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 | N/A | N/A | N/A | F(-2) | N/A | F(-1) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 32 | 0 | 34 | 0 | 0 | 40 | 34 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 0.00 | 1.06 | 0.00 | 0.00 | 1.25 | 1.06 |
time (sec) |
N/A | 0.517 | 1.564 | 0.243 | 0.000 | 0.085 | 0.000 | 0.000 | 0.149 | 26.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 231 | 223 | 0 | 0 | 0 | 0 | 0 | 129 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.649 | 0.800 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 149 | 0 | 0 | 0 | 0 | 0 | 90 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.526 | 0.465 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 77 | 0 | 0 | 0 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.370 | 0.194 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 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 | 15 | 15 | 15 | 16 | 15 | 25 | 34 | 16 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 1.67 | 2.27 | 1.07 | 1.00 | 1.00 |
time (sec) |
N/A | 0.173 | 0.005 | 0.296 | 0.026 | 0.078 | 0.644 | 0.111 | 0.144 | 25.669 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 32 | 75 | 33 | 27 | 34 | 57 | 34 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 2.34 | 1.03 | 0.84 | 1.06 | 1.78 | 1.06 |
time (sec) |
N/A | 0.503 | 0.314 | 0.029 | 0.131 | 0.072 | 41.854 | 0.154 | 0.152 | 25.672 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 32 | 240 | 57 | 0 | 34 | 73 | 34 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 7.50 | 1.78 | 0.00 | 1.06 | 2.28 | 1.06 |
time (sec) |
N/A | 0.530 | 0.764 | 0.033 | 0.160 | 0.096 | 0.000 | 0.166 | 0.145 | 25.946 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 34 | 32 | 1170 | 81 | 0 | 34 | 103 | 34 |
N.S. |
1 | 1.00 | 1.06 | 1.00 | 36.56 | 2.53 | 0.00 | 1.06 | 3.22 | 1.06 |
time (sec) |
N/A | 0.501 | 1.667 | 0.035 | 0.209 | 0.436 | 0.000 | 0.207 | 0.145 | 25.893 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 272 | 272 | 230 | 271 | 1115 | 655 | 411 | 766 | 270 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.00 | 4.10 | 2.41 | 1.51 | 2.82 | 0.99 | 0.00 |
time (sec) |
N/A | 0.598 | 0.244 | 14.782 | 0.063 | 0.085 | 30.459 | 0.135 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 115 | 129 | 530 | 267 | 216 | 286 | 128 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.03 | 4.24 | 2.14 | 1.73 | 2.29 | 1.02 | 0.00 |
time (sec) |
N/A | 0.405 | 0.131 | 2.657 | 0.046 | 0.082 | 15.498 | 0.121 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 41 | 47 | 186 | 81 | 65 | 73 | 45 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.15 | 4.54 | 1.98 | 1.59 | 1.78 | 1.10 | 0.00 |
time (sec) |
N/A | 0.268 | 0.043 | 0.478 | 0.041 | 0.078 | 9.847 | 0.119 | 0.162 | 0.000 |
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 | 15 | 15 | 15 | 14 | 13 | 13 | 65 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 4.33 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.171 | 0.004 | 0.116 | 0.030 | 0.069 | 1.472 | 0.113 | 0.154 | 25.726 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 28 | 30 | 29 | 24 | 30 | 29 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 1.07 | 1.04 | 0.86 | 1.07 | 1.04 | 1.07 |
time (sec) |
N/A | 0.443 | 2.242 | 0.011 | 0.096 | 0.092 | 7.041 | 0.127 | 0.165 | 25.918 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 28 | 343 | 51 | 26 | 30 | 51 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 12.25 | 1.82 | 0.93 | 1.07 | 1.82 | 1.07 |
time (sec) |
N/A | 0.465 | 2.104 | 0.014 | 0.119 | 0.073 | 11.864 | 0.169 | 0.161 | 25.750 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 30 | 28 | 1467 | 73 | 26 | 30 | 73 | 30 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 52.39 | 2.61 | 0.93 | 1.07 | 2.61 | 1.07 |
time (sec) |
N/A | 0.459 | 3.836 | 0.017 | 0.220 | 0.162 | 19.271 | 0.638 | 0.156 | 26.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | A | F(-1) | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 0 | 0 | 42 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.62 | 0.00 | 0.00 | 1.54 | 0.00 |
time (sec) |
N/A | 0.341 | 0.102 | 0.000 | 0.000 | 0.085 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | B | B | F | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 204 | 0 | 65 | 61 | 0 | 62 | 20 |
N.S. |
1 | 1.00 | 1.00 | 9.27 | 0.00 | 2.95 | 2.77 | 0.00 | 2.82 | 0.91 |
time (sec) |
N/A | 0.326 | 0.058 | 0.049 | 0.000 | 0.082 | 79.297 | 0.000 | 0.148 | 26.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | B | B | F | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 135 | 0 | 42 | 39 | 0 | 40 | 20 |
N.S. |
1 | 1.00 | 1.00 | 6.14 | 0.00 | 1.91 | 1.77 | 0.00 | 1.82 | 0.91 |
time (sec) |
N/A | 0.287 | 0.045 | 247.845 | 0.000 | 0.081 | 25.066 | 0.000 | 0.146 | 26.262 |
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 | 16 | 16 | 16 | 17 | 16 | 28 | 49 | 17 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.75 | 3.06 | 1.06 | 1.00 | 1.00 |
time (sec) |
N/A | 0.217 | 0.023 | 2.773 | 0.033 | 0.076 | 1.963 | 0.118 | 0.145 | 25.659 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 213 | 22 | 18 | 20 | 0 | 17 | 0 |
N.S. |
1 | 1.00 | 1.00 | 12.53 | 1.29 | 1.06 | 1.18 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.352 | 0.377 | 5.660 | 0.151 | 0.076 | 89.086 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 68 | 21 | 21 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 1.00 | 3.40 | 1.05 | 1.05 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.347 | 0.052 | 16.573 | 0.193 | 0.076 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | B | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 68 | 49 | 45 | 0 | 0 | 45 | 0 |
N.S. |
1 | 1.00 | 1.00 | 3.09 | 2.23 | 2.05 | 0.00 | 0.00 | 2.05 | 0.00 |
time (sec) |
N/A | 0.336 | 0.056 | 145.081 | 0.289 | 0.073 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 53 | 211 | 195 | 70 | 198 | 52 | 52 |
N.S. |
1 | 1.00 | 1.00 | 2.65 | 10.55 | 9.75 | 3.50 | 9.90 | 2.60 | 2.60 |
time (sec) |
N/A | 0.372 | 0.025 | 1.905 | 0.036 | 0.081 | 4.796 | 0.135 | 0.150 | 25.630 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 38 | 35 | 74 | 89 | 51 | 90 | 34 | 18 |
N.S. |
1 | 1.00 | 1.90 | 1.75 | 3.70 | 4.45 | 2.55 | 4.50 | 1.70 | 0.90 |
time (sec) |
N/A | 0.298 | 0.013 | 0.554 | 0.033 | 0.072 | 3.526 | 0.150 | 0.144 | 25.637 |
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 | 14 | 14 | 14 | 15 | 14 | 21 | 73 | 20 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 1.50 | 5.21 | 1.43 | 1.00 | 1.00 |
time (sec) |
N/A | 0.162 | 0.006 | 0.136 | 0.030 | 0.068 | 1.504 | 0.130 | 0.145 | 25.557 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 16 | 32 | 28 | 0 | 28 | 15 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 2.13 | 1.87 | 0.00 | 1.87 | 1.00 | 1.07 |
time (sec) |
N/A | 0.266 | 0.130 | 0.209 | 0.066 | 0.096 | 0.000 | 0.115 | 0.150 | 25.823 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 19 | 31 | 31 | 0 | 31 | 18 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.72 | 1.72 | 0.00 | 1.72 | 1.00 | 1.00 |
time (sec) |
N/A | 0.340 | 0.018 | 0.523 | 0.071 | 0.078 | 0.000 | 0.123 | 0.153 | 25.565 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 19 | 95 | 101 | 0 | 306 | 39 | 39 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 4.75 | 5.05 | 0.00 | 15.30 | 1.95 | 1.95 |
time (sec) |
N/A | 0.367 | 0.019 | 1.490 | 0.110 | 0.080 | 0.000 | 0.115 | 0.144 | 25.775 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 23 | 216 | 26 | 23 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.21 | 11.37 | 1.37 | 1.21 | 0.00 | 0.00 | 1.74 | 0.00 |
time (sec) |
N/A | 0.520 | 1.257 | 28.408 | 0.151 | 0.071 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | F(-2) | N/A | F(-1) | F(-2) | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 42 | 40 | 0 | 42 | 0 | 0 | 655 | 42 |
N.S. |
1 | 1.00 | 1.05 | 1.00 | 0.00 | 1.05 | 0.00 | 0.00 | 16.38 | 1.05 |
time (sec) |
N/A | 0.515 | 2.520 | 0.359 | 0.000 | 0.085 | 0.000 | 0.000 | 0.165 | 25.881 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 331 | 279 | 445 | 0 | 0 | 0 | 0 | 0 | 340 | 0 |
N.S. |
1 | 0.84 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.839 | 1.838 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 235 | 200 | 298 | 0 | 0 | 0 | 0 | 0 | 229 | 0 |
N.S. |
1 | 0.85 | 1.27 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.751 | 1.109 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 124 | 157 | 0 | 0 | 0 | 0 | 0 | 120 | 0 |
N.S. |
1 | 0.89 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.436 | 0.505 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 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 | 25 | 25 | 25 | 26 | 25 | 42 | 44 | 26 | 29 | 25 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.00 | 1.68 | 1.76 | 1.04 | 1.16 | 1.00 |
time (sec) |
N/A | 0.215 | 0.030 | 0.490 | 0.027 | 0.075 | 1.654 | 0.133 | 0.144 | 25.587 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 42 | 40 | 95 | 41 | 34 | 42 | 151 | 42 |
N.S. |
1 | 1.00 | 1.05 | 1.00 | 2.38 | 1.02 | 0.85 | 1.05 | 3.78 | 1.05 |
time (sec) |
N/A | 0.504 | 10.870 | 0.049 | 0.170 | 0.077 | 95.257 | 0.167 | 0.152 | 25.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 42 | 40 | 312 | 65 | 0 | 42 | 369 | 42 |
N.S. |
1 | 1.00 | 1.05 | 1.00 | 7.80 | 1.62 | 0.00 | 1.05 | 9.22 | 1.05 |
time (sec) |
N/A | 0.515 | 27.380 | 0.052 | 0.220 | 0.096 | 0.000 | 0.168 | 0.152 | 26.722 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 42 | 40 | 1583 | 89 | 0 | 42 | 772 | 42 |
N.S. |
1 | 1.00 | 1.05 | 1.00 | 39.58 | 2.22 | 0.00 | 1.05 | 19.30 | 1.05 |
time (sec) |
N/A | 0.528 | 91.618 | 0.063 | 0.326 | 0.447 | 0.000 | 0.190 | 0.173 | 25.651 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 27 | 31 | 30 | 22 | 0 | 26 | 26 |
N.S. |
1 | 1.00 | 1.00 | 1.04 | 1.19 | 1.15 | 0.85 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.403 | 0.872 | 13.764 | 0.197 | 0.076 | 31.391 | 0.000 | 0.156 | 25.372 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 31 | 29 | 59 | 52 | 26 | 31 | 606 | 31 |
N.S. |
1 | 1.00 | 1.07 | 1.00 | 2.03 | 1.79 | 0.90 | 1.07 | 20.90 | 1.07 |
time (sec) |
N/A | 0.391 | 107.551 | 0.010 | 0.202 | 0.073 | 17.211 | 0.166 | 0.166 | 26.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F(-2) | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 625 | 238 | 0 | 44 | 0 | 0 | 97 | 0 |
N.S. |
1 | 1.00 | 12.76 | 4.86 | 0.00 | 0.90 | 0.00 | 0.00 | 1.98 | 0.00 |
time (sec) |
N/A | 0.267 | 0.539 | 0.819 | 0.000 | 0.073 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F(-2) | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 642 | 243 | 0 | 45 | 0 | 0 | 99 | 0 |
N.S. |
1 | 1.00 | 12.84 | 4.86 | 0.00 | 0.90 | 0.00 | 0.00 | 1.98 | 0.00 |
time (sec) |
N/A | 0.269 | 0.550 | 0.671 | 0.000 | 0.083 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F(-2) | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 320 | 0 | 0 | 44 | 0 | 0 | 99 | 0 |
N.S. |
1 | 1.00 | 6.04 | 0.00 | 0.00 | 0.83 | 0.00 | 0.00 | 1.87 | 0.00 |
time (sec) |
N/A | 0.275 | 0.261 | 0.000 | 0.000 | 0.076 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F(-2) | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 316 | 0 | 0 | 43 | 0 | 0 | 97 | 0 |
N.S. |
1 | 1.00 | 6.08 | 0.00 | 0.00 | 0.83 | 0.00 | 0.00 | 1.87 | 0.00 |
time (sec) |
N/A | 0.254 | 0.249 | 0.000 | 0.000 | 0.101 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F(-2) | A | F(-2) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 641 | 233 | 0 | 43 | 0 | 0 | 85 | 0 |
N.S. |
1 | 1.00 | 13.08 | 4.76 | 0.00 | 0.88 | 0.00 | 0.00 | 1.73 | 0.00 |
time (sec) |
N/A | 0.270 | 0.471 | 0.866 | 0.000 | 0.077 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F(-2) | A | F(-2) | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 645 | 238 | 0 | 44 | 0 | 0 | 87 | 0 |
N.S. |
1 | 1.00 | 12.90 | 4.76 | 0.00 | 0.88 | 0.00 | 0.00 | 1.74 | 0.00 |
time (sec) |
N/A | 0.244 | 0.354 | 0.849 | 0.000 | 0.074 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 56 | 0 | 0 | 83 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 0.84 | 0.00 | 0.00 | 1.24 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.330 | 0.278 | 0.000 | 0.000 | 0.081 | 0.000 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 59 | 0 | 0 | 90 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 1.14 | 0.00 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.329 | 0.215 | 0.000 | 0.000 | 0.080 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 49 | 0 | 0 | 70 | 0 | 56 | 43 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 1.27 | 0.00 | 1.02 | 0.78 | 0.00 |
time (sec) |
N/A | 0.283 | 0.094 | 0.000 | 0.000 | 0.075 | 0.000 | 0.122 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 49 | 0 | 0 | 70 | 0 | 56 | 41 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 1.27 | 0.00 | 1.02 | 0.75 | 0.00 |
time (sec) |
N/A | 0.260 | 0.098 | 0.000 | 0.000 | 0.073 | 0.000 | 0.127 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 43 | 0 | 0 | 53 | 0 | 42 | 33 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.00 | 0.00 | 1.18 | 0.00 | 0.93 | 0.73 | 0.00 |
time (sec) |
N/A | 0.209 | 0.084 | 0.000 | 0.000 | 0.072 | 0.000 | 0.111 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 40 | 39 | 64 | 45 | 0 | 54 | 39 | 32 |
N.S. |
1 | 1.00 | 1.25 | 1.22 | 2.00 | 1.41 | 0.00 | 1.69 | 1.22 | 1.00 |
time (sec) |
N/A | 0.189 | 0.046 | 0.589 | 0.032 | 0.083 | 0.000 | 0.112 | 0.166 | 25.784 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 45 | 0 | 0 | 46 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.96 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.282 | 0.073 | 0.000 | 0.000 | 0.077 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 49 | 0 | 0 | 53 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.96 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.283 | 0.074 | 0.000 | 0.000 | 0.100 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 49 | 0 | 0 | 53 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.96 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.285 | 0.078 | 0.000 | 0.000 | 0.094 | 0.000 | 0.000 | 0.153 | 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 | 22 | 22 | 22 | 26 | 23 | 26 | 19 | 26 | 25 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.18 | 1.05 | 1.18 | 0.86 | 1.18 | 1.14 | 1.00 |
time (sec) |
N/A | 0.195 | 0.022 | 0.109 | 0.074 | 0.067 | 0.518 | 0.117 | 0.155 | 25.753 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 23 | 22 | 24 | 0 | 32 | 18 | 20 |
N.S. |
1 | 1.00 | 1.10 | 1.15 | 1.10 | 1.20 | 0.00 | 1.60 | 0.90 | 1.00 |
time (sec) |
N/A | 0.186 | 0.011 | 0.151 | 0.026 | 0.070 | 0.000 | 0.134 | 0.177 | 25.526 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 39 | 0 | 0 | 45 | 0 | 36 | 28 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 1.12 | 0.00 | 0.90 | 0.70 | 0.00 |
time (sec) |
N/A | 0.246 | 0.029 | 0.000 | 0.000 | 0.075 | 0.000 | 0.130 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 34 | 33 | 55 | 37 | 0 | 43 | 25 | 27 |
N.S. |
1 | 1.00 | 1.26 | 1.22 | 2.04 | 1.37 | 0.00 | 1.59 | 0.93 | 1.00 |
time (sec) |
N/A | 0.189 | 0.016 | 0.355 | 0.034 | 0.075 | 0.000 | 0.109 | 0.146 | 25.508 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 74 | 48 | 0 | 0 | 0 | 0 | 0 | 190 | 0 |
N.S. |
1 | 1.12 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.88 | 0.00 |
time (sec) |
N/A | 0.253 | 0.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.149 | 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 | 99 | 94 | 85 | 86 | 87 | 98 | 112 | 89 | 106 | 85 |
N.S. |
1 | 0.95 | 0.86 | 0.87 | 0.88 | 0.99 | 1.13 | 0.90 | 1.07 | 0.86 |
time (sec) |
N/A | 0.297 | 0.063 | 0.350 | 0.032 | 0.078 | 6.224 | 0.131 | 0.148 | 25.561 |
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 | 85 | 81 | 74 | 75 | 75 | 86 | 97 | 75 | 94 | 73 |
N.S. |
1 | 0.95 | 0.87 | 0.88 | 0.88 | 1.01 | 1.14 | 0.88 | 1.11 | 0.86 |
time (sec) |
N/A | 0.282 | 0.045 | 0.240 | 0.027 | 0.073 | 2.983 | 0.120 | 0.145 | 25.461 |
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 | 68 | 63 | 64 | 65 | 74 | 85 | 65 | 82 | 61 |
N.S. |
1 | 0.96 | 0.89 | 0.90 | 0.92 | 1.04 | 1.20 | 0.92 | 1.15 | 0.86 |
time (sec) |
N/A | 0.266 | 0.036 | 0.191 | 0.027 | 0.070 | 1.944 | 0.113 | 0.155 | 25.570 |
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 | 57 | 51 | 49 | 53 | 51 | 59 | 70 | 51 | 67 | 49 |
N.S. |
1 | 0.89 | 0.86 | 0.93 | 0.89 | 1.04 | 1.23 | 0.89 | 1.18 | 0.86 |
time (sec) |
N/A | 0.248 | 0.028 | 0.142 | 0.027 | 0.097 | 0.938 | 0.128 | 0.149 | 25.893 |
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 | 33 | 36 | 31 | 37 | 36 | 38 | 44 | 37 | 49 | 33 |
N.S. |
1 | 1.09 | 0.94 | 1.12 | 1.09 | 1.15 | 1.33 | 1.12 | 1.48 | 1.00 |
time (sec) |
N/A | 0.209 | 0.011 | 0.070 | 0.026 | 0.070 | 0.539 | 0.125 | 0.145 | 25.616 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 51 | 50 | 62 | 80 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 0.96 | 0.94 | 1.17 | 1.51 | 0.00 | 0.00 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.366 | 0.027 | 0.154 | 0.028 | 0.000 | 0.000 | 0.000 | 0.152 | 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 | 47 | 47 | 45 | 48 | 46 | 46 | 66 | 47 | 54 | 43 |
N.S. |
1 | 1.00 | 0.96 | 1.02 | 0.98 | 0.98 | 1.40 | 1.00 | 1.15 | 0.91 |
time (sec) |
N/A | 0.249 | 0.018 | 0.141 | 0.027 | 0.082 | 1.220 | 0.132 | 0.148 | 26.023 |
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 | 72 | 67 | 65 | 62 | 62 | 70 | 94 | 65 | 73 | 54 |
N.S. |
1 | 0.93 | 0.90 | 0.86 | 0.86 | 0.97 | 1.31 | 0.90 | 1.01 | 0.75 |
time (sec) |
N/A | 0.262 | 0.043 | 0.187 | 0.030 | 0.085 | 2.269 | 0.114 | 0.145 | 25.607 |
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 | 86 | 79 | 77 | 72 | 75 | 82 | 112 | 80 | 85 | 68 |
N.S. |
1 | 0.92 | 0.90 | 0.84 | 0.87 | 0.95 | 1.30 | 0.93 | 0.99 | 0.79 |
time (sec) |
N/A | 0.264 | 0.043 | 0.249 | 0.031 | 0.081 | 4.725 | 0.137 | 0.153 | 25.516 |
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 | 100 | 93 | 87 | 84 | 86 | 94 | 122 | 92 | 97 | 79 |
N.S. |
1 | 0.93 | 0.87 | 0.84 | 0.86 | 0.94 | 1.22 | 0.92 | 0.97 | 0.79 |
time (sec) |
N/A | 0.296 | 0.058 | 0.348 | 0.033 | 0.075 | 9.836 | 0.118 | 0.148 | 25.573 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 154 | 137 | 0 | 0 | 0 | 0 | 0 | 464 | 0 |
N.S. |
1 | 0.98 | 0.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.96 | 0.00 |
time (sec) |
N/A | 0.422 | 0.221 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 201 | 190 | 238 | 0 | 444 | 0 | 221 | 307 | 395 |
N.S. |
1 | 0.97 | 0.92 | 1.15 | 0.00 | 2.14 | 0.00 | 1.07 | 1.48 | 1.91 |
time (sec) |
N/A | 0.479 | 0.253 | 0.783 | 0.000 | 0.090 | 0.000 | 0.124 | 0.152 | 25.706 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 162 | 151 | 190 | 0 | 364 | 0 | 176 | 228 | 288 |
N.S. |
1 | 0.97 | 0.90 | 1.14 | 0.00 | 2.18 | 0.00 | 1.05 | 1.37 | 1.72 |
time (sec) |
N/A | 0.430 | 0.172 | 0.523 | 0.000 | 0.088 | 0.000 | 0.148 | 0.143 | 26.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 132 | 122 | 154 | 0 | 299 | 0 | 146 | 179 | 229 |
N.S. |
1 | 0.97 | 0.90 | 1.13 | 0.00 | 2.20 | 0.00 | 1.07 | 1.32 | 1.68 |
time (sec) |
N/A | 0.380 | 0.124 | 0.388 | 0.000 | 0.086 | 0.000 | 0.125 | 0.143 | 26.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 102 | 94 | 122 | 0 | 245 | 359 | 113 | 119 | 166 |
N.S. |
1 | 0.94 | 0.86 | 1.12 | 0.00 | 2.25 | 3.29 | 1.04 | 1.09 | 1.52 |
time (sec) |
N/A | 0.337 | 0.091 | 0.311 | 0.000 | 0.081 | 95.057 | 0.137 | 0.152 | 25.940 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 81 | 78 | 89 | 0 | 190 | 274 | 92 | 82 | 120 |
N.S. |
1 | 1.03 | 0.99 | 1.13 | 0.00 | 2.41 | 3.47 | 1.16 | 1.04 | 1.52 |
time (sec) |
N/A | 0.283 | 0.066 | 0.188 | 0.000 | 0.081 | 40.300 | 0.124 | 0.149 | 25.699 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 123 | 150 | 166 | 0 | 0 | 0 | 0 | 95 | 0 |
N.S. |
1 | 0.95 | 1.16 | 1.29 | 0.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.443 | 0.234 | 0.141 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 87 | 95 | 0 | 199 | 0 | 99 | 89 | 262 |
N.S. |
1 | 1.00 | 1.01 | 1.10 | 0.00 | 2.31 | 0.00 | 1.15 | 1.03 | 3.05 |
time (sec) |
N/A | 0.339 | 0.125 | 0.262 | 0.000 | 0.090 | 0.000 | 0.133 | 0.156 | 26.361 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 117 | 105 | 145 | 0 | 261 | 0 | 129 | 139 | 474 |
N.S. |
1 | 0.97 | 0.87 | 1.20 | 0.00 | 2.16 | 0.00 | 1.07 | 1.15 | 3.92 |
time (sec) |
N/A | 0.394 | 0.258 | 0.381 | 0.000 | 0.099 | 0.000 | 0.152 | 0.151 | 26.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 141 | 132 | 181 | 0 | 318 | 0 | 164 | 206 | 505 |
N.S. |
1 | 0.95 | 0.89 | 1.21 | 0.00 | 2.13 | 0.00 | 1.10 | 1.38 | 3.39 |
time (sec) |
N/A | 0.439 | 0.405 | 0.556 | 0.000 | 0.116 | 0.000 | 0.140 | 0.150 | 26.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 184 | 172 | 225 | 0 | 404 | 0 | 210 | 274 | 627 |
N.S. |
1 | 0.97 | 0.91 | 1.18 | 0.00 | 2.13 | 0.00 | 1.11 | 1.44 | 3.30 |
time (sec) |
N/A | 0.476 | 0.508 | 0.838 | 0.000 | 0.137 | 0.000 | 0.127 | 0.157 | 26.513 |
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 | 42 | 42 | 35 | 38 | 37 | 33 | 46 | 37 | 36 | 39 |
N.S. |
1 | 1.00 | 0.83 | 0.90 | 0.88 | 0.79 | 1.10 | 0.88 | 0.86 | 0.93 |
time (sec) |
N/A | 0.241 | 0.021 | 0.076 | 0.108 | 0.075 | 0.073 | 0.142 | 0.146 | 0.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 485 | 483 | 468 | 876 | 0 | 1270 | 0 | 741 | 1118 | 1240 |
N.S. |
1 | 1.00 | 0.96 | 1.81 | 0.00 | 2.62 | 0.00 | 1.53 | 2.31 | 2.56 |
time (sec) |
N/A | 1.026 | 0.936 | 3.440 | 0.000 | 0.133 | 0.000 | 0.167 | 0.151 | 26.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 338 | 337 | 324 | 594 | 0 | 880 | 0 | 495 | 727 | 775 |
N.S. |
1 | 1.00 | 0.96 | 1.76 | 0.00 | 2.60 | 0.00 | 1.46 | 2.15 | 2.29 |
time (sec) |
N/A | 0.788 | 0.558 | 1.756 | 0.000 | 0.100 | 0.000 | 0.160 | 0.153 | 25.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 226 | 204 | 384 | 0 | 567 | 0 | 307 | 436 | 457 |
N.S. |
1 | 1.00 | 0.90 | 1.70 | 0.00 | 2.51 | 0.00 | 1.36 | 1.93 | 2.02 |
time (sec) |
N/A | 0.563 | 0.432 | 0.929 | 0.000 | 0.097 | 0.000 | 0.134 | 0.151 | 25.978 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 152 | 123 | 170 | 0 | 336 | 379 | 167 | 212 | 242 |
N.S. |
1 | 0.99 | 0.80 | 1.10 | 0.00 | 2.18 | 2.46 | 1.08 | 1.38 | 1.57 |
time (sec) |
N/A | 0.418 | 0.210 | 0.427 | 0.000 | 0.087 | 86.757 | 0.124 | 0.146 | 26.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 81 | 78 | 89 | 0 | 190 | 274 | 92 | 82 | 120 |
N.S. |
1 | 1.03 | 0.99 | 1.13 | 0.00 | 2.41 | 3.47 | 1.16 | 1.04 | 1.52 |
time (sec) |
N/A | 0.279 | 0.051 | 0.101 | 0.000 | 0.089 | 35.474 | 0.120 | 0.150 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 213 | 200 | 300 | 0 | 0 | 0 | 0 | 883 | 0 |
N.S. |
1 | 0.93 | 0.88 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 3.87 | 0.00 |
time (sec) |
N/A | 0.700 | 0.487 | 0.585 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 163 | 166 | 184 | 0 | 429 | 0 | 189 | 330 | 590 |
N.S. |
1 | 0.99 | 1.01 | 1.12 | 0.00 | 2.60 | 0.00 | 1.15 | 2.00 | 3.58 |
time (sec) |
N/A | 0.509 | 0.319 | 1.095 | 0.000 | 0.157 | 0.000 | 0.135 | 0.155 | 28.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 259 | 248 | 215 | 310 | 0 | 1341 | 0 | 490 | 1470 | 1715 |
N.S. |
1 | 0.96 | 0.83 | 1.20 | 0.00 | 5.18 | 0.00 | 1.89 | 5.68 | 6.62 |
time (sec) |
N/A | 0.620 | 0.588 | 2.197 | 0.000 | 1.132 | 0.000 | 0.309 | 0.159 | 30.923 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 356 | 341 | 310 | 486 | 0 | 3013 | 0 | 1128 | 3818 | 2707 |
N.S. |
1 | 0.96 | 0.87 | 1.37 | 0.00 | 8.46 | 0.00 | 3.17 | 10.72 | 7.60 |
time (sec) |
N/A | 0.907 | 1.129 | 4.455 | 0.000 | 8.131 | 0.000 | 0.214 | 0.174 | 43.236 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 519 | 500 | 469 | 725 | 0 | 5824 | 0 | 2191 | 7805 | 4334 |
N.S. |
1 | 0.96 | 0.90 | 1.40 | 0.00 | 11.22 | 0.00 | 4.22 | 15.04 | 8.35 |
time (sec) |
N/A | 1.245 | 1.951 | 9.283 | 0.000 | 40.845 | 0.000 | 1.298 | 0.209 | 57.951 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 174 | 131 | 292 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.99 | 0.75 | 1.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.634 | 0.068 | 0.659 | 0.000 | 0.000 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 248 | 339 | 433 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 0.96 | 1.31 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.958 | 0.406 | 1.002 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 762 | 762 | 626 | 555 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.804 | 1.228 | 0.882 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 782 | 782 | 663 | 637 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 1.912 | 1.380 | 1.208 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 136 | 111 | 0 | 123 | 0 | 0 | 0 | 130 | 0 |
N.S. |
1 | 0.94 | 0.77 | 0.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.532 | 0.081 | 0.000 | 0.043 | 0.000 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 587 | 583 | 478 | 0 | 0 | 0 | 0 | 0 | 200 | 0 |
N.S. |
1 | 0.99 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 1.289 | 1.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 311 | 311 | 290 | 279 | 0 | 0 | 0 | 0 | 114 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.771 | 0.248 | 0.418 | 0.000 | 0.000 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 371 | 386 | 365 | 0 | 0 | 0 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.04 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.826 | 0.182 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 443 | 443 | 826 | 219 | 0 | 0 | 0 | 0 | 73 | 0 |
N.S. |
1 | 1.00 | 1.86 | 0.49 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 1.075 | 0.791 | 0.207 | 0.000 | 0.000 | 0.000 | 0.000 | 0.151 | 0.000 |