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 | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 55 | 0 | 0 | 0 | 0 | 0 | 79 | 0 |
N.S. |
1 | 1.00 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 0.391 | 0.037 | 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 | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 100 | 96 | 145 | 161 | 194 | 2426 | 0 | 200 | 84 |
N.S. |
1 | 1.10 | 1.05 | 1.59 | 1.77 | 2.13 | 26.66 | 0.00 | 2.20 | 0.92 |
time (sec) |
N/A | 0.490 | 0.137 | 0.145 | 0.082 | 0.085 | 4.791 | 0.000 | 0.162 | 23.531 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 75 | 50 | 74 | 77 | 81 | 541 | 0 | 78 | 57 |
N.S. |
1 | 1.14 | 0.76 | 1.12 | 1.17 | 1.23 | 8.20 | 0.00 | 1.18 | 0.86 |
time (sec) |
N/A | 0.447 | 0.115 | 0.106 | 0.073 | 0.076 | 1.343 | 0.000 | 0.167 | 22.850 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 46 | 29 | 30 | 35 | 29 | 126 | 0 | 31 | 29 |
N.S. |
1 | 1.12 | 0.71 | 0.73 | 0.85 | 0.71 | 3.07 | 0.00 | 0.76 | 0.71 |
time (sec) |
N/A | 0.404 | 0.021 | 0.096 | 0.076 | 0.121 | 0.425 | 0.000 | 0.150 | 22.631 |
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 | 44 | 44 | 43 | 0 | 0 | 0 | 0 | 0 | 112 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.55 | 0.00 |
time (sec) |
N/A | 0.370 | 0.023 | 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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 67 | 0 | 0 | 0 | 0 | 0 | 488 | 0 |
N.S. |
1 | 1.00 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 11.09 | 0.00 |
time (sec) |
N/A | 0.373 | 0.036 | 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 | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 58 | 0 | 0 | 0 | 0 | 0 | 141 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.17 | 0.00 |
time (sec) |
N/A | 0.382 | 0.036 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
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 | 65 | 65 | 53 | 0 | 0 | 0 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.00 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.370 | 0.038 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
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 | 62 | 62 | 59 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.378 | 0.032 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 60 | 0 | 0 | 0 | 0 | 0 | 81 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.375 | 0.045 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 62 | 0 | 0 | 0 | 0 | 0 | 150 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.31 | 0.00 |
time (sec) |
N/A | 0.381 | 0.047 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
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 | 79 | 79 | 77 | 0 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.414 | 0.035 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 0.000 |
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 | 58 | 58 | 56 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.404 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 32 | 32 | 26 | 38 | 0 | 0 | 32 | 37 |
N.S. |
1 | 1.00 | 0.86 | 0.86 | 0.70 | 1.03 | 0.00 | 0.00 | 0.86 | 1.00 |
time (sec) |
N/A | 0.366 | 0.038 | 0.782 | 0.037 | 0.075 | 0.000 | 0.000 | 0.166 | 23.151 |
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 | 65 | 68 | 65 | 0 | 0 | 0 | 0 | 0 | 68 | 0 |
N.S. |
1 | 1.05 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 0.429 | 0.029 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
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 | 65 | 68 | 65 | 0 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.05 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.395 | 0.026 | 0.000 | 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 | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 66 | 63 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.05 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.381 | 0.024 | 0.000 | 0.000 | 0.000 | 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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 59 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.382 | 0.015 | 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 | A | F | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 39 | 33 | 0 | 59 | 175 | 0 | 36 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.00 | 1.51 | 4.49 | 0.00 | 0.92 | 0.95 |
time (sec) |
N/A | 0.376 | 0.022 | 1.141 | 0.000 | 0.075 | 9.808 | 0.000 | 0.156 | 23.485 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 82 | 51 | 46 | 0 | 129 | 1103 | 0 | 87 | 100 |
N.S. |
1 | 0.98 | 0.61 | 0.55 | 0.00 | 1.54 | 13.13 | 0.00 | 1.04 | 1.19 |
time (sec) |
N/A | 0.423 | 0.042 | 3.761 | 0.000 | 0.077 | 55.882 | 0.000 | 0.160 | 23.594 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 126 | 74 | 68 | 0 | 229 | 3526 | 0 | 183 | 167 |
N.S. |
1 | 0.93 | 0.55 | 0.50 | 0.00 | 1.70 | 26.12 | 0.00 | 1.36 | 1.24 |
time (sec) |
N/A | 0.458 | 0.059 | 9.790 | 0.000 | 0.082 | 179.307 | 0.000 | 0.157 | 23.648 |
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 | 83 | 94 | 50 | 64 | 69 | 69 | 100 | 57 | 66 | 82 |
N.S. |
1 | 1.13 | 0.60 | 0.77 | 0.83 | 0.83 | 1.20 | 0.69 | 0.80 | 0.99 |
time (sec) |
N/A | 0.451 | 0.076 | 0.140 | 0.107 | 0.077 | 0.843 | 0.155 | 0.153 | 23.183 |
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 | 45 | 48 | 32 | 28 | 58 | 39 | 66 | 47 | 35 | 36 |
N.S. |
1 | 1.07 | 0.71 | 0.62 | 1.29 | 0.87 | 1.47 | 1.04 | 0.78 | 0.80 |
time (sec) |
N/A | 0.421 | 0.032 | 0.086 | 0.109 | 0.071 | 0.290 | 0.131 | 0.164 | 23.158 |
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 | 58 | 62 | 40 | 66 | 48 | 60 | 90 | 45 | 45 | 61 |
N.S. |
1 | 1.07 | 0.69 | 1.14 | 0.83 | 1.03 | 1.55 | 0.78 | 0.78 | 1.05 |
time (sec) |
N/A | 0.417 | 0.049 | 0.118 | 0.109 | 0.074 | 0.784 | 0.128 | 0.162 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 37 | 29 | 42 | 18 | 26 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 1.68 | 1.32 | 1.91 | 0.82 | 1.18 | 0.82 |
time (sec) |
N/A | 0.337 | 0.018 | 0.080 | 0.105 | 0.071 | 0.251 | 0.113 | 0.163 | 0.035 |
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 | 33 | 33 | 30 | 45 | 27 | 47 | 80 | 30 | 25 | 37 |
N.S. |
1 | 1.00 | 0.91 | 1.36 | 0.82 | 1.42 | 2.42 | 0.91 | 0.76 | 1.12 |
time (sec) |
N/A | 0.330 | 0.007 | 0.105 | 0.107 | 0.071 | 0.811 | 0.124 | 0.145 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 39 | 57 | 32 | 44 | 36 | 73 | 53 | 23 | 31 |
N.S. |
1 | 1.11 | 1.63 | 0.91 | 1.26 | 1.03 | 2.09 | 1.51 | 0.66 | 0.89 |
time (sec) |
N/A | 0.393 | 0.090 | 0.096 | 0.107 | 0.076 | 4.453 | 0.140 | 0.145 | 23.166 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 28 | 28 | 27 | 47 | 87 | 74 | 25 | 38 |
N.S. |
1 | 1.00 | 0.97 | 0.97 | 0.93 | 1.62 | 3.00 | 2.55 | 0.86 | 1.31 |
time (sec) |
N/A | 0.364 | 0.040 | 0.112 | 0.130 | 0.072 | 1.272 | 0.154 | 0.160 | 23.040 |
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 | 46 | 44 | 67 | 40 | 51 | 47 | 87 | 64 | 33 | 38 |
N.S. |
1 | 0.96 | 1.46 | 0.87 | 1.11 | 1.02 | 1.89 | 1.39 | 0.72 | 0.83 |
time (sec) |
N/A | 0.397 | 0.031 | 0.120 | 0.129 | 0.075 | 4.408 | 0.111 | 0.146 | 23.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 40 | 29 | 133 | 124 | 26 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 1.82 | 1.32 | 6.05 | 5.64 | 1.18 | 0.82 |
time (sec) |
N/A | 0.359 | 0.022 | 0.092 | 0.136 | 0.070 | 1.667 | 0.151 | 0.153 | 23.103 |
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 | 140 | 153 | 89 | 102 | 141 | 104 | 163 | 92 | 120 | 154 |
N.S. |
1 | 1.09 | 0.64 | 0.73 | 1.01 | 0.74 | 1.16 | 0.66 | 0.86 | 1.10 |
time (sec) |
N/A | 0.615 | 0.246 | 0.148 | 0.223 | 0.077 | 0.900 | 0.144 | 0.162 | 0.043 |
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 | 112 | 121 | 75 | 94 | 118 | 92 | 151 | 81 | 101 | 131 |
N.S. |
1 | 1.08 | 0.67 | 0.84 | 1.05 | 0.82 | 1.35 | 0.72 | 0.90 | 1.17 |
time (sec) |
N/A | 0.558 | 0.105 | 0.145 | 0.120 | 0.078 | 0.950 | 0.131 | 0.164 | 0.036 |
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 | 89 | 86 | 67 | 86 | 95 | 82 | 136 | 69 | 82 | 108 |
N.S. |
1 | 0.97 | 0.75 | 0.97 | 1.07 | 0.92 | 1.53 | 0.78 | 0.92 | 1.21 |
time (sec) |
N/A | 0.459 | 0.122 | 0.130 | 0.160 | 0.076 | 0.922 | 0.153 | 0.150 | 0.034 |
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 | 61 | 56 | 59 | 75 | 72 | 70 | 129 | 54 | 63 | 82 |
N.S. |
1 | 0.92 | 0.97 | 1.23 | 1.18 | 1.15 | 2.11 | 0.89 | 1.03 | 1.34 |
time (sec) |
N/A | 0.374 | 0.091 | 0.112 | 0.138 | 0.102 | 1.000 | 0.124 | 0.157 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 57 | 125 | 114 | 76 | 76 | 182 | 84 | 51 | 77 |
N.S. |
1 | 0.97 | 2.12 | 1.93 | 1.29 | 1.29 | 3.08 | 1.42 | 0.86 | 1.31 |
time (sec) |
N/A | 0.494 | 0.102 | 0.119 | 0.175 | 0.114 | 5.214 | 0.125 | 0.150 | 23.283 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 53 | 84 | 83 | 80 | 91 | 151 | 140 | 80 | 87 |
N.S. |
1 | 0.91 | 1.45 | 1.43 | 1.38 | 1.57 | 2.60 | 2.41 | 1.38 | 1.50 |
time (sec) |
N/A | 0.499 | 0.225 | 0.136 | 0.196 | 0.116 | 2.295 | 0.140 | 0.162 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 63 | 147 | 87 | 86 | 95 | 223 | 192 | 65 | 90 |
N.S. |
1 | 0.94 | 2.19 | 1.30 | 1.28 | 1.42 | 3.33 | 2.87 | 0.97 | 1.34 |
time (sec) |
N/A | 0.508 | 0.144 | 0.135 | 0.114 | 0.125 | 3.257 | 0.138 | 0.144 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 70 | 91 | 73 | 99 | 73 | 269 | 233 | 72 | 90 |
N.S. |
1 | 0.93 | 1.21 | 0.97 | 1.32 | 0.97 | 3.59 | 3.11 | 0.96 | 1.20 |
time (sec) |
N/A | 0.457 | 0.042 | 0.148 | 0.171 | 0.075 | 3.631 | 0.133 | 0.150 | 23.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 97 | 99 | 81 | 122 | 84 | 413 | 240 | 91 | 113 |
N.S. |
1 | 0.95 | 0.97 | 0.79 | 1.20 | 0.82 | 4.05 | 2.35 | 0.89 | 1.11 |
time (sec) |
N/A | 0.514 | 0.042 | 0.157 | 0.115 | 0.077 | 5.615 | 0.137 | 0.163 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 124 | 107 | 89 | 145 | 95 | 520 | 297 | 110 | 136 |
N.S. |
1 | 0.96 | 0.83 | 0.69 | 1.12 | 0.74 | 4.03 | 2.30 | 0.85 | 1.05 |
time (sec) |
N/A | 0.569 | 0.049 | 0.184 | 0.130 | 0.074 | 5.960 | 0.170 | 0.163 | 23.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 151 | 115 | 97 | 168 | 106 | 644 | 424 | 129 | 159 |
N.S. |
1 | 0.97 | 0.74 | 0.62 | 1.08 | 0.68 | 4.13 | 2.72 | 0.83 | 1.02 |
time (sec) |
N/A | 0.609 | 0.056 | 0.183 | 0.157 | 0.077 | 13.250 | 0.132 | 0.156 | 0.048 |
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 | 164 | 177 | 91 | 110 | 164 | 114 | 182 | 104 | 139 | 177 |
N.S. |
1 | 1.08 | 0.55 | 0.67 | 1.00 | 0.70 | 1.11 | 0.63 | 0.85 | 1.08 |
time (sec) |
N/A | 0.698 | 0.211 | 0.158 | 0.149 | 0.109 | 0.957 | 0.165 | 0.159 | 0.043 |
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 | 136 | 147 | 83 | 102 | 141 | 104 | 172 | 92 | 120 | 154 |
N.S. |
1 | 1.08 | 0.61 | 0.75 | 1.04 | 0.76 | 1.26 | 0.68 | 0.88 | 1.13 |
time (sec) |
N/A | 0.624 | 0.121 | 0.155 | 0.208 | 0.091 | 0.905 | 0.127 | 0.152 | 0.038 |
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 | 113 | 115 | 75 | 94 | 118 | 92 | 155 | 81 | 101 | 108 |
N.S. |
1 | 1.02 | 0.66 | 0.83 | 1.04 | 0.81 | 1.37 | 0.72 | 0.89 | 0.96 |
time (sec) |
N/A | 0.519 | 0.148 | 0.135 | 0.133 | 0.085 | 0.926 | 0.144 | 0.156 | 23.206 |
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 | 83 | 88 | 67 | 83 | 95 | 82 | 146 | 66 | 82 | 105 |
N.S. |
1 | 1.06 | 0.81 | 1.00 | 1.14 | 0.99 | 1.76 | 0.80 | 0.99 | 1.27 |
time (sec) |
N/A | 0.422 | 0.104 | 0.123 | 0.163 | 0.107 | 0.977 | 0.130 | 0.147 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 67 | 135 | 144 | 100 | 88 | 209 | 95 | 69 | 110 |
N.S. |
1 | 0.89 | 1.80 | 1.92 | 1.33 | 1.17 | 2.79 | 1.27 | 0.92 | 1.47 |
time (sec) |
N/A | 0.538 | 0.135 | 0.123 | 0.175 | 0.178 | 5.268 | 0.153 | 0.154 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 77 | 143 | 107 | 102 | 104 | 182 | 152 | 79 | 108 |
N.S. |
1 | 0.93 | 1.72 | 1.29 | 1.23 | 1.25 | 2.19 | 1.83 | 0.95 | 1.30 |
time (sec) |
N/A | 0.545 | 0.166 | 0.144 | 0.131 | 0.082 | 2.232 | 0.156 | 0.148 | 23.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 80 | 155 | 106 | 107 | 118 | 224 | 212 | 92 | 111 |
N.S. |
1 | 0.87 | 1.68 | 1.15 | 1.16 | 1.28 | 2.43 | 2.30 | 1.00 | 1.21 |
time (sec) |
N/A | 0.545 | 0.196 | 0.138 | 0.143 | 0.090 | 2.722 | 0.136 | 0.156 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 84 | 156 | 104 | 110 | 105 | 275 | 250 | 112 | 114 |
N.S. |
1 | 0.95 | 1.77 | 1.18 | 1.25 | 1.19 | 3.12 | 2.84 | 1.27 | 1.30 |
time (sec) |
N/A | 0.558 | 0.164 | 0.148 | 0.140 | 0.079 | 3.320 | 0.174 | 0.154 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 97 | 99 | 81 | 122 | 84 | 347 | 300 | 91 | 113 |
N.S. |
1 | 0.95 | 0.97 | 0.79 | 1.20 | 0.82 | 3.40 | 2.94 | 0.89 | 1.11 |
time (sec) |
N/A | 0.523 | 0.048 | 0.149 | 0.120 | 0.111 | 4.974 | 0.131 | 0.154 | 23.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 124 | 107 | 89 | 145 | 95 | 474 | 297 | 110 | 136 |
N.S. |
1 | 0.96 | 0.83 | 0.69 | 1.12 | 0.74 | 3.67 | 2.30 | 0.85 | 1.05 |
time (sec) |
N/A | 0.576 | 0.046 | 0.180 | 0.122 | 0.076 | 5.807 | 0.153 | 0.161 | 0.046 |
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 | 189 | 215 | 99 | 118 | 187 | 126 | 228 | 117 | 158 | 200 |
N.S. |
1 | 1.14 | 0.52 | 0.62 | 0.99 | 0.67 | 1.21 | 0.62 | 0.84 | 1.06 |
time (sec) |
N/A | 0.894 | 0.318 | 0.230 | 0.122 | 0.079 | 0.920 | 0.137 | 0.161 | 0.051 |
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 | 161 | 179 | 91 | 110 | 164 | 114 | 211 | 104 | 139 | 177 |
N.S. |
1 | 1.11 | 0.57 | 0.68 | 1.02 | 0.71 | 1.31 | 0.65 | 0.86 | 1.10 |
time (sec) |
N/A | 0.828 | 0.149 | 0.220 | 0.149 | 0.081 | 0.939 | 0.159 | 0.165 | 23.018 |
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 | 138 | 151 | 83 | 102 | 141 | 104 | 194 | 94 | 120 | 154 |
N.S. |
1 | 1.09 | 0.60 | 0.74 | 1.02 | 0.75 | 1.41 | 0.68 | 0.87 | 1.12 |
time (sec) |
N/A | 0.757 | 0.169 | 0.168 | 0.124 | 0.081 | 0.973 | 0.139 | 0.161 | 0.038 |
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 | 108 | 122 | 75 | 91 | 118 | 92 | 189 | 78 | 101 | 128 |
N.S. |
1 | 1.13 | 0.69 | 0.84 | 1.09 | 0.85 | 1.75 | 0.72 | 0.94 | 1.19 |
time (sec) |
N/A | 0.468 | 0.111 | 0.164 | 0.148 | 0.132 | 0.948 | 0.154 | 0.158 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 109 | 142 | 239 | 105 | 95 | 343 | 100 | 75 | 110 |
N.S. |
1 | 1.08 | 1.41 | 2.37 | 1.04 | 0.94 | 3.40 | 0.99 | 0.74 | 1.09 |
time (sec) |
N/A | 0.743 | 0.131 | 0.152 | 0.119 | 0.089 | 6.363 | 0.135 | 0.152 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 99 | 152 | 134 | 125 | 116 | 289 | 164 | 99 | 131 |
N.S. |
1 | 0.93 | 1.43 | 1.26 | 1.18 | 1.09 | 2.73 | 1.55 | 0.93 | 1.24 |
time (sec) |
N/A | 0.712 | 0.176 | 0.190 | 0.191 | 0.084 | 2.557 | 0.141 | 0.173 | 23.162 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 98 | 106 | 132 | 129 | 125 | 337 | 224 | 111 | 133 |
N.S. |
1 | 0.84 | 0.91 | 1.14 | 1.11 | 1.08 | 2.91 | 1.93 | 0.96 | 1.15 |
time (sec) |
N/A | 0.727 | 0.288 | 0.171 | 0.162 | 0.195 | 3.391 | 0.144 | 0.152 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 106 | 164 | 122 | 131 | 129 | 355 | 270 | 131 | 135 |
N.S. |
1 | 0.88 | 1.37 | 1.02 | 1.09 | 1.08 | 2.96 | 2.25 | 1.09 | 1.12 |
time (sec) |
N/A | 0.720 | 0.213 | 0.191 | 0.141 | 0.085 | 3.741 | 0.155 | 0.160 | 24.303 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 114 | 125 | 104 | 109 | 106 | 502 | 316 | 84 | 113 |
N.S. |
1 | 0.98 | 1.08 | 0.90 | 0.94 | 0.91 | 4.33 | 2.72 | 0.72 | 0.97 |
time (sec) |
N/A | 0.723 | 0.303 | 0.171 | 0.146 | 0.082 | 6.189 | 0.146 | 0.155 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 126 | 107 | 89 | 145 | 95 | 605 | 354 | 110 | 136 |
N.S. |
1 | 0.98 | 0.83 | 0.69 | 1.12 | 0.74 | 4.69 | 2.74 | 0.85 | 1.05 |
time (sec) |
N/A | 0.697 | 0.057 | 0.209 | 0.127 | 0.083 | 6.936 | 0.139 | 0.161 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 153 | 115 | 97 | 168 | 106 | 799 | 424 | 129 | 159 |
N.S. |
1 | 0.98 | 0.74 | 0.62 | 1.08 | 0.68 | 5.12 | 2.72 | 0.83 | 1.02 |
time (sec) |
N/A | 0.756 | 0.050 | 0.207 | 0.116 | 0.076 | 15.047 | 0.144 | 0.151 | 0.053 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 160 | 81 | 130 | 129 | 95 | 0 | 0 | 180 | 163 |
N.S. |
1 | 1.12 | 0.57 | 0.91 | 0.90 | 0.66 | 0.00 | 0.00 | 1.26 | 1.14 |
time (sec) |
N/A | 0.925 | 0.091 | 0.158 | 0.218 | 0.117 | 0.000 | 0.000 | 0.165 | 24.170 |
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 | 111 | 126 | 72 | 121 | 105 | 86 | 0 | 101 | 152 | 158 |
N.S. |
1 | 1.14 | 0.65 | 1.09 | 0.95 | 0.77 | 0.00 | 0.91 | 1.37 | 1.42 |
time (sec) |
N/A | 0.743 | 0.059 | 0.135 | 0.124 | 0.085 | 0.000 | 0.158 | 0.152 | 23.656 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 90 | 64 | 113 | 83 | 78 | 0 | 0 | 125 | 129 |
N.S. |
1 | 0.98 | 0.70 | 1.23 | 0.90 | 0.85 | 0.00 | 0.00 | 1.36 | 1.40 |
time (sec) |
N/A | 0.606 | 0.052 | 0.132 | 0.266 | 0.077 | 0.000 | 0.000 | 0.160 | 23.256 |
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 | 64 | 66 | 53 | 95 | 61 | 69 | 0 | 78 | 96 | 90 |
N.S. |
1 | 1.03 | 0.83 | 1.48 | 0.95 | 1.08 | 0.00 | 1.22 | 1.50 | 1.41 |
time (sec) |
N/A | 0.437 | 0.045 | 0.124 | 0.141 | 0.073 | 0.000 | 0.130 | 0.147 | 23.085 |
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 | 43 | 41 | 46 | 74 | 40 | 62 | 0 | 53 | 45 | 71 |
N.S. |
1 | 0.95 | 1.07 | 1.72 | 0.93 | 1.44 | 0.00 | 1.23 | 1.05 | 1.65 |
time (sec) |
N/A | 0.384 | 0.021 | 0.100 | 0.188 | 0.073 | 0.000 | 0.147 | 0.141 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 46 | 55 | 61 | 0 | 56 | 0 | 80 | 51 | 68 |
N.S. |
1 | 0.96 | 1.15 | 1.27 | 0.00 | 1.17 | 0.00 | 1.67 | 1.06 | 1.42 |
time (sec) |
N/A | 0.484 | 0.031 | 0.117 | 0.000 | 0.077 | 0.000 | 0.148 | 0.161 | 23.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 67 | 68 | 77 | 0 | 80 | 0 | 159 | 84 | 91 |
N.S. |
1 | 0.93 | 0.94 | 1.07 | 0.00 | 1.11 | 0.00 | 2.21 | 1.17 | 1.26 |
time (sec) |
N/A | 0.523 | 0.033 | 0.135 | 0.000 | 0.078 | 0.000 | 0.128 | 0.154 | 23.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 96 | 83 | 99 | 0 | 99 | 0 | 224 | 108 | 117 |
N.S. |
1 | 0.93 | 0.81 | 0.96 | 0.00 | 0.96 | 0.00 | 2.17 | 1.05 | 1.14 |
time (sec) |
N/A | 0.697 | 0.049 | 0.160 | 0.000 | 0.074 | 0.000 | 0.141 | 0.152 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 125 | 91 | 116 | 0 | 107 | 0 | 283 | 130 | 140 |
N.S. |
1 | 0.98 | 0.71 | 0.91 | 0.00 | 0.84 | 0.00 | 2.21 | 1.02 | 1.09 |
time (sec) |
N/A | 0.894 | 0.055 | 0.171 | 0.000 | 0.077 | 0.000 | 0.146 | 0.158 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 155 | 80 | 162 | 153 | 125 | 0 | 0 | 235 | 189 |
N.S. |
1 | 0.98 | 0.51 | 1.03 | 0.97 | 0.79 | 0.00 | 0.00 | 1.49 | 1.20 |
time (sec) |
N/A | 0.987 | 0.127 | 0.173 | 0.155 | 0.087 | 0.000 | 0.000 | 0.155 | 0.056 |
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 | 133 | 113 | 72 | 153 | 130 | 117 | 0 | 176 | 208 | 166 |
N.S. |
1 | 0.85 | 0.54 | 1.15 | 0.98 | 0.88 | 0.00 | 1.32 | 1.56 | 1.25 |
time (sec) |
N/A | 0.739 | 0.103 | 0.152 | 0.152 | 0.077 | 0.000 | 0.138 | 0.152 | 23.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 105 | 64 | 147 | 109 | 109 | 0 | 0 | 181 | 143 |
N.S. |
1 | 1.12 | 0.68 | 1.56 | 1.16 | 1.16 | 0.00 | 0.00 | 1.93 | 1.52 |
time (sec) |
N/A | 0.565 | 0.087 | 0.145 | 0.128 | 0.077 | 0.000 | 0.000 | 0.161 | 23.125 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 76 | 57 | 161 | 88 | 102 | 0 | 0 | 112 | 108 |
N.S. |
1 | 1.03 | 0.77 | 2.18 | 1.19 | 1.38 | 0.00 | 0.00 | 1.51 | 1.46 |
time (sec) |
N/A | 0.453 | 0.082 | 0.122 | 0.154 | 0.077 | 0.000 | 0.000 | 0.153 | 0.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 29 | 33 | 73 | 60 | 0 | 66 | 71 | 32 |
N.S. |
1 | 1.00 | 0.91 | 1.03 | 2.28 | 1.88 | 0.00 | 2.06 | 2.22 | 1.00 |
time (sec) |
N/A | 0.353 | 0.007 | 0.118 | 0.153 | 0.077 | 0.000 | 0.137 | 0.146 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 71 | 78 | 147 | 0 | 93 | 0 | 245 | 125 | 119 |
N.S. |
1 | 0.90 | 0.99 | 1.86 | 0.00 | 1.18 | 0.00 | 3.10 | 1.58 | 1.51 |
time (sec) |
N/A | 0.563 | 0.046 | 0.142 | 0.000 | 0.076 | 0.000 | 0.176 | 0.156 | 23.117 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 96 | 91 | 118 | 0 | 118 | 0 | 307 | 166 | 146 |
N.S. |
1 | 0.83 | 0.78 | 1.02 | 0.00 | 1.02 | 0.00 | 2.65 | 1.43 | 1.26 |
time (sec) |
N/A | 0.746 | 0.052 | 0.162 | 0.000 | 0.079 | 0.000 | 0.161 | 0.154 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 127 | 103 | 181 | 0 | 136 | 0 | 332 | 192 | 169 |
N.S. |
1 | 0.82 | 0.66 | 1.17 | 0.00 | 0.88 | 0.00 | 2.14 | 1.24 | 1.09 |
time (sec) |
N/A | 0.938 | 0.064 | 0.184 | 0.000 | 0.077 | 0.000 | 0.179 | 0.157 | 23.185 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 188 | 156 | 111 | 202 | 0 | 144 | 0 | 372 | 212 | 192 |
N.S. |
1 | 0.83 | 0.59 | 1.07 | 0.00 | 0.77 | 0.00 | 1.98 | 1.13 | 1.02 |
time (sec) |
N/A | 1.159 | 0.072 | 0.208 | 0.000 | 0.075 | 0.000 | 0.180 | 0.162 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 150 | 122 | 195 | 185 | 153 | 0 | 0 | 295 | 302 |
N.S. |
1 | 0.91 | 0.74 | 1.18 | 1.12 | 0.93 | 0.00 | 0.00 | 1.79 | 1.83 |
time (sec) |
N/A | 1.038 | 0.170 | 0.192 | 0.156 | 0.121 | 0.000 | 0.000 | 0.154 | 23.167 |
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 | 137 | 131 | 72 | 190 | 163 | 145 | 0 | 186 | 268 | 234 |
N.S. |
1 | 0.96 | 0.53 | 1.39 | 1.19 | 1.06 | 0.00 | 1.36 | 1.96 | 1.71 |
time (sec) |
N/A | 0.812 | 0.091 | 0.167 | 0.147 | 0.114 | 0.000 | 0.158 | 0.152 | 23.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 99 | 77 | 292 | 144 | 138 | 0 | 0 | 241 | 259 |
N.S. |
1 | 0.93 | 0.72 | 2.73 | 1.35 | 1.29 | 0.00 | 0.00 | 2.25 | 2.42 |
time (sec) |
N/A | 0.605 | 0.072 | 0.142 | 0.136 | 0.121 | 0.000 | 0.000 | 0.170 | 0.058 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 63 | 35 | 41 | 132 | 91 | 0 | 121 | 96 | 143 |
N.S. |
1 | 0.97 | 0.54 | 0.63 | 2.03 | 1.40 | 0.00 | 1.86 | 1.48 | 2.20 |
time (sec) |
N/A | 0.476 | 0.024 | 0.138 | 0.165 | 0.075 | 0.000 | 0.150 | 0.149 | 23.116 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 63 | 35 | 40 | 126 | 89 | 0 | 145 | 142 | 183 |
N.S. |
1 | 0.97 | 0.54 | 0.62 | 1.94 | 1.37 | 0.00 | 2.23 | 2.18 | 2.82 |
time (sec) |
N/A | 0.411 | 0.014 | 0.135 | 0.217 | 0.076 | 0.000 | 0.154 | 0.151 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 89 | 71 | 275 | 0 | 130 | 0 | 189 | 232 | 209 |
N.S. |
1 | 0.82 | 0.66 | 2.55 | 0.00 | 1.20 | 0.00 | 1.75 | 2.15 | 1.94 |
time (sec) |
N/A | 0.733 | 0.098 | 0.161 | 0.000 | 0.080 | 0.000 | 0.147 | 0.161 | 23.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 126 | 101 | 248 | 0 | 155 | 0 | 269 | 308 | 234 |
N.S. |
1 | 0.85 | 0.68 | 1.68 | 0.00 | 1.05 | 0.00 | 1.82 | 2.08 | 1.58 |
time (sec) |
N/A | 0.941 | 0.072 | 0.208 | 0.000 | 0.081 | 0.000 | 0.143 | 0.159 | 23.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 159 | 113 | 223 | 0 | 173 | 0 | 338 | 293 | 257 |
N.S. |
1 | 0.85 | 0.60 | 1.19 | 0.00 | 0.93 | 0.00 | 1.81 | 1.57 | 1.37 |
time (sec) |
N/A | 1.150 | 0.078 | 0.240 | 0.000 | 0.079 | 0.000 | 0.156 | 0.156 | 23.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 220 | 176 | 121 | 331 | 0 | 181 | 0 | 393 | 370 | 328 |
N.S. |
1 | 0.80 | 0.55 | 1.50 | 0.00 | 0.82 | 0.00 | 1.79 | 1.68 | 1.49 |
time (sec) |
N/A | 1.366 | 0.090 | 0.277 | 0.000 | 0.081 | 0.000 | 0.140 | 0.160 | 23.259 |
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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 183 | 126 | 235 | 250 | 187 | 0 | 252 | 424 | 323 |
N.S. |
1 | 0.93 | 0.64 | 1.19 | 1.27 | 0.95 | 0.00 | 1.28 | 2.15 | 1.64 |
time (sec) |
N/A | 1.343 | 0.378 | 0.213 | 0.181 | 0.091 | 0.000 | 0.153 | 0.153 | 0.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 160 | 95 | 229 | 229 | 179 | 0 | 0 | 405 | 350 |
N.S. |
1 | 0.95 | 0.57 | 1.36 | 1.36 | 1.07 | 0.00 | 0.00 | 2.41 | 2.08 |
time (sec) |
N/A | 0.872 | 0.156 | 0.201 | 0.129 | 0.082 | 0.000 | 0.000 | 0.167 | 23.259 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 127 | 94 | 466 | 208 | 172 | 0 | 220 | 386 | 281 |
N.S. |
1 | 0.92 | 0.68 | 3.38 | 1.51 | 1.25 | 0.00 | 1.59 | 2.80 | 2.04 |
time (sec) |
N/A | 0.671 | 0.250 | 0.155 | 0.268 | 0.095 | 0.000 | 0.158 | 0.157 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 129 | 43 | 49 | 197 | 118 | 0 | 0 | 72 | 347 |
N.S. |
1 | 1.33 | 0.44 | 0.51 | 2.03 | 1.22 | 0.00 | 0.00 | 0.74 | 3.58 |
time (sec) |
N/A | 0.588 | 0.038 | 0.168 | 0.274 | 0.075 | 0.000 | 0.000 | 0.152 | 23.264 |
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 | 97 | 100 | 42 | 48 | 197 | 116 | 0 | 148 | 72 | 295 |
N.S. |
1 | 1.03 | 0.43 | 0.49 | 2.03 | 1.20 | 0.00 | 1.53 | 0.74 | 3.04 |
time (sec) |
N/A | 0.485 | 0.032 | 0.165 | 0.126 | 0.074 | 0.000 | 0.131 | 0.157 | 23.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 97 | 43 | 49 | 189 | 116 | 0 | 199 | 72 | 49 |
N.S. |
1 | 1.00 | 0.44 | 0.51 | 1.95 | 1.20 | 0.00 | 2.05 | 0.74 | 0.51 |
time (sec) |
N/A | 0.446 | 0.019 | 0.160 | 0.139 | 0.074 | 0.000 | 0.149 | 0.151 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 129 | 79 | 451 | 0 | 163 | 0 | 243 | 32 | 327 |
N.S. |
1 | 0.94 | 0.58 | 3.29 | 0.00 | 1.19 | 0.00 | 1.77 | 0.23 | 2.39 |
time (sec) |
N/A | 0.817 | 0.168 | 0.188 | 0.000 | 0.081 | 0.000 | 0.163 | 200.019 | 23.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 180 | 156 | 109 | 423 | 0 | 188 | 0 | 323 | 337 | 352 |
N.S. |
1 | 0.87 | 0.61 | 2.35 | 0.00 | 1.04 | 0.00 | 1.79 | 1.87 | 1.96 |
time (sec) |
N/A | 1.134 | 0.086 | 0.252 | 0.000 | 0.082 | 0.000 | 0.146 | 0.144 | 23.199 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 191 | 121 | 397 | 0 | 206 | 0 | 392 | 32 | 375 |
N.S. |
1 | 0.87 | 0.55 | 1.81 | 0.00 | 0.94 | 0.00 | 1.79 | 0.15 | 1.71 |
time (sec) |
N/A | 1.386 | 0.086 | 0.274 | 0.000 | 0.088 | 0.000 | 0.135 | 200.019 | 23.246 |
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 | 50 | 66 | 42 | 28 | 40 | 38 | 37 | 21 | 38 | 22 |
N.S. |
1 | 1.32 | 0.84 | 0.56 | 0.80 | 0.76 | 0.74 | 0.42 | 0.76 | 0.44 |
time (sec) |
N/A | 0.374 | 0.041 | 0.250 | 0.157 | 0.068 | 0.127 | 0.140 | 0.157 | 23.249 |
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 | 36 | 41 | 37 | 25 | 28 | 33 | 27 | 19 | 27 | 21 |
N.S. |
1 | 1.14 | 1.03 | 0.69 | 0.78 | 0.92 | 0.75 | 0.53 | 0.75 | 0.58 |
time (sec) |
N/A | 0.331 | 0.025 | 0.122 | 0.168 | 0.071 | 0.133 | 0.125 | 0.149 | 0.030 |