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 | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 111 | 1983 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.08 | 19.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.309 | 15.160 | 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 | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 113 | 1987 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.08 | 18.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.334 | 15.438 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 113 | 1997 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.08 | 19.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.354 | 15.521 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 212 | 149 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.99 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.385 | 1.392 | 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 | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 127 | 126 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.97 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.293 | 1.378 | 0.000 | 0.000 | 0.000 | 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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 72 | 71 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.97 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.249 | 0.695 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 83 | 2137 | 0 | 0 | 0 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.98 | 25.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.238 | 6.178 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 83 | 1343 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.98 | 15.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.270 | 14.162 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 83 | 1342 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.98 | 15.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.267 | 14.904 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 83 | 1914 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.98 | 22.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.267 | 15.205 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 63 | 60 | 55 | 95 | 69 | 116 | 64 | 91 | 52 |
N.S. |
1 | 0.88 | 0.83 | 0.76 | 1.32 | 0.96 | 1.61 | 0.89 | 1.26 | 0.72 |
time (sec) |
N/A | 0.258 | 0.032 | 1.154 | 0.033 | 0.094 | 0.540 | 0.251 | 0.155 | 15.547 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 46 | 43 | 45 | 64 | 50 | 80 | 44 | 60 | 46 |
N.S. |
1 | 0.94 | 0.88 | 0.92 | 1.31 | 1.02 | 1.63 | 0.90 | 1.22 | 0.94 |
time (sec) |
N/A | 0.245 | 0.077 | 0.628 | 0.029 | 0.091 | 0.260 | 0.185 | 0.165 | 16.225 |
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 | 30 | 28 | 30 | 26 | 33 | 37 | 42 | 29 | 29 | 32 |
N.S. |
1 | 0.93 | 1.00 | 0.87 | 1.10 | 1.23 | 1.40 | 0.97 | 0.97 | 1.07 |
time (sec) |
N/A | 0.218 | 0.014 | 0.384 | 0.032 | 0.083 | 0.120 | 0.200 | 0.156 | 16.025 |
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 | 28 | 37 | 38 | 24 | 33 | 35 | 0 | 35 | 76 | 32 |
N.S. |
1 | 1.32 | 1.36 | 0.86 | 1.18 | 1.25 | 0.00 | 1.25 | 2.71 | 1.14 |
time (sec) |
N/A | 0.247 | 0.016 | 0.377 | 0.028 | 0.086 | 0.000 | 0.159 | 0.155 | 15.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 41 | 46 | 39 | 29 | 50 | 0 | 31 | 86 | 51 |
N.S. |
1 | 1.28 | 1.44 | 1.22 | 0.91 | 1.56 | 0.00 | 0.97 | 2.69 | 1.59 |
time (sec) |
N/A | 0.256 | 0.019 | 0.507 | 0.027 | 0.085 | 0.000 | 0.171 | 0.150 | 15.033 |
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 | 51 | 66 | 58 | 55 | 49 | 83 | 0 | 58 | 110 | 61 |
N.S. |
1 | 1.29 | 1.14 | 1.08 | 0.96 | 1.63 | 0.00 | 1.14 | 2.16 | 1.20 |
time (sec) |
N/A | 0.266 | 0.022 | 0.958 | 0.027 | 0.087 | 0.000 | 0.135 | 0.150 | 15.642 |
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 | 64 | 60 | 73 | 57 | 56 | 89 | 66 | 72 | 393 | 51 |
N.S. |
1 | 0.94 | 1.14 | 0.89 | 0.88 | 1.39 | 1.03 | 1.12 | 6.14 | 0.80 |
time (sec) |
N/A | 0.287 | 0.026 | 1.541 | 0.106 | 0.083 | 1.290 | 0.380 | 0.153 | 15.305 |
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 | 48 | 48 | 57 | 47 | 45 | 72 | 54 | 57 | 224 | 40 |
N.S. |
1 | 1.00 | 1.19 | 0.98 | 0.94 | 1.50 | 1.12 | 1.19 | 4.67 | 0.83 |
time (sec) |
N/A | 0.280 | 0.016 | 0.839 | 0.109 | 0.095 | 0.828 | 0.355 | 0.151 | 15.571 |
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 | 32 | 36 | 41 | 37 | 33 | 53 | 42 | 43 | 105 | 29 |
N.S. |
1 | 1.12 | 1.28 | 1.16 | 1.03 | 1.66 | 1.31 | 1.34 | 3.28 | 0.91 |
time (sec) |
N/A | 0.261 | 0.017 | 0.536 | 0.111 | 0.081 | 0.556 | 0.226 | 0.155 | 15.491 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 16 | 15 | 31 | 0 | 15 | 31 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 2.07 | 0.00 | 1.00 | 2.07 | 1.13 |
time (sec) |
N/A | 0.157 | 0.001 | 0.850 | 0.032 | 0.072 | 0.000 | 0.118 | 0.146 | 15.315 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 26 | 43 | 33 | 25 | 34 | 0 | 53 | 42 | 19 |
N.S. |
1 | 1.37 | 2.26 | 1.74 | 1.32 | 1.79 | 0.00 | 2.79 | 2.21 | 1.00 |
time (sec) |
N/A | 0.255 | 0.069 | 0.991 | 0.108 | 0.076 | 0.000 | 0.140 | 0.150 | 15.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 41 | 51 | 48 | 41 | 76 | 0 | 111 | 78 | 35 |
N.S. |
1 | 1.24 | 1.55 | 1.45 | 1.24 | 2.30 | 0.00 | 3.36 | 2.36 | 1.06 |
time (sec) |
N/A | 0.264 | 0.020 | 0.682 | 0.110 | 0.080 | 0.000 | 0.147 | 0.150 | 15.674 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 49 | 51 | 63 | 52 | 110 | 0 | 170 | 113 | 46 |
N.S. |
1 | 0.96 | 1.00 | 1.24 | 1.02 | 2.16 | 0.00 | 3.33 | 2.22 | 0.90 |
time (sec) |
N/A | 0.267 | 0.026 | 1.280 | 0.105 | 0.079 | 0.000 | 0.163 | 0.158 | 15.963 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 91 | 126 | 86 | 147 | 99 | 190 | 94 | 154 | 124 |
N.S. |
1 | 0.91 | 1.26 | 0.86 | 1.47 | 0.99 | 1.90 | 0.94 | 1.54 | 1.24 |
time (sec) |
N/A | 0.304 | 0.332 | 5.581 | 0.034 | 0.094 | 1.139 | 0.347 | 0.151 | 15.184 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 71 | 107 | 76 | 114 | 79 | 128 | 73 | 101 | 92 |
N.S. |
1 | 0.92 | 1.39 | 0.99 | 1.48 | 1.03 | 1.66 | 0.95 | 1.31 | 1.19 |
time (sec) |
N/A | 0.281 | 0.183 | 2.971 | 0.032 | 0.090 | 0.567 | 0.289 | 0.150 | 15.627 |
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 | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 46 | 83 | 41 | 67 | 53 | 61 | 46 | 46 | 61 |
N.S. |
1 | 0.96 | 1.73 | 0.85 | 1.40 | 1.10 | 1.27 | 0.96 | 0.96 | 1.27 |
time (sec) |
N/A | 0.248 | 0.075 | 1.550 | 0.028 | 0.090 | 0.265 | 0.156 | 0.144 | 15.367 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 55 | 84 | 50 | 64 | 79 | 0 | 66 | 353 | 58 |
N.S. |
1 | 1.04 | 1.58 | 0.94 | 1.21 | 1.49 | 0.00 | 1.25 | 6.66 | 1.09 |
time (sec) |
N/A | 0.274 | 0.157 | 1.298 | 0.033 | 0.094 | 0.000 | 0.159 | 0.150 | 15.529 |
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 | 57 | 64 | 81 | 64 | 60 | 100 | 0 | 71 | 187 | 68 |
N.S. |
1 | 1.12 | 1.42 | 1.12 | 1.05 | 1.75 | 0.00 | 1.25 | 3.28 | 1.19 |
time (sec) |
N/A | 0.293 | 0.124 | 1.759 | 0.035 | 0.100 | 0.000 | 0.122 | 0.146 | 15.459 |
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 | 51 | 69 | 77 | 71 | 61 | 97 | 0 | 68 | 141 | 83 |
N.S. |
1 | 1.35 | 1.51 | 1.39 | 1.20 | 1.90 | 0.00 | 1.33 | 2.76 | 1.63 |
time (sec) |
N/A | 0.288 | 0.191 | 3.460 | 0.034 | 0.088 | 0.000 | 0.156 | 0.143 | 15.256 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 90 | 275 | 88 | 84 | 137 | 0 | 113 | 574 | 126 |
N.S. |
1 | 0.95 | 2.89 | 0.93 | 0.88 | 1.44 | 0.00 | 1.19 | 6.04 | 1.33 |
time (sec) |
N/A | 0.334 | 2.309 | 7.359 | 0.108 | 0.093 | 0.000 | 0.748 | 0.152 | 15.373 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 75 | 395 | 78 | 71 | 113 | 0 | 96 | 364 | 97 |
N.S. |
1 | 0.97 | 5.13 | 1.01 | 0.92 | 1.47 | 0.00 | 1.25 | 4.73 | 1.26 |
time (sec) |
N/A | 0.320 | 1.468 | 4.052 | 0.109 | 0.083 | 0.000 | 0.532 | 0.148 | 15.198 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 60 | 281 | 68 | 58 | 86 | 0 | 81 | 208 | 69 |
N.S. |
1 | 1.02 | 4.76 | 1.15 | 0.98 | 1.46 | 0.00 | 1.37 | 3.53 | 1.17 |
time (sec) |
N/A | 0.310 | 1.100 | 2.127 | 0.107 | 0.085 | 0.000 | 0.378 | 0.147 | 15.081 |
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 | 40 | 44 | 41 | 46 | 44 | 58 | 0 | 49 | 106 | 42 |
N.S. |
1 | 1.10 | 1.02 | 1.15 | 1.10 | 1.45 | 0.00 | 1.22 | 2.65 | 1.05 |
time (sec) |
N/A | 0.226 | 0.088 | 1.502 | 0.039 | 0.077 | 0.000 | 0.127 | 0.146 | 15.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 40 | 82 | 66 | 46 | 67 | 0 | 46 | 91 | 44 |
N.S. |
1 | 1.11 | 2.28 | 1.83 | 1.28 | 1.86 | 0.00 | 1.28 | 2.53 | 1.22 |
time (sec) |
N/A | 0.305 | 1.999 | 1.839 | 0.105 | 0.080 | 0.000 | 0.161 | 0.149 | 15.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 49 | 160 | 73 | 59 | 98 | 0 | 176 | 117 | 53 |
N.S. |
1 | 1.09 | 3.56 | 1.62 | 1.31 | 2.18 | 0.00 | 3.91 | 2.60 | 1.18 |
time (sec) |
N/A | 0.319 | 0.983 | 3.043 | 0.106 | 0.078 | 0.000 | 0.152 | 0.152 | 15.201 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 66 | 256 | 107 | 72 | 136 | 0 | 273 | 172 | 68 |
N.S. |
1 | 1.02 | 3.94 | 1.65 | 1.11 | 2.09 | 0.00 | 4.20 | 2.65 | 1.05 |
time (sec) |
N/A | 0.320 | 2.464 | 4.767 | 0.108 | 0.080 | 0.000 | 0.177 | 0.149 | 16.436 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 63 | 99 | 67 | 81 | 84 | 0 | 73 | 766 | 103 |
N.S. |
1 | 0.91 | 1.43 | 0.97 | 1.17 | 1.22 | 0.00 | 1.06 | 11.10 | 1.49 |
time (sec) |
N/A | 0.301 | 0.196 | 1.243 | 0.033 | 0.130 | 0.000 | 0.183 | 0.175 | 16.230 |
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 | 45 | 45 | 41 | 42 | 50 | 41 | 0 | 45 | 207 | 64 |
N.S. |
1 | 1.00 | 0.91 | 0.93 | 1.11 | 0.91 | 0.00 | 1.00 | 4.60 | 1.42 |
time (sec) |
N/A | 0.280 | 0.079 | 0.721 | 0.034 | 0.105 | 0.000 | 0.151 | 0.156 | 16.079 |
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 | 23 | 23 | 26 | 35 | 26 | 21 | 117 | 22 | 35 | 63 |
N.S. |
1 | 1.00 | 1.13 | 1.52 | 1.13 | 0.91 | 5.09 | 0.96 | 1.52 | 2.74 |
time (sec) |
N/A | 0.218 | 0.131 | 0.382 | 0.025 | 0.086 | 5.403 | 0.143 | 0.146 | 16.082 |
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 | 46 | 52 | 43 | 68 | 50 | 42 | 0 | 53 | 135 | 65 |
N.S. |
1 | 1.13 | 0.93 | 1.48 | 1.09 | 0.91 | 0.00 | 1.15 | 2.93 | 1.41 |
time (sec) |
N/A | 0.283 | 0.075 | 0.637 | 0.027 | 0.119 | 0.000 | 0.118 | 0.153 | 16.289 |
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 | 74 | 77 | 100 | 119 | 87 | 126 | 0 | 102 | 283 | 98 |
N.S. |
1 | 1.04 | 1.35 | 1.61 | 1.18 | 1.70 | 0.00 | 1.38 | 3.82 | 1.32 |
time (sec) |
N/A | 0.312 | 0.157 | 0.986 | 0.033 | 0.173 | 0.000 | 0.193 | 0.166 | 16.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 118 | 138 | 180 | 145 | 265 | 0 | 162 | 414 | 160 |
N.S. |
1 | 1.09 | 1.28 | 1.67 | 1.34 | 2.45 | 0.00 | 1.50 | 3.83 | 1.48 |
time (sec) |
N/A | 0.358 | 0.449 | 1.723 | 0.036 | 0.291 | 0.000 | 0.144 | 0.170 | 15.754 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 98 | 229 | 101 | 95 | 373 | 0 | 121 | 654 | 1109 |
N.S. |
1 | 1.18 | 2.76 | 1.22 | 1.14 | 4.49 | 0.00 | 1.46 | 7.88 | 13.36 |
time (sec) |
N/A | 0.403 | 2.452 | 1.616 | 0.140 | 0.120 | 0.000 | 0.262 | 0.183 | 15.343 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 70 | 206 | 72 | 66 | 297 | 0 | 75 | 196 | 410 |
N.S. |
1 | 1.19 | 3.49 | 1.22 | 1.12 | 5.03 | 0.00 | 1.27 | 3.32 | 6.95 |
time (sec) |
N/A | 0.331 | 1.177 | 1.003 | 0.112 | 0.114 | 0.000 | 0.304 | 0.160 | 15.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 53 | 184 | 48 | 45 | 226 | 0 | 51 | 78 | 126 |
N.S. |
1 | 1.15 | 4.00 | 1.04 | 0.98 | 4.91 | 0.00 | 1.11 | 1.70 | 2.74 |
time (sec) |
N/A | 0.301 | 0.409 | 0.694 | 0.113 | 0.104 | 0.000 | 0.250 | 0.150 | 15.639 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 182 | 46 | 44 | 231 | 0 | 65 | 85 | 460 |
N.S. |
1 | 1.00 | 4.04 | 1.02 | 0.98 | 5.13 | 0.00 | 1.44 | 1.89 | 10.22 |
time (sec) |
N/A | 0.271 | 0.281 | 0.333 | 0.110 | 0.109 | 0.000 | 0.152 | 0.158 | 16.382 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 77 | 204 | 68 | 66 | 310 | 0 | 87 | 164 | 637 |
N.S. |
1 | 1.24 | 3.29 | 1.10 | 1.06 | 5.00 | 0.00 | 1.40 | 2.65 | 10.27 |
time (sec) |
N/A | 0.337 | 1.479 | 0.816 | 0.117 | 0.114 | 0.000 | 0.150 | 0.160 | 17.283 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 109 | 390 | 90 | 106 | 533 | 0 | 134 | 280 | 2644 |
N.S. |
1 | 1.27 | 4.53 | 1.05 | 1.23 | 6.20 | 0.00 | 1.56 | 3.26 | 30.74 |
time (sec) |
N/A | 0.399 | 2.811 | 1.315 | 0.114 | 0.117 | 0.000 | 0.195 | 0.165 | 19.749 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 147 | 671 | 118 | 161 | 833 | 0 | 212 | 423 | 4324 |
N.S. |
1 | 1.22 | 5.59 | 0.98 | 1.34 | 6.94 | 0.00 | 1.77 | 3.52 | 36.03 |
time (sec) |
N/A | 0.486 | 2.574 | 2.359 | 0.118 | 0.129 | 0.000 | 0.183 | 0.191 | 20.831 |
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 | 77 | 70 | 109 | 72 | 98 | 118 | 0 | 91 | 756 | 170 |
N.S. |
1 | 0.91 | 1.42 | 0.94 | 1.27 | 1.53 | 0.00 | 1.18 | 9.82 | 2.21 |
time (sec) |
N/A | 0.305 | 0.319 | 3.762 | 0.047 | 0.144 | 0.000 | 0.194 | 0.175 | 15.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 48 | 81 | 50 | 59 | 53 | 0 | 48 | 107 | 97 |
N.S. |
1 | 0.94 | 1.59 | 0.98 | 1.16 | 1.04 | 0.00 | 0.94 | 2.10 | 1.90 |
time (sec) |
N/A | 0.277 | 0.638 | 2.098 | 0.031 | 0.095 | 0.000 | 0.152 | 0.146 | 15.199 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 44 | 79 | 59 | 57 | 52 | 0 | 46 | 108 | 90 |
N.S. |
1 | 0.90 | 1.61 | 1.20 | 1.16 | 1.06 | 0.00 | 0.94 | 2.20 | 1.84 |
time (sec) |
N/A | 0.254 | 0.312 | 1.467 | 0.029 | 0.085 | 0.000 | 0.138 | 0.148 | 15.006 |
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 | 83 | 84 | 112 | 91 | 117 | 138 | 0 | 118 | 740 | 106 |
N.S. |
1 | 1.01 | 1.35 | 1.10 | 1.41 | 1.66 | 0.00 | 1.42 | 8.92 | 1.28 |
time (sec) |
N/A | 0.310 | 0.261 | 2.283 | 0.037 | 0.209 | 0.000 | 0.147 | 0.174 | 15.281 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 108 | 130 | 141 | 192 | 312 | 0 | 173 | 1057 | 160 |
N.S. |
1 | 0.97 | 1.17 | 1.27 | 1.73 | 2.81 | 0.00 | 1.56 | 9.52 | 1.44 |
time (sec) |
N/A | 0.349 | 0.951 | 4.213 | 0.037 | 0.338 | 0.000 | 0.147 | 0.204 | 15.420 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 148 | 162 | 201 | 279 | 557 | 0 | 308 | 1312 | 206 |
N.S. |
1 | 1.06 | 1.16 | 1.44 | 1.99 | 3.98 | 0.00 | 2.20 | 9.37 | 1.47 |
time (sec) |
N/A | 0.395 | 1.377 | 7.773 | 0.041 | 0.628 | 0.000 | 0.184 | 0.415 | 16.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 131 | 286 | 125 | 127 | 514 | 0 | 145 | 799 | 765 |
N.S. |
1 | 1.10 | 2.40 | 1.05 | 1.07 | 4.32 | 0.00 | 1.22 | 6.71 | 6.43 |
time (sec) |
N/A | 0.420 | 4.065 | 5.147 | 0.108 | 0.120 | 0.000 | 0.396 | 0.206 | 16.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 104 | 249 | 85 | 96 | 393 | 0 | 107 | 470 | 285 |
N.S. |
1 | 1.16 | 2.77 | 0.94 | 1.07 | 4.37 | 0.00 | 1.19 | 5.22 | 3.17 |
time (sec) |
N/A | 0.340 | 2.235 | 2.882 | 0.110 | 0.112 | 0.000 | 0.319 | 0.168 | 15.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 95 | 346 | 77 | 75 | 458 | 0 | 83 | 519 | 711 |
N.S. |
1 | 1.12 | 4.07 | 0.91 | 0.88 | 5.39 | 0.00 | 0.98 | 6.11 | 8.36 |
time (sec) |
N/A | 0.332 | 5.379 | 1.675 | 0.113 | 0.111 | 0.000 | 0.269 | 0.163 | 15.572 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 111 | 240 | 90 | 106 | 435 | 0 | 114 | 562 | 2056 |
N.S. |
1 | 1.21 | 2.61 | 0.98 | 1.15 | 4.73 | 0.00 | 1.24 | 6.11 | 22.35 |
time (sec) |
N/A | 0.271 | 1.386 | 0.447 | 0.106 | 0.119 | 0.000 | 0.155 | 0.172 | 16.760 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 141 | 288 | 102 | 163 | 604 | 0 | 175 | 784 | 3146 |
N.S. |
1 | 1.17 | 2.38 | 0.84 | 1.35 | 4.99 | 0.00 | 1.45 | 6.48 | 26.00 |
time (sec) |
N/A | 0.413 | 3.293 | 3.185 | 0.114 | 0.129 | 0.000 | 0.222 | 0.187 | 19.782 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 183 | 1588 | 124 | 235 | 979 | 0 | 212 | 993 | 4987 |
N.S. |
1 | 1.14 | 9.92 | 0.78 | 1.47 | 6.12 | 0.00 | 1.32 | 6.21 | 31.17 |
time (sec) |
N/A | 0.486 | 5.444 | 5.809 | 0.114 | 0.145 | 0.000 | 0.221 | 0.281 | 21.963 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 231 | 3028 | 152 | 319 | 1505 | 0 | 298 | 1216 | 6017 |
N.S. |
1 | 1.12 | 14.63 | 0.73 | 1.54 | 7.27 | 0.00 | 1.44 | 5.87 | 29.07 |
time (sec) |
N/A | 0.581 | 8.141 | 10.394 | 0.130 | 0.173 | 0.000 | 0.269 | 1.391 | 21.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 73 | 136 | 80 | 112 | 116 | 0 | 77 | 216 | 166 |
N.S. |
1 | 0.94 | 1.74 | 1.03 | 1.44 | 1.49 | 0.00 | 0.99 | 2.77 | 2.13 |
time (sec) |
N/A | 0.297 | 1.942 | 11.794 | 0.044 | 0.101 | 0.000 | 0.197 | 0.160 | 16.500 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 75 | 131 | 73 | 113 | 111 | 0 | 74 | 226 | 153 |
N.S. |
1 | 0.93 | 1.62 | 0.90 | 1.40 | 1.37 | 0.00 | 0.91 | 2.79 | 1.89 |
time (sec) |
N/A | 0.301 | 0.709 | 6.824 | 0.034 | 0.106 | 0.000 | 0.213 | 0.153 | 16.765 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 69 | 129 | 81 | 102 | 102 | 0 | 65 | 196 | 142 |
N.S. |
1 | 0.93 | 1.74 | 1.09 | 1.38 | 1.38 | 0.00 | 0.88 | 2.65 | 1.92 |
time (sec) |
N/A | 0.270 | 1.245 | 6.691 | 0.034 | 0.100 | 0.000 | 0.182 | 0.144 | 17.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 130 | 128 | 158 | 144 | 243 | 307 | 0 | 190 | 1871 | 190 |
N.S. |
1 | 0.98 | 1.22 | 1.11 | 1.87 | 2.36 | 0.00 | 1.46 | 14.39 | 1.46 |
time (sec) |
N/A | 0.359 | 0.829 | 9.878 | 0.039 | 0.409 | 0.000 | 0.156 | 0.229 | 18.950 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 151 | 176 | 193 | 344 | 584 | 0 | 305 | 2392 | 272 |
N.S. |
1 | 0.98 | 1.14 | 1.25 | 2.23 | 3.79 | 0.00 | 1.98 | 15.53 | 1.77 |
time (sec) |
N/A | 0.397 | 1.277 | 17.365 | 0.042 | 0.756 | 0.000 | 0.175 | 0.286 | 19.693 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 194 | 208 | 254 | 454 | 859 | 0 | 359 | 2744 | 327 |
N.S. |
1 | 1.01 | 1.08 | 1.32 | 2.36 | 4.47 | 0.00 | 1.87 | 14.29 | 1.70 |
time (sec) |
N/A | 0.458 | 4.899 | 29.097 | 0.043 | 1.423 | 0.000 | 0.260 | 6.480 | 19.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 170 | 523 | 134 | 193 | 664 | 0 | 188 | 1259 | 615 |
N.S. |
1 | 1.16 | 3.56 | 0.91 | 1.31 | 4.52 | 0.00 | 1.28 | 8.56 | 4.18 |
time (sec) |
N/A | 0.456 | 5.121 | 15.479 | 0.113 | 0.133 | 0.000 | 0.584 | 0.211 | 15.686 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 153 | 1333 | 124 | 163 | 763 | 0 | 147 | 1337 | 1117 |
N.S. |
1 | 1.12 | 9.73 | 0.91 | 1.19 | 5.57 | 0.00 | 1.07 | 9.76 | 8.15 |
time (sec) |
N/A | 0.400 | 9.949 | 9.061 | 0.111 | 0.132 | 0.000 | 0.515 | 0.209 | 15.694 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 161 | 1334 | 125 | 191 | 860 | 0 | 161 | 1422 | 2405 |
N.S. |
1 | 1.17 | 9.67 | 0.91 | 1.38 | 6.23 | 0.00 | 1.17 | 10.30 | 17.43 |
time (sec) |
N/A | 0.392 | 7.909 | 6.913 | 0.126 | 0.142 | 0.000 | 0.393 | 0.211 | 18.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 175 | 332 | 147 | 231 | 819 | 0 | 196 | 1496 | 3271 |
N.S. |
1 | 1.22 | 2.31 | 1.02 | 1.60 | 5.69 | 0.00 | 1.36 | 10.39 | 22.72 |
time (sec) |
N/A | 0.344 | 4.070 | 1.049 | 0.124 | 0.138 | 0.000 | 0.138 | 0.224 | 19.722 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 211 | 2089 | 149 | 311 | 1060 | 0 | 247 | 1851 | 4890 |
N.S. |
1 | 1.17 | 11.54 | 0.82 | 1.72 | 5.86 | 0.00 | 1.36 | 10.23 | 27.02 |
time (sec) |
N/A | 0.514 | 7.683 | 13.257 | 0.133 | 0.165 | 0.000 | 0.321 | 0.260 | 22.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 230 | 263 | 3340 | 171 | 409 | 1649 | 0 | 302 | 2154 | 7057 |
N.S. |
1 | 1.14 | 14.52 | 0.74 | 1.78 | 7.17 | 0.00 | 1.31 | 9.37 | 30.68 |
time (sec) |
N/A | 0.583 | 8.374 | 22.671 | 0.145 | 0.193 | 0.000 | 0.292 | 1.516 | 22.914 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 285 | 319 | 547 | 199 | 520 | 2229 | 0 | 388 | 2455 | 7460 |
N.S. |
1 | 1.12 | 1.92 | 0.70 | 1.82 | 7.82 | 0.00 | 1.36 | 8.61 | 26.18 |
time (sec) |
N/A | 0.683 | 9.912 | 45.069 | 0.130 | 0.226 | 0.000 | 0.407 | 14.794 | 23.614 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 107 | 139 | 322 | 0 | 456 | 0 | 1280 | 199 | 0 |
N.S. |
1 | 0.96 | 1.25 | 2.90 | 0.00 | 4.11 | 0.00 | 11.53 | 1.79 | 0.00 |
time (sec) |
N/A | 0.324 | 1.176 | 28.317 | 0.000 | 1.675 | 0.000 | 0.625 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 79 | 74 | 234 | 0 | 386 | 0 | 800 | 133 | 0 |
N.S. |
1 | 0.99 | 0.92 | 2.92 | 0.00 | 4.82 | 0.00 | 10.00 | 1.66 | 0.00 |
time (sec) |
N/A | 0.284 | 0.496 | 10.569 | 0.000 | 0.413 | 0.000 | 0.451 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 56 | 119 | 58 | 0 | 312 | 0 | 377 | 57 | 46 |
N.S. |
1 | 1.04 | 2.20 | 1.07 | 0.00 | 5.78 | 0.00 | 6.98 | 1.06 | 0.85 |
time (sec) |
N/A | 0.253 | 0.328 | 0.272 | 0.000 | 0.178 | 0.000 | 0.298 | 0.170 | 16.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 72 | 70 | 540 | 3317 | 963 | 0 | 402 | 22 | 0 |
N.S. |
1 | 1.03 | 1.00 | 7.71 | 47.39 | 13.76 | 0.00 | 5.74 | 0.31 | 0.00 |
time (sec) |
N/A | 0.302 | 0.168 | 1.497 | 0.414 | 0.246 | 0.000 | 0.519 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 113 | 527 | 1200 | 0 | 1342 | 0 | 574 | 24 | 0 |
N.S. |
1 | 1.04 | 4.83 | 11.01 | 0.00 | 12.31 | 0.00 | 5.27 | 0.22 | 0.00 |
time (sec) |
N/A | 0.322 | 3.818 | 1.594 | 0.000 | 0.366 | 0.000 | 0.644 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | B | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 161 | 182 | 0 | 1944 | 0 | 1953 | 0 | 866 | 24 | 0 |
N.S. |
1 | 1.13 | 0.00 | 12.07 | 0.00 | 12.13 | 0.00 | 5.38 | 0.15 | 0.00 |
time (sec) |
N/A | 0.388 | 0.000 | 1.618 | 0.000 | 1.162 | 0.000 | 1.169 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 219 | 229 | 263 | 1257 | 0 | 1775 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.05 | 1.20 | 5.74 | 0.00 | 8.11 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.559 | 2.461 | 49.500 | 0.000 | 3.746 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 169 | 208 | 933 | 0 | 1621 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.02 | 1.26 | 5.65 | 0.00 | 9.82 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.454 | 1.858 | 42.960 | 0.000 | 1.049 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 115 | 526 | 636 | 0 | 1471 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.97 | 4.46 | 5.39 | 0.00 | 12.47 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.372 | 2.635 | 24.107 | 0.000 | 0.429 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | C | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 77 | 284 | 353 | 3227 | 1227 | 0 | 0 | 15 | 0 |
N.S. |
1 | 0.97 | 3.59 | 4.47 | 40.85 | 15.53 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.241 | 0.304 | 5.033 | 0.577 | 0.301 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 67 | 130 | 195 | 0 | 499 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.97 | 1.88 | 2.83 | 0.00 | 7.23 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.330 | 0.431 | 4.003 | 0.000 | 0.242 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 112 | 176 | 359 | 0 | 629 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.98 | 1.54 | 3.15 | 0.00 | 5.52 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.393 | 0.526 | 5.081 | 0.000 | 0.567 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 175 | 178 | 548 | 0 | 849 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.05 | 1.07 | 3.28 | 0.00 | 5.08 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.476 | 1.679 | 6.350 | 0.000 | 2.049 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 128 | 149 | 438 | 0 | 527 | 0 | 2026 | 295 | 0 |
N.S. |
1 | 0.95 | 1.10 | 3.24 | 0.00 | 3.90 | 0.00 | 15.01 | 2.19 | 0.00 |
time (sec) |
N/A | 0.332 | 1.382 | 36.375 | 0.000 | 6.883 | 0.000 | 2.123 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 102 | 99 | 337 | 0 | 443 | 0 | 1431 | 195 | 0 |
N.S. |
1 | 0.98 | 0.95 | 3.24 | 0.00 | 4.26 | 0.00 | 13.76 | 1.88 | 0.00 |
time (sec) |
N/A | 0.302 | 1.023 | 32.079 | 0.000 | 1.702 | 0.000 | 1.374 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 79 | 84 | 81 | 0 | 373 | 0 | 867 | 87 | 66 |
N.S. |
1 | 1.01 | 1.08 | 1.04 | 0.00 | 4.78 | 0.00 | 11.12 | 1.12 | 0.85 |
time (sec) |
N/A | 0.269 | 0.182 | 0.233 | 0.000 | 0.406 | 0.000 | 0.844 | 0.176 | 18.614 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | B | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 506 | 1301 | 0 | 1075 | 0 | 718 | 57 | 0 |
N.S. |
1 | 1.00 | 5.56 | 14.30 | 0.00 | 11.81 | 0.00 | 7.89 | 0.63 | 0.00 |
time (sec) |
N/A | 0.329 | 3.470 | 6.801 | 0.000 | 0.399 | 0.000 | 4.010 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 118 | 622 | 901 | 0 | 1300 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.04 | 5.46 | 7.90 | 0.00 | 11.40 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.362 | 3.864 | 1.578 | 0.000 | 0.417 | 0.000 | 0.000 | 0.235 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 172 | 684 | 1451 | 0 | 1801 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.08 | 4.30 | 9.13 | 0.00 | 11.33 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.391 | 4.001 | 1.610 | 0.000 | 1.376 | 0.000 | 0.000 | 0.944 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 290 | 302 | 353 | 1644 | 0 | 1973 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.04 | 1.22 | 5.67 | 0.00 | 6.80 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.698 | 4.374 | 42.323 | 0.000 | 13.736 | 0.000 | 0.000 | 0.223 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 220 | 258 | 1306 | 0 | 1777 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.03 | 1.21 | 6.10 | 0.00 | 8.30 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.579 | 2.835 | 16.064 | 0.000 | 3.775 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 165 | 703 | 971 | 0 | 1627 | 0 | 0 | 61 | 0 |
N.S. |
1 | 0.99 | 4.23 | 5.85 | 0.00 | 9.80 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.488 | 3.862 | 11.237 | 0.000 | 1.064 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 116 | 527 | 673 | 0 | 1457 | 0 | 0 | 44 | 0 |
N.S. |
1 | 0.98 | 4.47 | 5.70 | 0.00 | 12.35 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.294 | 1.244 | 6.285 | 0.000 | 0.427 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 106 | 410 | 477 | 0 | 1446 | 0 | 0 | 61 | 0 |
N.S. |
1 | 0.95 | 3.69 | 4.30 | 0.00 | 13.03 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.387 | 3.868 | 3.138 | 0.000 | 0.459 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 110 | 100 | 250 | 0 | 597 | 0 | 0 | 61 | 0 |
N.S. |
1 | 0.98 | 0.89 | 2.23 | 0.00 | 5.33 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.410 | 0.251 | 3.657 | 0.000 | 0.648 | 0.000 | 0.000 | 0.418 | 0.000 |