Detailed conclusion table per each integral is given by 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 just an F.
In this table,the column N.S. in the table below, which stands for normalized size is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To help make the table fit, Mathematica was abbreviated to MMA.
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 76 | 73 | 95 | 99 | 0 | 110 | 130 |
N.S. | 1 | 1.00 | 0.89 | 0.86 | 1.12 | 1.16 | 0.00 | 1.29 | 1.53 |
time (sec) |
N/A | 0.045 | 0.180 | 0.149 | 0.287 | 2.272 | 0.000 | 0.459 | 3.941 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 60 | 60 | 70 | 88 | 0 | 96 | 102 |
N.S. | 1 | 1.00 | 0.95 | 0.95 | 1.11 | 1.40 | 0.00 | 1.52 | 1.62 |
time (sec) |
N/A | 0.035 | 0.156 | 0.099 | 0.293 | 2.363 | 0.000 | 0.447 | 2.511 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 47 | 47 | 58 | 74 | 0 | 80 | 75 |
N.S. | 1 | 1.00 | 1.00 | 1.00 | 1.23 | 1.57 | 0.00 | 1.70 | 1.60 |
time (sec) |
N/A | 0.034 | 0.024 | 0.087 | 0.282 | 2.944 | 0.000 | 0.475 | 1.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 30 | 29 | 60 | 37 | 63 | 47 |
N.S. | 1 | 1.00 | 1.00 | 1.25 | 1.21 | 2.50 | 1.54 | 2.62 | 1.96 |
time (sec) |
N/A | 0.017 | 0.015 | 0.039 | 0.291 | 2.515 | 2.550 | 0.438 | 0.685 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 24 | 23 | 36 | 41 | 49 | 20 |
N.S. | 1 | 1.00 | 1.00 | 1.50 | 1.44 | 2.25 | 2.56 | 3.06 | 1.25 |
time (sec) |
N/A | 0.005 | 0.004 | 0.026 | 0.292 | 2.807 | 1.087 | 0.450 | 0.610 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 26 | 21 | 20 | 17 | 17 | 39 | 15 |
N.S. | 1 | 1.00 | 1.73 | 1.40 | 1.33 | 1.13 | 1.13 | 2.60 | 1.00 |
time (sec) |
N/A | 0.014 | 0.010 | 0.059 | 0.284 | 2.613 | 1.133 | 0.433 | 0.600 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 32 | 38 | 34 | 29 | 0 | 56 | 50 |
N.S. | 1 | 1.00 | 0.84 | 1.00 | 0.89 | 0.76 | 0.00 | 1.47 | 1.32 |
time (sec) |
N/A | 0.025 | 0.060 | 0.079 | 0.279 | 3.085 | 0.000 | 0.409 | 1.063 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 57 | 49 | 46 | 42 | 0 | 72 | 55 |
N.S. | 1 | 1.00 | 1.06 | 0.91 | 0.85 | 0.78 | 0.00 | 1.33 | 1.02 |
time (sec) |
N/A | 0.031 | 0.075 | 0.093 | 0.282 | 3.649 | 0.000 | 0.422 | 0.654 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 73 | 60 | 57 | 53 | 0 | 86 | 79 |
N.S. | 1 | 1.00 | 0.96 | 0.79 | 0.75 | 0.70 | 0.00 | 1.13 | 1.04 |
time (sec) |
N/A | 0.038 | 0.112 | 0.104 | 0.282 | 3.052 | 0.000 | 0.443 | 4.170 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 487 | 111 | 133 | 124 | 0 | 138 | 170 |
N.S. | 1 | 1.00 | 3.99 | 0.91 | 1.09 | 1.02 | 0.00 | 1.13 | 1.39 |
time (sec) |
N/A | 0.070 | 1.623 | 0.115 | 0.278 | 2.100 | 0.000 | 0.454 | 5.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 877 | 112 | 145 | 111 | 0 | 122 | 141 |
N.S. | 1 | 1.00 | 9.14 | 1.17 | 1.51 | 1.16 | 0.00 | 1.27 | 1.47 |
time (sec) |
N/A | 0.065 | 6.441 | 0.072 | 0.286 | 2.902 | 0.000 | 0.528 | 3.960 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 318 | 75 | 85 | 96 | 0 | 106 | 112 |
N.S. | 1 | 1.00 | 4.30 | 1.01 | 1.15 | 1.30 | 0.00 | 1.43 | 1.51 |
time (sec) |
N/A | 0.060 | 0.707 | 0.069 | 0.291 | 2.745 | 0.000 | 0.471 | 2.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 219 | 70 | 81 | 83 | 0 | 90 | 83 |
N.S. | 1 | 1.00 | 4.06 | 1.30 | 1.50 | 1.54 | 0.00 | 1.67 | 1.54 |
time (sec) |
N/A | 0.041 | 0.648 | 0.045 | 0.280 | 2.509 | 0.000 | 0.459 | 1.175 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 171 | 44 | 41 | 76 | 0 | 79 | 56 |
N.S. | 1 | 1.00 | 5.03 | 1.29 | 1.21 | 2.24 | 0.00 | 2.32 | 1.65 |
time (sec) |
N/A | 0.021 | 0.523 | 0.052 | 0.284 | 2.911 | 0.000 | 0.422 | 0.710 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 47 | 44 | 52 | 53 | 0 | 79 | 33 |
N.S. | 1 | 1.00 | 1.38 | 1.29 | 1.53 | 1.56 | 0.00 | 2.32 | 0.97 |
time (sec) |
N/A | 0.040 | 0.017 | 0.066 | 0.286 | 2.809 | 0.000 | 0.445 | 0.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 34 | 52 | 48 | 36 | 0 | 64 | 57 |
N.S. | 1 | 1.00 | 0.76 | 1.16 | 1.07 | 0.80 | 0.00 | 1.42 | 1.27 |
time (sec) |
N/A | 0.046 | 0.044 | 0.072 | 0.291 | 3.186 | 0.000 | 0.443 | 1.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 41 | 64 | 61 | 49 | 0 | 80 | 61 |
N.S. | 1 | 1.00 | 0.72 | 1.12 | 1.07 | 0.86 | 0.00 | 1.40 | 1.07 |
time (sec) |
N/A | 0.063 | 0.092 | 0.088 | 0.290 | 3.560 | 0.000 | 0.440 | 0.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 53 | 90 | 83 | 63 | 0 | 96 | 89 |
N.S. | 1 | 1.00 | 0.61 | 1.03 | 0.95 | 0.72 | 0.00 | 1.10 | 1.02 |
time (sec) |
N/A | 0.059 | 0.148 | 0.098 | 0.286 | 2.907 | 0.000 | 0.450 | 4.193 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 61 | 96 | 95 | 76 | 0 | 112 | 105 |
N.S. | 1 | 1.00 | 0.59 | 0.93 | 0.92 | 0.74 | 0.00 | 1.09 | 1.02 |
time (sec) |
N/A | 0.085 | 0.149 | 0.131 | 0.288 | 2.393 | 0.000 | 0.458 | 4.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 487 | 146 | 179 | 124 | 0 | 138 | 170 |
N.S. | 1 | 1.00 | 4.27 | 1.28 | 1.57 | 1.09 | 0.00 | 1.21 | 1.49 |
time (sec) |
N/A | 0.096 | 1.550 | 0.095 | 0.286 | 2.760 | 0.000 | 0.473 | 5.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 877 | 123 | 156 | 111 | 0 | 122 | 141 |
N.S. | 1 | 1.00 | 9.43 | 1.32 | 1.68 | 1.19 | 0.00 | 1.31 | 1.52 |
time (sec) |
N/A | 0.086 | 6.432 | 0.069 | 0.286 | 2.136 | 0.000 | 0.486 | 4.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 154 | 94 | 104 | 98 | 0 | 106 | 112 |
N.S. | 1 | 1.00 | 2.14 | 1.31 | 1.44 | 1.36 | 0.00 | 1.47 | 1.56 |
time (sec) |
N/A | 0.056 | 5.572 | 0.059 | 0.286 | 4.009 | 0.000 | 0.515 | 2.574 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 235 | 80 | 91 | 98 | 0 | 100 | 88 |
N.S. | 1 | 1.00 | 3.56 | 1.21 | 1.38 | 1.48 | 0.00 | 1.52 | 1.33 |
time (sec) |
N/A | 0.035 | 0.957 | 0.050 | 0.284 | 4.070 | 0.000 | 0.472 | 0.737 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 211 | 55 | 64 | 91 | 0 | 80 | 57 |
N.S. | 1 | 1.00 | 4.40 | 1.15 | 1.33 | 1.90 | 0.00 | 1.67 | 1.19 |
time (sec) |
N/A | 0.048 | 0.901 | 0.074 | 0.278 | 3.170 | 0.000 | 0.478 | 0.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 81 | 71 | 74 | 65 | 0 | 100 | 88 |
N.S. | 1 | 1.00 | 1.37 | 1.20 | 1.25 | 1.10 | 0.00 | 1.69 | 1.49 |
time (sec) |
N/A | 0.049 | 0.071 | 0.082 | 0.292 | 3.057 | 0.000 | 0.481 | 0.725 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 44 | 74 | 71 | 50 | 0 | 80 | 63 |
N.S. | 1 | 1.00 | 0.70 | 1.17 | 1.13 | 0.79 | 0.00 | 1.27 | 1.00 |
time (sec) |
N/A | 0.055 | 0.065 | 0.095 | 0.290 | 3.422 | 0.000 | 0.462 | 0.670 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 51 | 100 | 94 | 63 | 0 | 96 | 89 |
N.S. | 1 | 1.00 | 0.60 | 1.18 | 1.11 | 0.74 | 0.00 | 1.13 | 1.05 |
time (sec) |
N/A | 0.072 | 0.133 | 0.111 | 0.286 | 3.494 | 0.000 | 0.490 | 4.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 63 | 121 | 117 | 76 | 0 | 112 | 105 |
N.S. |
1 | 1.00 | 0.60 | 1.15 | 1.11 | 0.72 | 0.00 | 1.07 | 1.00 |
time (sec) |
N/A | 0.080 | 0.160 | 0.128 | 0.284 | 3.322 | 0.000 | 0.439 | 4.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 73 | 143 | 143 | 89 | 0 | 128 | 121 |
N.S. |
1 | 1.00 | 0.57 | 1.11 | 1.11 | 0.69 | 0.00 | 0.99 | 0.94 |
time (sec) |
N/A | 0.101 | 0.207 | 0.157 | 0.281 | 3.641 | 0.000 | 0.533 | 3.492 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 136 | 211 | 204 | 270 | 137 | 0 | 154 | 199 |
N.S. | 1 | 1.00 | 1.55 | 1.50 | 1.99 | 1.01 | 0.00 | 1.13 | 1.46 |
time (sec) |
N/A | 0.136 | 0.840 | 0.131 | 0.283 | 3.293 | 0.000 | 0.467 | 4.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 498 | 157 | 190 | 124 | 0 | 138 | 170 |
N.S. | 1 | 1.00 | 4.49 | 1.41 | 1.71 | 1.12 | 0.00 | 1.24 | 1.53 |
time (sec) |
N/A | 0.106 | 1.536 | 0.086 | 0.287 | 2.416 | 0.000 | 0.492 | 5.470 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 96 | 877 | 142 | 175 | 111 | 0 | 122 | 141 |
N.S. | 1 | 1.00 | 9.14 | 1.48 | 1.82 | 1.16 | 0.00 | 1.27 | 1.47 |
time (sec) |
N/A | 0.083 | 6.426 | 0.075 | 0.293 | 2.782 | 0.000 | 0.499 | 3.989 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 773 | 104 | 116 | 110 | 0 | 116 | 117 |
N.S. | 1 | 1.00 | 8.49 | 1.14 | 1.27 | 1.21 | 0.00 | 1.27 | 1.29 |
time (sec) |
N/A | 0.062 | 6.275 | 0.061 | 0.301 | 3.350 | 0.000 | 0.442 | 0.878 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 272 | 91 | 110 | 111 | 0 | 129 | 115 |
N.S. | 1 | 1.00 | 3.73 | 1.25 | 1.51 | 1.52 | 0.00 | 1.77 | 1.58 |
time (sec) |
N/A | 0.057 | 1.385 | 0.092 | 0.287 | 3.119 | 0.000 | 0.488 | 0.905 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 241 | 82 | 85 | 105 | 0 | 129 | 117 |
N.S. | 1 | 1.00 | 3.30 | 1.12 | 1.16 | 1.44 | 0.00 | 1.77 | 1.60 |
time (sec) |
N/A | 0.058 | 1.795 | 0.106 | 0.302 | 2.941 | 0.000 | 0.471 | 0.891 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 91 | 93 | 97 | 80 | 0 | 116 | 93 |
N.S. | 1 | 1.00 | 1.25 | 1.27 | 1.33 | 1.10 | 0.00 | 1.59 | 1.27 |
time (sec) |
N/A | 0.062 | 0.108 | 0.113 | 0.281 | 3.391 | 0.000 | 0.467 | 0.687 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 56 | 111 | 104 | 63 | 0 | 96 | 89 |
N.S. |
1 | 1.00 | 0.64 | 1.28 | 1.20 | 0.72 | 0.00 | 1.10 | 1.02 |
time (sec) |
N/A | 0.074 | 0.107 | 0.110 | 0.282 | 2.288 | 0.000 | 0.457 | 4.125 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 63 | 133 | 128 | 76 | 0 | 112 | 105 |
N.S. |
1 | 1.00 | 0.62 | 1.30 | 1.25 | 0.75 | 0.00 | 1.10 | 1.03 |
time (sec) |
N/A | 0.085 | 0.156 | 0.151 | 0.287 | 2.738 | 0.000 | 0.474 | 4.428 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 127 | 73 | 169 | 165 | 89 | 0 | 128 | 121 |
N.S. |
1 | 1.00 | 0.57 | 1.33 | 1.30 | 0.70 | 0.00 | 1.01 | 0.95 |
time (sec) |
N/A | 0.115 | 0.208 | 0.091 | 0.278 | 1.972 | 0.000 | 0.491 | 3.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-2) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 83 | 185 | 187 | 102 | 0 | 144 | 137 |
N.S. |
1 | 1.00 | 0.56 | 1.26 | 1.27 | 0.69 | 0.00 | 0.98 | 0.93 |
time (sec) |
N/A | 0.120 | 0.277 | 0.118 | 0.298 | 3.499 | 0.000 | 0.513 | 3.636 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 229 | 248 | 314 | 150 | 0 | 170 | 228 |
N.S. | 1 | 1.00 | 1.47 | 1.59 | 2.01 | 0.96 | 0.00 | 1.09 | 1.46 |
time (sec) |
N/A | 0.151 | 1.288 | 0.147 | 0.291 | 2.654 | 0.000 | 0.569 | 4.843 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 374 | 134 | 205 | 124 | 0 | 114 | 96 |
N.S. | 1 | 1.00 | 3.63 | 1.30 | 1.99 | 1.20 | 0.00 | 1.11 | 0.93 |
time (sec) |
N/A | 0.071 | 3.352 | 0.094 | 0.282 | 4.572 | 0.000 | 0.445 | 0.933 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 250 | 108 | 162 | 112 | 0 | 101 | 95 |
N.S. | 1 | 1.00 | 2.94 | 1.27 | 1.91 | 1.32 | 0.00 | 1.19 | 1.12 |
time (sec) |
N/A | 0.069 | 1.446 | 0.068 | 0.294 | 3.025 | 0.000 | 0.440 | 0.727 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 194 | 74 | 119 | 97 | 0 | 84 | 67 |
N.S. | 1 | 1.00 | 3.80 | 1.45 | 2.33 | 1.90 | 0.00 | 1.65 | 1.31 |
time (sec) |
N/A | 0.075 | 0.828 | 0.049 | 0.300 | 2.724 | 0.000 | 0.456 | 0.679 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 109 | 46 | 75 | 65 | 0 | 54 | 31 |
N.S. | 1 | 1.00 | 2.87 | 1.21 | 1.97 | 1.71 | 0.00 | 1.42 | 0.82 |
time (sec) |
N/A | 0.049 | 0.193 | 0.043 | 0.273 | 2.710 | 0.000 | 0.444 | 0.647 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 17 | 17 | 23 | 22 | 0 | 16 | 16 |
N.S. | 1 | 1.00 | 0.77 | 0.77 | 1.05 | 1.00 | 0.00 | 0.73 | 0.73 |
time (sec) |
N/A | 0.017 | 0.028 | 0.036 | 0.293 | 2.312 | 0.000 | 0.436 | 0.589 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 58 | 32 | 49 | 37 | 0 | 28 | 23 |
N.S. | 1 | 1.00 | 2.00 | 1.10 | 1.69 | 1.28 | 0.00 | 0.97 | 0.79 |
time (sec) |
N/A | 0.010 | 0.135 | 0.038 | 0.494 | 2.799 | 0.000 | 0.440 | 0.638 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 89 | 56 | 92 | 46 | 0 | 58 | 66 |
N.S. | 1 | 1.00 | 2.02 | 1.27 | 2.09 | 1.05 | 0.00 | 1.32 | 1.50 |
time (sec) |
N/A | 0.042 | 0.242 | 0.060 | 0.485 | 2.877 | 0.000 | 0.462 | 0.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 117 | 74 | 133 | 57 | 0 | 73 | 89 |
N.S. | 1 | 1.00 | 1.58 | 1.00 | 1.80 | 0.77 | 0.00 | 0.99 | 1.20 |
time (sec) |
N/A | 0.066 | 0.255 | 0.066 | 0.498 | 2.325 | 0.000 | 0.446 | 0.725 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 94 | 143 | 85 | 176 | 70 | 0 | 88 | 70 |
N.S. |
1 | 1.00 | 1.52 | 0.90 | 1.87 | 0.74 | 0.00 | 0.94 | 0.74 |
time (sec) |
N/A | 0.065 | 0.330 | 0.072 | 0.498 | 3.102 | 0.000 | 0.444 | 0.907 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 173 | 100 | 217 | 79 | 0 | 101 | 98 |
N.S. | 1 | 1.00 | 1.47 | 0.85 | 1.84 | 0.67 | 0.00 | 0.86 | 0.83 |
time (sec) |
N/A | 0.072 | 0.321 | 0.080 | 0.507 | 2.659 | 0.000 | 0.431 | 2.454 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 123 | 300 | 120 | 190 | 162 | 0 | 122 | 122 |
N.S. | 1 | 1.00 | 2.44 | 0.98 | 1.54 | 1.32 | 0.00 | 0.99 | 0.99 |
time (sec) |
N/A | 0.127 | 1.998 | 0.087 | 0.281 | 3.747 | 0.000 | 0.510 | 0.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 247 | 92 | 145 | 146 | 0 | 106 | 92 |
N.S. | 1 | 1.00 | 2.78 | 1.03 | 1.63 | 1.64 | 0.00 | 1.19 | 1.03 |
time (sec) |
N/A | 0.109 | 1.260 | 0.069 | 0.281 | 2.947 | 0.000 | 0.460 | 0.688 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 160 | 62 | 98 | 114 | 0 | 77 | 43 |
N.S. | 1 | 1.00 | 2.42 | 0.94 | 1.48 | 1.73 | 0.00 | 1.17 | 0.65 |
time (sec) |
N/A | 0.083 | 0.375 | 0.073 | 0.283 | 3.117 | 0.000 | 0.469 | 0.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 45 | 32 | 46 | 49 | 0 | 31 | 30 |
N.S. | 1 | 1.00 | 0.82 | 0.58 | 0.84 | 0.89 | 0.00 | 0.56 | 0.55 |
time (sec) |
N/A | 0.046 | 0.074 | 0.047 | 0.274 | 3.301 | 0.000 | 0.493 | 0.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 60 | 32 | 47 | 51 | 0 | 31 | 30 |
N.S. | 1 | 1.00 | 1.09 | 0.58 | 0.85 | 0.93 | 0.00 | 0.56 | 0.55 |
time (sec) |
N/A | 0.036 | 0.143 | 0.048 | 0.284 | 2.408 | 0.000 | 0.457 | 0.597 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 112 | 46 | 72 | 80 | 0 | 50 | 35 |
N.S. | 1 | 1.00 | 1.96 | 0.81 | 1.26 | 1.40 | 0.00 | 0.88 | 0.61 |
time (sec) |
N/A | 0.049 | 0.295 | 0.046 | 0.502 | 2.992 | 0.000 | 0.439 | 0.630 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 151 | 72 | 118 | 90 | 0 | 79 | 91 |
N.S. | 1 | 1.00 | 2.10 | 1.00 | 1.64 | 1.25 | 0.00 | 1.10 | 1.26 |
time (sec) |
N/A | 0.095 | 0.510 | 0.069 | 0.500 | 2.807 | 0.000 | 0.455 | 0.698 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 110 | 110 | 177 | 88 | 164 | 99 | 0 | 95 | 113 |
N.S. | 1 | 1.00 | 1.61 | 0.80 | 1.49 | 0.90 | 0.00 | 0.86 | 1.03 |
time (sec) |
N/A | 0.124 | 0.383 | 0.077 | 0.513 | 2.484 | 0.000 | 0.441 | 0.735 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 199 | 101 | 207 | 108 | 0 | 108 | 135 |
N.S. |
1 | 1.00 | 1.60 | 0.81 | 1.67 | 0.87 | 0.00 | 0.87 | 1.09 |
time (sec) |
N/A | 0.133 | 0.357 | 0.083 | 0.492 | 2.482 | 0.000 | 0.460 | 0.782 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 162 | 351 | 135 | 211 | 206 | 0 | 139 | 141 |
N.S. | 1 | 1.00 | 2.17 | 0.83 | 1.30 | 1.27 | 0.00 | 0.86 | 0.87 |
time (sec) |
N/A | 0.201 | 1.021 | 0.119 | 0.294 | 2.247 | 0.000 | 0.453 | 0.679 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 128 | 294 | 105 | 165 | 190 | 0 | 122 | 111 |
N.S. | 1 | 1.00 | 2.30 | 0.82 | 1.29 | 1.48 | 0.00 | 0.95 | 0.87 |
time (sec) |
N/A | 0.178 | 1.334 | 0.089 | 0.282 | 3.957 | 0.000 | 0.518 | 0.682 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 209 | 75 | 119 | 158 | 0 | 94 | 58 |
N.S. | 1 | 1.00 | 1.99 | 0.71 | 1.13 | 1.50 | 0.00 | 0.90 | 0.55 |
time (sec) |
N/A | 0.155 | 0.514 | 0.076 | 0.299 | 2.709 | 0.000 | 0.502 | 0.688 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 57 | 45 | 67 | 75 | 0 | 46 | 45 |
N.S. | 1 | 1.00 | 0.69 | 0.54 | 0.81 | 0.90 | 0.00 | 0.55 | 0.54 |
time (sec) |
N/A | 0.085 | 0.116 | 0.065 | 0.281 | 2.876 | 0.000 | 0.488 | 0.616 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 71 | 32 | 47 | 73 | 0 | 31 | 30 |
N.S. | 1 | 1.00 | 0.86 | 0.39 | 0.57 | 0.88 | 0.00 | 0.37 | 0.36 |
time (sec) |
N/A | 0.065 | 0.178 | 0.078 | 0.283 | 2.876 | 0.000 | 0.481 | 0.597 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 86 | 45 | 67 | 75 | 0 | 46 | 45 |
N.S. | 1 | 1.00 | 1.04 | 0.54 | 0.81 | 0.90 | 0.00 | 0.55 | 0.54 |
time (sec) |
N/A | 0.056 | 0.235 | 0.055 | 0.288 | 2.504 | 0.000 | 0.476 | 0.619 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 162 | 59 | 92 | 116 | 0 | 68 | 81 |
N.S. | 1 | 1.00 | 1.84 | 0.67 | 1.05 | 1.32 | 0.00 | 0.77 | 0.92 |
time (sec) |
N/A | 0.079 | 0.285 | 0.056 | 0.497 | 1.892 | 0.000 | 0.429 | 0.692 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 169 | 85 | 137 | 126 | 0 | 96 | 113 |
N.S. | 1 | 1.00 | 1.64 | 0.83 | 1.33 | 1.22 | 0.00 | 0.93 | 1.10 |
time (sec) |
N/A | 0.149 | 0.574 | 0.077 | 0.487 | 2.025 | 0.000 | 0.494 | 0.728 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 181 | 101 | 184 | 135 | 0 | 113 | 137 |
N.S. | 1 | 1.00 | 1.23 | 0.69 | 1.25 | 0.92 | 0.00 | 0.77 | 0.93 |
time (sec) |
N/A | 0.193 | 0.577 | 0.092 | 0.519 | 2.641 | 0.000 | 0.510 | 0.758 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 193 | 403 | 148 | 231 | 250 | 0 | 155 | 160 |
N.S. | 1 | 1.00 | 2.09 | 0.77 | 1.20 | 1.30 | 0.00 | 0.80 | 0.83 |
time (sec) |
N/A | 0.274 | 1.497 | 0.069 | 0.285 | 2.985 | 0.000 | 0.485 | 0.754 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 349 | 118 | 186 | 234 | 0 | 139 | 130 |
N.S. | 1 | 1.00 | 2.19 | 0.74 | 1.17 | 1.47 | 0.00 | 0.87 | 0.82 |
time (sec) |
N/A | 0.245 | 1.263 | 0.060 | 0.292 | 3.286 | 0.000 | 0.467 | 0.702 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 136 | 193 | 88 | 139 | 202 | 0 | 110 | 83 |
N.S. | 1 | 1.00 | 1.42 | 0.65 | 1.02 | 1.49 | 0.00 | 0.81 | 0.61 |
time (sec) |
N/A | 0.217 | 0.915 | 0.095 | 0.298 | 4.541 | 0.000 | 0.516 | 0.668 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 120 | 69 | 56 | 87 | 99 | 0 | 59 | 58 |
N.S. | 1 | 1.00 | 0.58 | 0.47 | 0.72 | 0.82 | 0.00 | 0.49 | 0.48 |
time (sec) |
N/A | 0.114 | 0.208 | 0.075 | 0.274 | 9.540 | 0.000 | 0.493 | 0.673 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 112 | 87 | 58 | 87 | 99 | 0 | 59 | 58 |
N.S. | 1 | 1.00 | 0.78 | 0.52 | 0.78 | 0.88 | 0.00 | 0.53 | 0.52 |
time (sec) |
N/A | 0.107 | 0.245 | 0.086 | 0.284 | 4.039 | 0.000 | 0.476 | 0.662 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 112 | 99 | 58 | 87 | 99 | 0 | 59 | 58 |
N.S. | 1 | 1.00 | 0.88 | 0.52 | 0.78 | 0.88 | 0.00 | 0.53 | 0.52 |
time (sec) |
N/A | 0.088 | 0.273 | 0.077 | 0.277 | 2.200 | 0.000 | 0.455 | 0.675 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 112 | 112 | 58 | 87 | 99 | 0 | 59 | 58 |
N.S. | 1 | 1.00 | 1.00 | 0.52 | 0.78 | 0.88 | 0.00 | 0.53 | 0.52 |
time (sec) |
N/A | 0.081 | 0.257 | 0.059 | 0.293 | 5.492 | 0.000 | 0.502 | 0.669 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 224 | 72 | 112 | 152 | 0 | 83 | 102 |
N.S. | 1 | 1.00 | 2.02 | 0.65 | 1.01 | 1.37 | 0.00 | 0.75 | 0.92 |
time (sec) |
N/A | 0.121 | 0.399 | 0.059 | 0.512 | 3.103 | 0.000 | 0.457 | 0.725 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 126 | 263 | 98 | 158 | 162 | 0 | 112 | 137 |
N.S. | 1 | 1.00 | 2.09 | 0.78 | 1.25 | 1.29 | 0.00 | 0.89 | 1.09 |
time (sec) |
N/A | 0.208 | 0.461 | 0.102 | 0.540 | 6.683 | 0.000 | 0.461 | 0.755 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 176 | 289 | 114 | 204 | 171 | 0 | 128 | 159 |
N.S. | 1 | 1.00 | 1.64 | 0.65 | 1.16 | 0.97 | 0.00 | 0.73 | 0.90 |
time (sec) |
N/A | 0.270 | 0.564 | 0.099 | 0.498 | 8.727 | 0.000 | 0.483 | 0.811 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 200 | 401 | 131 | 206 | 278 | 0 | 155 | 149 |
N.S. | 1 | 1.00 | 2.00 | 0.66 | 1.03 | 1.39 | 0.00 | 0.78 | 0.74 |
time (sec) |
N/A | 0.325 | 1.847 | 0.066 | 0.279 | 6.533 | 0.000 | 0.532 | 0.715 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 177 | 219 | 101 | 159 | 246 | 0 | 126 | 99 |
N.S. | 1 | 1.00 | 1.24 | 0.57 | 0.90 | 1.39 | 0.00 | 0.71 | 0.56 |
time (sec) |
N/A | 0.294 | 1.858 | 0.067 | 0.288 | 7.016 | 0.000 | 0.517 | 0.691 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 97 | 71 | 107 | 123 | 0 | 72 | 127 |
N.S. | 1 | 1.00 | 0.61 | 0.45 | 0.67 | 0.77 | 0.00 | 0.45 | 0.80 |
time (sec) |
N/A | 0.150 | 0.178 | 0.054 | 0.292 | 4.098 | 0.000 | 0.497 | 0.764 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 97 | 58 | 87 | 123 | 0 | 59 | 58 |
N.S. | 1 | 1.00 | 0.61 | 0.36 | 0.55 | 0.77 | 0.00 | 0.37 | 0.36 |
time (sec) |
N/A | 0.150 | 0.220 | 0.103 | 0.282 | 4.044 | 0.000 | 0.527 | 0.720 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 110 | 45 | 67 | 123 | 0 | 46 | 45 |
N.S. | 1 | 1.00 | 0.79 | 0.32 | 0.48 | 0.88 | 0.00 | 0.33 | 0.32 |
time (sec) |
N/A | 0.131 | 0.251 | 0.096 | 0.283 | 3.066 | 0.000 | 0.491 | 0.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 143 | 125 | 58 | 87 | 123 | 0 | 59 | 58 |
N.S. | 1 | 1.00 | 0.87 | 0.41 | 0.61 | 0.86 | 0.00 | 0.41 | 0.41 |
time (sec) |
N/A | 0.113 | 0.260 | 0.085 | 0.302 | 15.421 | 0.000 | 0.505 | 0.689 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 143 | 138 | 71 | 107 | 123 | 0 | 72 | 127 |
N.S. | 1 | 1.00 | 0.97 | 0.50 | 0.75 | 0.86 | 0.00 | 0.50 | 0.89 |
time (sec) |
N/A | 0.102 | 0.290 | 0.066 | 0.281 | 4.586 | 0.000 | 0.508 | 0.763 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 144 | 280 | 85 | 132 | 188 | 0 | 100 | 125 |
N.S. | 1 | 1.00 | 1.94 | 0.59 | 0.92 | 1.31 | 0.00 | 0.69 | 0.87 |
time (sec) |
N/A | 0.145 | 0.549 | 0.068 | 0.502 | 3.736 | 0.000 | 0.465 | 0.798 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 319 | 111 | 178 | 198 | 0 | 129 | 159 |
N.S. | 1 | 1.00 | 2.01 | 0.70 | 1.12 | 1.25 | 0.00 | 0.81 | 1.00 |
time (sec) |
N/A | 0.275 | 0.684 | 0.096 | 0.518 | 2.541 | 0.000 | 0.485 | 0.832 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 215 | 215 | 345 | 127 | 224 | 207 | 0 | 145 | 181 |
N.S. | 1 | 1.00 | 1.60 | 0.59 | 1.04 | 0.96 | 0.00 | 0.67 | 0.84 |
time (sec) |
N/A | 0.347 | 0.761 | 0.122 | 0.506 | 2.486 | 0.000 | 0.510 | 0.950 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 122 | 122 | 58 | 82 | 0 | 82 | 0 | 120 | 331 |
N.S. | 1 | 1.00 | 0.48 | 0.67 | 0.00 | 0.67 | 0.00 | 0.98 | 2.71 |
time (sec) |
N/A | 0.138 | 0.145 | 0.324 | 0.000 | 2.674 | 0.000 | 0.826 | 5.925 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 86 | 48 | 72 | 0 | 72 | 0 | 101 | 115 |
N.S. | 1 | 1.00 | 0.56 | 0.84 | 0.00 | 0.84 | 0.00 | 1.17 | 1.34 |
time (sec) |
N/A | 0.104 | 0.124 | 0.115 | 0.000 | 2.679 | 0.000 | 0.837 | 4.458 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 36 | 62 | 0 | 60 | 0 | 82 | 108 |
N.S. | 1 | 1.00 | 0.64 | 1.11 | 0.00 | 1.07 | 0.00 | 1.46 | 1.93 |
time (sec) |
N/A | 0.056 | 0.108 | 0.098 | 0.000 | 4.016 | 0.000 | 0.794 | 1.389 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | B | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 29 | 42 | 0 | 41 | 0 | 62 | 41 |
N.S. | 1 | 1.00 | 1.12 | 1.62 | 0.00 | 1.58 | 0.00 | 2.38 | 1.58 |
time (sec) |
N/A | 0.022 | 0.074 | 0.080 | 0.000 | 3.750 | 0.000 | 0.753 | 0.191 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | A | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 60 | 89 | 146 | 133 | 0 | 130 | -1 |
N.S. | 1 | 1.00 | 1.62 | 2.41 | 3.95 | 3.59 | 0.00 | 3.51 | -0.03 |
time (sec) |
N/A | 0.014 | 0.097 | 0.133 | 0.567 | 3.547 | 0.000 | 0.958 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | B | B | A | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 62 | 123 | 791 | 242 | 0 | 282 | -1 |
N.S. | 1 | 1.00 | 1.00 | 1.98 | 12.76 | 3.90 | 0.00 | 4.55 | -0.02 |
time (sec) |
N/A | 0.044 | 0.207 | 0.276 | 0.592 | 3.226 | 0.000 | 0.814 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | B | B | A | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 47 | 221 | 1059 | 270 | 0 | 378 | -1 |
N.S. | 1 | 1.00 | 0.46 | 2.17 | 10.38 | 2.65 | 0.00 | 3.71 | -0.01 |
time (sec) |
N/A | 0.085 | 0.106 | 0.173 | 0.628 | 3.289 | 0.000 | 1.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | B | B | A | F(-1) | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 138 | 47 | 310 | 1921 | 290 | 0 | 475 | -1 |
N.S. |
1 | 1.00 | 0.34 | 2.25 | 13.92 | 2.10 | 0.00 | 3.44 | -0.01 |
time (sec) |
N/A | 0.123 | 0.100 | 0.197 | 0.749 | 2.360 | 0.000 | 1.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | C | B | B | A | F | B | F |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 174 | 47 | 399 | 6638 | 310 | 0 | 571 | -1 |
N.S. | 1 | 1.00 | 0.27 | 2.29 | 38.15 | 1.78 | 0.00 | 3.28 | -0.01 |
time (sec) |
N/A | 0.170 | 0.096 | 0.228 | 0.872 | 2.825 | 0.000 | 0.988 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 162 | 70 | 93 | 0 | 98 | 0 | 180 | 429 |
N.S. | 1 | 1.00 | 0.43 | 0.57 | 0.00 | 0.60 | 0.00 | 1.11 | 2.65 |
time (sec) |
N/A | 0.193 | 0.503 | 0.121 | 0.000 | 2.639 | 0.000 | 1.090 | 6.701 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
A | A | A | A | F | A | F | A | B |
verified |
N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 60 | 83 | 0 | 87 | 0 | 151 | 346 |
N.S. | 1 | 1.00 | 0.52 | 0.72 | 0.00 | 0.75 | 0.00 | 1.30 | 2.98 |
time (sec) |
N/A | 0.135 | 0.181 | 0.106 | 0.000 | 2.632 | 0.000 | 1.163 | 5.084 |