 | 68 | 100 | 79 | 21 | 361 |
N.S. |
1 | 0.00 | 0.43 | 0.36 | 0.00 | 0.65 | 0.95 | 0.75 | 0.20 | 3.44 |
time (sec) |
N/A | 0.000 | 0.010 | 0.036 | 0.000 | 0.068 | 0.102 | 0.159 | 0.172 | 10.599 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | F(-1) | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 327 | 0 | 285 | 55 | 0 | 171 | 224 | 0 | 56 | 81 |
N.S. |
1 | 0.00 | 0.87 | 0.17 | 0.00 | 0.52 | 0.69 | 0.00 | 0.17 | 0.25 |
time (sec) |
N/A | 0.000 | 0.067 | 1.961 | 0.000 | 0.134 | 0.283 | 0.000 | 200.030 | 10.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 484 | 0 | 440 | 70 | 0 | 365 | 102 | 353 | 397 | 477 |
N.S. |
1 | 0.00 | 0.91 | 0.14 | 0.00 | 0.75 | 0.21 | 0.73 | 0.82 | 0.99 |
time (sec) |
N/A | 0.000 | 0.120 | 0.297 | 0.000 | 0.109 | 0.710 | 0.258 | 0.243 | 10.623 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 102 | 149 | 20 | 80 | 68 | 80 | 80 | 211 | 37 |
N.S. |
1 | 1.10 | 1.60 | 0.22 | 0.86 | 0.73 | 0.86 | 0.86 | 2.27 | 0.40 |
time (sec) |
N/A | 0.490 | 0.067 | 0.088 | 0.101 | 0.065 | 0.068 | 0.109 | 0.231 | 10.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 128 | 68 | 73 | 157 | 92 | 0 | 1488 | 483 |
N.S. |
1 | 1.00 | 1.38 | 0.73 | 0.78 | 1.69 | 0.99 | 0.00 | 16.00 | 5.19 |
time (sec) |
N/A | 0.538 | 0.182 | 0.505 | 0.105 | 0.069 | 0.457 | 0.000 | 0.324 | 11.722 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 0 | 97 | 64 | 0 | 163 | 46 | 0 | 98 | 181 |
N.S. |
1 | 0.00 | 0.48 | 0.32 | 0.00 | 0.80 | 0.23 | 0.00 | 0.48 | 0.89 |
time (sec) |
N/A | 0.000 | 0.014 | 0.036 | 0.000 | 0.075 | 0.213 | 0.000 | 0.176 | 10.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | B | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 0 | 58 | 50 | 0 | 105 | 56 | 77 | 95 | 85 |
N.S. |
1 | 0.00 | 1.00 | 0.86 | 0.00 | 1.81 | 0.97 | 1.33 | 1.64 | 1.47 |
time (sec) |
N/A | 0.000 | 0.028 | 0.053 | 0.000 | 0.066 | 0.057 | 0.136 | 0.182 | 0.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | F | A | F(-2) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 103 | 139 | 34 | 0 | 33 | 0 | 35 | 207 | 34 |
N.S. |
1 | 2.51 | 3.39 | 0.83 | 0.00 | 0.80 | 0.00 | 0.85 | 5.05 | 0.83 |
time (sec) |
N/A | 0.845 | 0.100 | 0.000 | 0.000 | 0.069 | 0.000 | 0.197 | 0.177 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 61 | 55 | 39 | 49 | 60 | 97 | 55 | 57 | 42 |
N.S. |
1 | 1.09 | 0.98 | 0.70 | 0.88 | 1.07 | 1.73 | 0.98 | 1.02 | 0.75 |
time (sec) |
N/A | 0.425 | 0.027 | 0.043 | 0.100 | 0.065 | 0.260 | 0.151 | 0.166 | 0.182 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 53 | 49 | 41 | 40 | 40 | 54 | 42 | 39 | 52 |
N.S. |
1 | 0.88 | 0.82 | 0.68 | 0.67 | 0.67 | 0.90 | 0.70 | 0.65 | 0.87 |
time (sec) |
N/A | 0.398 | 0.015 | 0.047 | 0.101 | 0.073 | 0.093 | 0.130 | 0.167 | 0.135 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 157 | 69 | 54 | 0 | 153 | 41 | 0 | 55 | 146 |
N.S. |
1 | 0.90 | 0.40 | 0.31 | 0.00 | 0.88 | 0.24 | 0.00 | 0.32 | 0.84 |
time (sec) |
N/A | 1.055 | 0.011 | 0.062 | 0.000 | 0.085 | 0.399 | 0.000 | 0.163 | 0.284 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 140 | 127 | 47 | 0 | 132 | 42 | 134 | 179 | 126 |
N.S. |
1 | 1.32 | 1.20 | 0.44 | 0.00 | 1.25 | 0.40 | 1.26 | 1.69 | 1.19 |
time (sec) |
N/A | 0.677 | 0.097 | 0.066 | 0.000 | 0.077 | 0.201 | 0.157 | 0.164 | 10.195 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 0 | 147 | 130 | 0 | 229 | 282 | 57 | 301 | 1389 |
N.S. |
1 | 0.00 | 1.00 | 0.88 | 0.00 | 1.56 | 1.92 | 0.39 | 2.05 | 9.45 |
time (sec) |
N/A | 0.000 | 0.442 | 0.140 | 0.000 | 0.115 | 0.243 | 0.119 | 0.204 | 12.316 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 0 | 169 | 43 | 0 | 162 | 180 | 163 | 271 | 1081 |
N.S. |
1 | 0.00 | 0.80 | 0.20 | 0.00 | 0.76 | 0.85 | 0.77 | 1.28 | 5.10 |
time (sec) |
N/A | 0.000 | 0.033 | 0.113 | 0.000 | 0.079 | 0.167 | 0.165 | 0.242 | 11.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 291 | 0 | 249 | 51 | 0 | 273 | 634 | 235 | 580 | 969 |
N.S. |
1 | 0.00 | 0.86 | 0.18 | 0.00 | 0.94 | 2.18 | 0.81 | 1.99 | 3.33 |
time (sec) |
N/A | 0.000 | 0.230 | 0.180 | 0.000 | 0.097 | 0.811 | 0.166 | 0.231 | 11.652 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 0 | 87 | 76 | 0 | 89 | 143 | 113 | 683 | 117 |
N.S. |
1 | 0.00 | 0.70 | 0.61 | 0.00 | 0.71 | 1.14 | 0.90 | 5.46 | 0.94 |
time (sec) |
N/A | 0.000 | 0.072 | 0.501 | 0.000 | 0.078 | 1.922 | 0.164 | 0.271 | 11.543 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 404 | 0 | 84 | 67 | 0 | 217 | 60 | 0 | 530 | 1145 |
N.S. |
1 | 0.00 | 0.21 | 0.17 | 0.00 | 0.54 | 0.15 | 0.00 | 1.31 | 2.83 |
time (sec) |
N/A | 0.000 | 0.041 | 0.109 | 0.000 | 0.102 | 0.234 | 0.000 | 0.273 | 11.271 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 142 | 59 | 50 | 0 | 93 | 1216 | 0 | 198 | 91 |
N.S. |
1 | 1.30 | 0.54 | 0.46 | 0.00 | 0.85 | 11.16 | 0.00 | 1.82 | 0.83 |
time (sec) |
N/A | 0.645 | 0.010 | 0.031 | 0.000 | 0.084 | 0.443 | 0.000 | 0.241 | 10.437 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 0 | 242 | 33 | 0 | 177 | 218 | 156 | 517 | 959 |
N.S. |
1 | 0.00 | 1.05 | 0.14 | 0.00 | 0.77 | 0.94 | 0.68 | 2.24 | 4.15 |
time (sec) |
N/A | 0.000 | 0.045 | 0.121 | 0.000 | 0.089 | 0.231 | 0.122 | 0.185 | 0.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 364 | 0 | 290 | 57 | 0 | 254 | 304 | 272 | 636 | 131 |
N.S. |
1 | 0.00 | 0.80 | 0.16 | 0.00 | 0.70 | 0.84 | 0.75 | 1.75 | 0.36 |
time (sec) |
N/A | 0.000 | 0.040 | 0.105 | 0.000 | 0.083 | 0.200 | 0.130 | 0.190 | 10.423 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 85 | 99 | 70 | 0 | 66 | 100 | 64 | 108 | 76 |
N.S. |
1 | 1.09 | 1.27 | 0.90 | 0.00 | 0.85 | 1.28 | 0.82 | 1.38 | 0.97 |
time (sec) |
N/A | 0.512 | 0.017 | 0.055 | 0.000 | 0.065 | 0.075 | 0.115 | 0.172 | 0.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | C | F | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 0 | 161 | 29 | 0 | 142 | 29 | 169 | 237 | 593 |
N.S. |
1 | 0.00 | 0.64 | 0.12 | 0.00 | 0.57 | 0.12 | 0.68 | 0.95 | 2.37 |
time (sec) |
N/A | 0.000 | 0.028 | 0.054 | 0.000 | 0.075 | 0.191 | 0.191 | 0.174 | 10.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-2) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 127 | 173 | 76 | 0 | 0 | 0 | 0 | 377 | 2068 |
N.S. |
1 | 1.14 | 1.56 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 3.40 | 18.63 |
time (sec) |
N/A | 0.513 | 0.204 | 0.302 | 0.000 | 0.000 | 0.000 | 0.000 | 0.286 | 10.913 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | F(-1) | F | F(-1) | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 0 | 252 | 0 | 0 | 0 | 0 | 0 | 101 | 0 |
N.S. |
1 | 0.00 | 1.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.000 | 2.891 | 180.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.037 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 200 | 134 | 27 | 169 | 112 | 20 | 179 | 112 | 33 |
N.S. |
1 | 1.03 | 0.69 | 0.14 | 0.87 | 0.57 | 0.10 | 0.92 | 0.57 | 0.17 |
time (sec) |
N/A | 0.657 | 0.033 | 0.109 | 0.107 | 0.070 | 0.071 | 0.112 | 0.190 | 0.099 |