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 | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 48 | 0 | 0 | 46 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.96 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.319 | 0.005 | 0.000 | 0.000 | 0.123 | 0.000 | 0.000 | 0.203 | 0.000 |
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 | 20 | 20 | 22 | 18 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.412 | 0.023 | 0.255 | 0.123 | 0.089 | 1.263 | 0.127 | 0.209 | 3.475 |
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 | 20 | 20 | 22 | 18 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.580 | 0.024 | 0.251 | 0.126 | 0.079 | 1.765 | 0.124 | 0.209 | 3.629 |
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 | 20 | 20 | 22 | 18 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.816 | 0.024 | 0.260 | 0.127 | 0.102 | 3.185 | 0.126 | 0.217 | 3.735 |
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 | 163 | 215 | 163 | 0 | 0 | 141 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.32 | 1.00 | 0.00 | 0.00 | 0.87 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.513 | 0.007 | 0.000 | 0.000 | 0.092 | 0.000 | 0.000 | 0.225 | 0.000 |
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 | 20 | 20 | 22 | 18 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 1.478 | 0.023 | 0.240 | 0.131 | 0.082 | 11.610 | 0.124 | 0.195 | 3.728 |
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 | 20 | 20 | 22 | 18 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 2.364 | 0.026 | 0.240 | 0.126 | 0.091 | 21.347 | 0.128 | 0.206 | 3.742 |
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 | 20 | 20 | 22 | 18 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 2.590 | 0.026 | 0.236 | 0.140 | 0.085 | 38.508 | 0.125 | 0.196 | 3.636 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 278 | 0 | 278 | 0 | 0 | 203 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 0.00 | 0.73 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.000 | 0.010 | 0.000 | 0.000 | 0.099 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 144 | 89 | 26 | 126 | 85 | 184 | 0 | 10 | 0 |
N.S. |
1 | 1.16 | 0.72 | 0.21 | 1.02 | 0.69 | 1.48 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.498 | 0.051 | 0.519 | 0.142 | 0.082 | 1.194 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 125 | 83 | 26 | 74 | 79 | 153 | 0 | 10 | 0 |
N.S. |
1 | 1.15 | 0.76 | 0.24 | 0.68 | 0.72 | 1.40 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.569 | 0.041 | 0.517 | 0.046 | 0.090 | 1.237 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 99 | 113 | 80 | 26 | 110 | 86 | 49 | 0 | 10 | 0 |
N.S. |
1 | 1.14 | 0.81 | 0.26 | 1.11 | 0.87 | 0.49 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.422 | 0.043 | 0.536 | 0.155 | 0.106 | 0.570 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 93 | 71 | 26 | 61 | 66 | 116 | 0 | 10 | 0 |
N.S. |
1 | 1.11 | 0.85 | 0.31 | 0.73 | 0.79 | 1.38 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.457 | 0.032 | 0.481 | 0.042 | 0.085 | 0.728 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 81 | 74 | 62 | 94 | 59 | 112 | 0 | 10 | 0 |
N.S. |
1 | 1.09 | 1.00 | 0.84 | 1.27 | 0.80 | 1.51 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.329 | 0.013 | 0.486 | 0.125 | 0.089 | 0.646 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 61 | 59 | 26 | 49 | 54 | 80 | 0 | 10 | 0 |
N.S. |
1 | 1.03 | 1.00 | 0.44 | 0.83 | 0.92 | 1.36 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.353 | 0.011 | 0.476 | 0.041 | 0.087 | 0.678 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 50 | 49 | 26 | 70 | 51 | 49 | 0 | 8 | 0 |
N.S. |
1 | 1.02 | 1.00 | 0.53 | 1.43 | 1.04 | 1.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.257 | 0.010 | 0.480 | 0.124 | 0.089 | 0.347 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 26 | 27 | 28 | 44 | 0 | 6 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 1.00 | 1.04 | 1.63 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.175 | 0.004 | 0.767 | 0.029 | 0.090 | 0.447 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 0 | 23 | 0 | 0 | 41 | 0 | 10 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.33 | 0.00 | 0.00 | 0.59 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.324 | 0.000 | 0.506 | 0.000 | 0.000 | 0.355 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 24 | 34 | 25 | 53 | 0 | 10 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 1.26 | 0.93 | 1.96 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.212 | 0.010 | 0.515 | 0.107 | 0.100 | 0.577 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 43 | 44 | 26 | 61 | 42 | 51 | 0 | 10 | 0 |
N.S. |
1 | 0.98 | 1.00 | 0.59 | 1.39 | 0.95 | 1.16 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.257 | 0.010 | 0.480 | 0.192 | 0.097 | 0.387 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 55 | 52 | 26 | 44 | 44 | 42 | 0 | 10 | 0 |
N.S. |
1 | 1.06 | 1.00 | 0.50 | 0.85 | 0.85 | 0.81 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.356 | 0.013 | 0.480 | 0.125 | 0.092 | 0.433 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 70 | 69 | 64 | 61 | 56 | 110 | 0 | 10 | 0 |
N.S. |
1 | 1.01 | 1.00 | 0.93 | 0.88 | 0.81 | 1.59 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.306 | 0.013 | 0.464 | 0.189 | 0.081 | 0.704 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 83 | 77 | 68 | 46 | 65 | 65 | 0 | 10 | 0 |
N.S. |
1 | 1.08 | 1.00 | 0.88 | 0.60 | 0.84 | 0.84 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.454 | 0.015 | 0.557 | 0.117 | 0.091 | 1.371 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 99 | 74 | 26 | 61 | 79 | 56 | 0 | 10 | 0 |
N.S. |
1 | 1.05 | 0.79 | 0.28 | 0.65 | 0.84 | 0.60 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.392 | 0.079 | 0.493 | 0.187 | 0.092 | 0.749 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 111 | 84 | 26 | 48 | 78 | 44 | 0 | 10 | 0 |
N.S. |
1 | 1.09 | 0.82 | 0.25 | 0.47 | 0.76 | 0.43 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.563 | 0.090 | 0.472 | 0.113 | 0.086 | 0.963 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 126 | 85 | 26 | 61 | 81 | 185 | 0 | 10 | 0 |
N.S. |
1 | 1.06 | 0.71 | 0.22 | 0.51 | 0.68 | 1.55 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.444 | 0.046 | 0.499 | 0.185 | 0.091 | 1.536 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | C | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 139 | 96 | 90 | 46 | 91 | 76 | 0 | 10 | 0 |
N.S. |
1 | 1.09 | 0.76 | 0.71 | 0.36 | 0.72 | 0.60 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.666 | 0.059 | 0.582 | 0.138 | 0.113 | 8.414 | 0.000 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 298 | 270 | 424 | 275 | 0 | 375 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.91 | 1.42 | 0.92 | 0.00 | 1.26 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.545 | 0.549 | 0.854 | 0.000 | 0.129 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 182 | 237 | 190 | 0 | 249 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.94 | 1.22 | 0.98 | 0.00 | 1.28 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.436 | 0.319 | 0.645 | 0.000 | 0.098 | 0.000 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 115 | 74 | 108 | 0 | 132 | 0 | 0 | 14 | 0 |
N.S. |
1 | 0.94 | 0.61 | 0.89 | 0.00 | 1.08 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.339 | 0.181 | 0.579 | 0.000 | 0.110 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 90 | 34 | 44 | 47 | 0 | 0 | 8 | 0 |
N.S. |
1 | 1.00 | 2.43 | 0.92 | 1.19 | 1.27 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.189 | 0.025 | 0.497 | 0.025 | 0.086 | 0.000 | 0.000 | 0.207 | 0.000 |
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 | 14 | 14 | 16 | 14 | 16 | 16 | 12 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.14 | 0.86 | 1.14 | 1.14 | 1.14 |
time (sec) |
N/A | 0.193 | 0.020 | 0.454 | 0.588 | 0.109 | 0.431 | 0.107 | 0.197 | 4.112 |
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 | 14 | 14 | 16 | 14 | 16 | 27 | 14 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.93 | 1.00 | 1.14 | 1.14 | 1.14 |
time (sec) |
N/A | 0.191 | 1.446 | 0.431 | 0.322 | 0.081 | 0.622 | 0.105 | 0.215 | 4.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 196 | 166 | 187 | 502 | 176 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.86 | 0.73 | 0.82 | 2.21 | 0.78 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.403 | 0.211 | 0.518 | 0.949 | 0.101 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 132 | 116 | 122 | 423 | 148 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.89 | 0.78 | 0.82 | 2.86 | 1.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.357 | 0.208 | 0.549 | 0.622 | 0.101 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 84 | 59 | 79 | 311 | 104 | 0 | 0 | 10 | 0 |
N.S. |
1 | 0.88 | 0.62 | 0.83 | 3.27 | 1.09 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.299 | 0.102 | 0.536 | 0.554 | 0.091 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 90 | 34 | 44 | 47 | 0 | 0 | 8 | 0 |
N.S. |
1 | 1.00 | 2.43 | 0.92 | 1.19 | 1.27 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.191 | 0.019 | 0.408 | 0.031 | 0.078 | 0.000 | 0.000 | 0.207 | 0.000 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.191 | 0.014 | 0.309 | 0.597 | 0.086 | 0.310 | 0.106 | 0.221 | 3.944 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.190 | 0.912 | 0.319 | 0.323 | 0.099 | 0.274 | 0.109 | 0.184 | 3.770 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 0 | 181 | 0 | 0 | 183 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.00 | 0.72 | 0.00 | 0.00 | 0.72 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.000 | 0.094 | 0.000 | 0.000 | 0.090 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 457 | 170 | 324 | 0 | 184 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.91 | 0.71 | 1.36 | 0.00 | 0.77 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 2.234 | 0.171 | 0.717 | 0.000 | 0.090 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 265 | 355 | 0 | 0 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 2.205 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 290 | 137 | 209 | 0 | 149 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.64 | 0.77 | 1.18 | 0.00 | 0.84 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.207 | 0.096 | 0.767 | 0.000 | 0.108 | 0.000 | 0.000 | 0.192 | 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 | 140 | 180 | 114 | 0 | 0 | 118 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.29 | 0.81 | 0.00 | 0.00 | 0.84 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.075 | 0.041 | 0.000 | 0.000 | 0.095 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 168 | 100 | 122 | 0 | 111 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.35 | 0.81 | 0.98 | 0.00 | 0.90 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.643 | 0.066 | 0.664 | 0.000 | 0.106 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 149 | 0 | 0 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.522 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 60 | 54 | 49 | 0 | 59 | 0 | 0 | 8 | 0 |
N.S. |
1 | 1.11 | 1.00 | 0.91 | 0.00 | 1.09 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.292 | 0.011 | 0.796 | 0.000 | 0.102 | 0.000 | 0.000 | 0.189 | 0.000 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.182 | 0.015 | 0.111 | 0.060 | 0.088 | 1.101 | 0.102 | 0.193 | 3.945 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.264 | 0.020 | 0.212 | 0.065 | 0.097 | 1.076 | 0.107 | 0.235 | 3.887 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.274 | 0.016 | 0.194 | 0.065 | 0.109 | 1.080 | 0.104 | 0.191 | 3.837 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.505 | 0.020 | 0.207 | 0.062 | 0.091 | 1.364 | 0.111 | 0.201 | 3.903 |
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 | 127 | 142 | 127 | 0 | 0 | 102 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.12 | 1.00 | 0.00 | 0.00 | 0.80 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.875 | 0.007 | 0.000 | 0.000 | 0.105 | 0.000 | 0.000 | 0.184 | 0.000 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.927 | 0.021 | 0.204 | 0.063 | 0.095 | 1.284 | 0.102 | 0.188 | 3.853 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 1.398 | 0.016 | 0.195 | 0.060 | 0.087 | 1.373 | 0.103 | 0.188 | 3.814 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 1.641 | 0.021 | 0.158 | 0.061 | 0.096 | 1.590 | 0.109 | 0.208 | 4.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 242 | 0 | 242 | 0 | 0 | 178 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 0.00 | 0.74 | 0.00 | 0.00 | 0.05 | 0.00 |
time (sec) |
N/A | 0.000 | 0.010 | 0.000 | 0.000 | 0.107 | 0.000 | 0.000 | 0.223 | 0.000 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 2.655 | 0.022 | 0.207 | 0.060 | 0.099 | 2.293 | 0.103 | 0.231 | 4.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 495 | 458 | 0 | 0 | 0 | 0 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 0.565 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 279 | 256 | 0 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.370 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 71 | 66 | 60 | 0 | 88 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.03 | 0.96 | 0.87 | 0.00 | 1.28 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.463 | 0.010 | 0.583 | 0.000 | 0.091 | 0.000 | 0.000 | 0.204 | 0.000 |
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 | 16 | 16 | 18 | 16 | 18 | 18 | 14 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.88 | 1.12 | 1.12 | 1.12 |
time (sec) |
N/A | 0.207 | 0.027 | 0.242 | 0.059 | 0.086 | 0.443 | 0.104 | 0.201 | 4.108 |
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 | 16 | 16 | 18 | 16 | 18 | 29 | 15 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.81 | 0.94 | 1.12 | 1.12 | 1.12 |
time (sec) |
N/A | 0.208 | 0.054 | 0.355 | 0.060 | 0.092 | 0.607 | 0.109 | 0.194 | 4.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 257 | 318 | 0 | 0 | 448 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.11 | 1.38 | 0.00 | 0.00 | 1.94 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.933 | 4.569 | 0.000 | 0.000 | 0.116 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 253 | 318 | 0 | 0 | 448 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.11 | 1.40 | 0.00 | 0.00 | 1.97 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.849 | 4.258 | 0.000 | 0.000 | 0.115 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 238 | 315 | 0 | 0 | 445 | 0 | 0 | 15 | 0 |
N.S. |
1 | 1.11 | 1.47 | 0.00 | 0.00 | 2.08 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.824 | 4.455 | 0.000 | 0.000 | 0.125 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 65 | 165 | 64 | 82 | 121 | 0 | 0 | 19 | 0 |
N.S. |
1 | 0.98 | 2.50 | 0.97 | 1.24 | 1.83 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.290 | 0.080 | 2.267 | 0.033 | 0.100 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 240 | 194 | 0 | 0 | 444 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.11 | 0.89 | 0.00 | 0.00 | 2.05 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.843 | 2.545 | 0.000 | 0.000 | 0.120 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 228 | 254 | 199 | 0 | 0 | 460 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.11 | 0.87 | 0.00 | 0.00 | 2.02 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.821 | 2.582 | 0.000 | 0.000 | 0.125 | 0.000 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 280 | 343 | 244 | 0 | 0 | 689 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.22 | 0.87 | 0.00 | 0.00 | 2.46 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.027 | 3.580 | 0.000 | 0.000 | 0.119 | 0.000 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 0 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.390 | 0.000 | 0.000 | 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 | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 0 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.389 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 99 | 0 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.364 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 100 | 0 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.356 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 11 | 11 | 10 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 0.85 | 0.77 | 0.00 | 1.46 | 0.00 |
time (sec) |
N/A | 0.186 | 0.007 | 0.424 | 0.031 | 0.079 | 0.235 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 11 | 11 | 10 | 0 | 17 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 0.85 | 0.77 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.181 | 0.006 | 0.348 | 0.026 | 0.083 | 0.121 | 0.000 | 0.233 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 10 | 9 | 9 | 10 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.00 | 1.00 | 1.11 | 0.00 | 2.11 | 0.00 |
time (sec) |
N/A | 0.184 | 0.010 | 0.384 | 0.032 | 0.081 | 0.131 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 12 | 11 | 11 | 12 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 1.00 | 1.09 | 0.00 | 1.73 | 0.00 |
time (sec) |
N/A | 0.188 | 0.005 | 0.451 | 0.029 | 0.077 | 0.279 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 11 | 11 | 15 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 0.85 | 1.15 | 0.00 | 1.46 | 0.00 |
time (sec) |
N/A | 0.184 | 0.005 | 0.625 | 0.024 | 0.084 | 0.457 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 18 | 17 | 18 | 34 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.06 | 2.00 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.191 | 0.009 | 0.728 | 0.027 | 0.091 | 0.599 | 0.000 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 231 | 0 | 231 | 0 | 0 | 169 | 301 | 0 | 20 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 0.00 | 0.73 | 1.30 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.000 | 0.008 | 0.000 | 0.000 | 0.088 | 13.242 | 0.000 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 438 | 154 | 317 | 0 | 167 | 0 | 0 | 20 | 0 |
N.S. |
1 | 2.04 | 0.72 | 1.47 | 0.00 | 0.78 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 2.010 | 0.166 | 8.533 | 0.000 | 0.095 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 247 | 336 | 0 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.36 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.948 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 271 | 120 | 202 | 0 | 132 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.73 | 0.76 | 1.29 | 0.00 | 0.84 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.065 | 0.094 | 2.780 | 0.000 | 0.100 | 0.000 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 161 | 120 | 0 | 0 | 105 | 151 | 0 | 20 | 0 |
N.S. |
1 | 1.34 | 1.00 | 0.00 | 0.00 | 0.88 | 1.26 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.899 | 0.007 | 0.000 | 0.000 | 0.091 | 1.484 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 149 | 83 | 114 | 0 | 94 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.43 | 0.80 | 1.10 | 0.00 | 0.90 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.524 | 0.062 | 1.136 | 0.000 | 0.090 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 132 | 0 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.412 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 44 | 45 | 0 | 47 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.94 | 0.00 | 0.98 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.226 | 0.020 | 1.078 | 0.000 | 0.095 | 0.000 | 0.000 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 11 | 11 | 10 | 0 | 17 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 0.85 | 0.77 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.170 | 0.000 | 0.401 | 0.024 | 0.083 | 0.112 | 0.000 | 0.193 | 0.000 |
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 | 20 | 20 | 22 | 18 | 20 | 20 | 19 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 0.95 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.192 | 0.022 | 0.253 | 0.132 | 0.096 | 1.128 | 0.121 | 0.199 | 3.784 |
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 | 20 | 20 | 22 | 18 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.186 | 0.022 | 0.259 | 0.117 | 0.091 | 1.016 | 0.125 | 0.218 | 3.728 |
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 | 20 | 20 | 22 | 18 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.412 | 0.023 | 0.235 | 0.116 | 0.088 | 1.231 | 0.128 | 0.249 | 3.637 |
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 | 109 | 123 | 109 | 0 | 0 | 93 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.13 | 1.00 | 0.00 | 0.00 | 0.85 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.757 | 0.007 | 0.000 | 0.000 | 0.095 | 0.000 | 0.000 | 0.209 | 0.000 |
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 | 20 | 20 | 22 | 18 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.808 | 0.023 | 0.256 | 0.133 | 0.093 | 3.378 | 0.123 | 0.222 | 3.645 |
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 | 20 | 20 | 22 | 18 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 1.262 | 0.023 | 0.267 | 0.135 | 0.092 | 5.707 | 0.125 | 0.234 | 3.657 |
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 | 20 | 20 | 22 | 18 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 1.476 | 0.022 | 0.194 | 0.147 | 0.082 | 11.300 | 0.130 | 0.191 | 3.670 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 0 | 224 | 0 | 0 | 168 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.00 | 0.00 | 0.75 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.000 | 0.010 | 0.000 | 0.000 | 0.105 | 0.000 | 0.000 | 0.209 | 0.000 |
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 | 20 | 20 | 22 | 18 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 2.474 | 0.023 | 0.260 | 0.123 | 0.082 | 35.216 | 0.130 | 0.184 | 3.571 |
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 | 20 | 20 | 22 | 18 | 20 | 20 | 20 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.10 | 0.90 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 2.259 | 0.025 | 0.261 | 0.117 | 0.096 | 65.727 | 0.130 | 0.226 | 3.614 |
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 | 19 | 19 | 21 | 17 | 19 | 19 | 19 | 19 | 19 | 19 |
N.S. |
1 | 1.00 | 1.11 | 0.89 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.183 | 0.052 | 0.301 | 0.126 | 0.130 | 1.153 | 0.136 | 0.188 | 3.669 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |