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 | C | A | C | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 53 | 39 | 295 | 43 | 57 | 0 | 0 | 7 | 0 |
N.S. |
1 | 1.36 | 1.00 | 7.56 | 1.10 | 1.46 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.354 | 0.057 | 0.378 | 0.074 | 0.078 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | C | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 55 | 33 | 454 | 43 | 69 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.57 | 0.94 | 12.97 | 1.23 | 1.97 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.360 | 0.033 | 1.047 | 0.082 | 0.075 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 56 | 43 | 0 | 47 | 65 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.27 | 0.98 | 0.00 | 1.07 | 1.48 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.363 | 0.040 | 0.000 | 0.077 | 0.078 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | C | A | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 53 | 37 | 321 | 32 | 65 | 0 | 0 | 7 | 0 |
N.S. |
1 | 1.36 | 0.95 | 8.23 | 0.82 | 1.67 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.350 | 0.060 | 0.688 | 0.146 | 0.088 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | C | A | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 55 | 33 | 478 | 32 | 77 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.57 | 0.94 | 13.66 | 0.91 | 2.20 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.348 | 0.041 | 1.445 | 0.146 | 0.094 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | A | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 56 | 43 | 0 | 36 | 73 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.27 | 0.98 | 0.00 | 0.82 | 1.66 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.350 | 0.038 | 0.000 | 0.148 | 0.078 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 50 | 35 | 24 | 54 | 101 | 0 | 0 | 5 | 20 |
N.S. |
1 | 1.28 | 0.90 | 0.62 | 1.38 | 2.59 | 0.00 | 0.00 | 0.13 | 0.51 |
time (sec) |
N/A | 0.346 | 0.012 | 0.252 | 0.117 | 0.077 | 0.000 | 0.000 | 0.158 | 27.746 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | A | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 52 | 49 | 76 | 56 | 102 | 0 | 0 | 7 | 0 |
N.S. |
1 | 1.27 | 1.20 | 1.85 | 1.37 | 2.49 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.349 | 0.016 | 0.417 | 0.112 | 0.077 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 54 | 47 | 47 | 57 | 129 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.46 | 1.27 | 1.27 | 1.54 | 3.49 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.358 | 0.016 | 0.463 | 0.114 | 0.078 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 55 | 55 | 43 | 61 | 116 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.20 | 1.20 | 0.93 | 1.33 | 2.52 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.362 | 0.017 | 3.245 | 0.114 | 0.082 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 50 | 45 | 24 | 49 | 101 | 0 | 0 | 5 | 22 |
N.S. |
1 | 1.28 | 1.15 | 0.62 | 1.26 | 2.59 | 0.00 | 0.00 | 0.13 | 0.56 |
time (sec) |
N/A | 0.353 | 0.014 | 0.273 | 0.112 | 0.079 | 0.000 | 0.000 | 0.158 | 27.322 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | A | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 52 | 49 | 76 | 51 | 102 | 0 | 0 | 7 | 0 |
N.S. |
1 | 1.27 | 1.20 | 1.85 | 1.24 | 2.49 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.352 | 0.017 | 0.424 | 0.115 | 0.089 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 54 | 47 | 47 | 59 | 127 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.46 | 1.27 | 1.27 | 1.59 | 3.43 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.377 | 0.018 | 0.485 | 0.113 | 0.079 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 55 | 55 | 43 | 61 | 116 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.20 | 1.20 | 0.93 | 1.33 | 2.52 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.383 | 0.019 | 1.789 | 0.113 | 0.077 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | C | A | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 53 | 38 | 314 | 31 | 84 | 0 | 0 | 7 | 0 |
N.S. |
1 | 1.39 | 1.00 | 8.26 | 0.82 | 2.21 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.341 | 0.027 | 0.680 | 0.153 | 0.433 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | C | A | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 55 | 33 | 480 | 32 | 106 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.57 | 0.94 | 13.71 | 0.91 | 3.03 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.343 | 0.029 | 0.837 | 0.141 | 0.084 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | A | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 56 | 43 | 0 | 36 | 92 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.30 | 1.00 | 0.00 | 0.84 | 2.14 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.341 | 0.034 | 0.000 | 0.143 | 0.124 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | C | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 53 | 38 | 293 | 37 | 76 | 0 | 0 | 7 | 0 |
N.S. |
1 | 1.39 | 1.00 | 7.71 | 0.97 | 2.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.347 | 0.018 | 0.323 | 0.077 | 0.077 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | C | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 55 | 33 | 456 | 45 | 97 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.57 | 0.94 | 13.03 | 1.29 | 2.77 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.365 | 0.027 | 0.460 | 0.073 | 0.079 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 56 | 43 | 0 | 47 | 84 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.30 | 1.00 | 0.00 | 1.09 | 1.95 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.356 | 0.030 | 0.000 | 0.077 | 0.079 | 0.000 | 0.000 | 0.162 | 0.000 |
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 | 50 | 50 | 33 | 66 | 112 | 258 | 0 | 94 | 89 | 31 |
N.S. |
1 | 1.00 | 0.66 | 1.32 | 2.24 | 5.16 | 0.00 | 1.88 | 1.78 | 0.62 |
time (sec) |
N/A | 0.249 | 0.015 | 9.418 | 0.043 | 0.072 | 0.000 | 0.165 | 0.166 | 26.362 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 14 | 12 | 62 | 14 | 37 | 10 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 0.92 | 4.77 | 1.08 | 2.85 | 0.77 | 0.69 |
time (sec) |
N/A | 0.218 | 0.015 | 8.315 | 0.031 | 0.074 | 0.209 | 0.109 | 0.157 | 26.439 |
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 | 17 | 17 | 11 | 14 | 13 | 9 | 94 | 13 | 8 | 9 |
N.S. |
1 | 1.00 | 0.65 | 0.82 | 0.76 | 0.53 | 5.53 | 0.76 | 0.47 | 0.53 |
time (sec) |
N/A | 0.162 | 0.005 | 0.167 | 0.026 | 0.077 | 0.875 | 0.122 | 0.152 | 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 | 27 | 28 | 26 | 25 | 24 | 23 | 27 | 24 | 29 | 25 |
N.S. |
1 | 1.04 | 0.96 | 0.93 | 0.89 | 0.85 | 1.00 | 0.89 | 1.07 | 0.93 |
time (sec) |
N/A | 0.207 | 0.008 | 0.073 | 0.030 | 0.073 | 0.086 | 0.108 | 0.148 | 0.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 3 | 3 | 22 | 4 | 3 | 20 | 0 | 3 | 26 | 3 |
N.S. |
1 | 1.00 | 7.33 | 1.33 | 1.00 | 6.67 | 0.00 | 1.00 | 8.67 | 1.00 |
time (sec) |
N/A | 0.187 | 0.026 | 0.056 | 0.107 | 0.069 | 0.000 | 0.106 | 0.165 | 25.809 |
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 | 24 | 35 | 30 | 23 | 17 | 22 | 22 | 22 | 17 | 17 |
N.S. |
1 | 1.46 | 1.25 | 0.96 | 0.71 | 0.92 | 0.92 | 0.92 | 0.71 | 0.71 |
time (sec) |
N/A | 0.221 | 0.005 | 0.078 | 0.026 | 0.068 | 0.055 | 0.127 | 0.153 | 25.955 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 33 | 23 | 21 | 23 | 22 | 29 | 23 | 27 | 25 |
N.S. |
1 | 1.32 | 0.92 | 0.84 | 0.92 | 0.88 | 1.16 | 0.92 | 1.08 | 1.00 |
time (sec) |
N/A | 0.181 | 0.009 | 0.069 | 0.031 | 0.063 | 0.094 | 0.110 | 0.149 | 0.069 |
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 | 34 | 37 | 30 | 25 | 24 | 20 | 22 | 30 | 24 | 20 |
N.S. |
1 | 1.09 | 0.88 | 0.74 | 0.71 | 0.59 | 0.65 | 0.88 | 0.71 | 0.59 |
time (sec) |
N/A | 0.193 | 0.011 | 0.076 | 0.032 | 0.068 | 0.056 | 0.118 | 0.153 | 25.908 |
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 | 40 | 45 | 40 | 25 | 28 | 24 | 27 | 42 | 28 | 22 |
N.S. |
1 | 1.12 | 1.00 | 0.62 | 0.70 | 0.60 | 0.68 | 1.05 | 0.70 | 0.55 |
time (sec) |
N/A | 0.202 | 0.017 | 0.096 | 0.026 | 0.067 | 0.063 | 0.114 | 0.150 | 0.114 |
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 | 31 | 32 | 31 | 26 | 25 | 25 | 26 | 25 | 29 | 25 |
N.S. |
1 | 1.03 | 1.00 | 0.84 | 0.81 | 0.81 | 0.84 | 0.81 | 0.94 | 0.81 |
time (sec) |
N/A | 0.220 | 0.016 | 0.083 | 0.106 | 0.072 | 0.079 | 0.114 | 0.151 | 26.004 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 23 | 0 | 22 | 20 | 22 | 20 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.00 | 0.85 | 0.77 | 0.85 | 0.77 | 0.85 |
time (sec) |
N/A | 0.172 | 0.023 | 0.030 | 0.000 | 0.072 | 4.180 | 0.114 | 0.161 | 0.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 23 | 0 | 22 | 20 | 22 | 20 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.00 | 0.85 | 0.77 | 0.85 | 0.77 | 0.85 |
time (sec) |
N/A | 0.177 | 0.023 | 0.031 | 0.000 | 0.072 | 2.820 | 0.116 | 0.160 | 27.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 23 | 0 | 22 | 20 | 22 | 19 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.00 | 0.85 | 0.77 | 0.85 | 0.73 | 0.85 |
time (sec) |
N/A | 0.181 | 0.027 | 0.033 | 0.000 | 0.078 | 3.485 | 0.111 | 0.154 | 27.098 |
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 | 43 | 42 | 43 | 52 | 0 | 28 | 0 | 40 | 29 | 37 |
N.S. |
1 | 0.98 | 1.00 | 1.21 | 0.00 | 0.65 | 0.00 | 0.93 | 0.67 | 0.86 |
time (sec) |
N/A | 0.207 | 0.037 | 0.058 | 0.000 | 0.077 | 0.000 | 0.138 | 0.152 | 27.659 |
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 | 21 | 21 | 15 | 14 | 13 | 14 | 105 | 13 | 11 | 9 |
N.S. |
1 | 1.00 | 0.71 | 0.67 | 0.62 | 0.67 | 5.00 | 0.62 | 0.52 | 0.43 |
time (sec) |
N/A | 0.165 | 0.007 | 0.175 | 0.027 | 0.074 | 1.389 | 0.113 | 0.163 | 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 | 13 | 13 | 12 | 13 | 24 | 14 | 10 | 14 | 12 | 13 |
N.S. |
1 | 1.00 | 0.92 | 1.00 | 1.85 | 1.08 | 0.77 | 1.08 | 0.92 | 1.00 |
time (sec) |
N/A | 0.161 | 0.011 | 0.065 | 0.031 | 0.075 | 0.123 | 0.121 | 0.169 | 27.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 6 | 7 | 14 | 6 | 3 | 6 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 1.17 | 2.33 | 1.00 | 0.50 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.167 | 0.004 | 0.043 | 0.032 | 0.069 | 0.052 | 0.111 | 0.168 | 27.253 |
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 | 32 | 47 | 38 | 28 | 33 | 38 | 184 | 33 | 24 | 26 |
N.S. |
1 | 1.47 | 1.19 | 0.88 | 1.03 | 1.19 | 5.75 | 1.03 | 0.75 | 0.81 |
time (sec) |
N/A | 0.418 | 0.021 | 0.050 | 0.031 | 0.074 | 0.361 | 0.118 | 0.153 | 0.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 17 | 16 | 16 | 15 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.00 | 0.94 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.170 | 0.006 | 0.260 | 0.110 | 0.073 | 0.072 | 0.110 | 0.160 | 0.058 |
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 | 20 | 20 | 20 | 22 | 29 | 23 | 34 | 23 | 22 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.45 | 1.15 | 1.70 | 1.15 | 1.10 | 0.95 |
time (sec) |
N/A | 0.169 | 0.026 | 0.094 | 0.029 | 0.072 | 0.133 | 0.121 | 0.154 | 27.440 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 31 | 34 | 33 | 33 | 32 | 73 | 41 | 29 |
N.S. |
1 | 1.00 | 0.89 | 0.97 | 0.94 | 0.94 | 0.91 | 2.09 | 1.17 | 0.83 |
time (sec) |
N/A | 0.176 | 0.011 | 0.174 | 0.028 | 0.076 | 0.092 | 0.135 | 0.153 | 0.122 |
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 | 12 | 13 | 12 | 13 | 12 | 12 | 15 | 12 | 15 | 12 |
N.S. |
1 | 1.08 | 1.00 | 1.08 | 1.00 | 1.00 | 1.25 | 1.00 | 1.25 | 1.00 |
time (sec) |
N/A | 0.174 | 0.007 | 0.062 | 0.026 | 0.079 | 0.053 | 0.115 | 0.163 | 0.072 |
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 | 42 | 27 | 29 | 28 | 28 | 27 | 29 | 36 | 40 |
N.S. |
1 | 1.17 | 0.75 | 0.81 | 0.78 | 0.78 | 0.75 | 0.81 | 1.00 | 1.11 |
time (sec) |
N/A | 0.217 | 0.015 | 0.134 | 0.028 | 0.072 | 0.070 | 0.123 | 0.158 | 27.554 |
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 | 54 | 66 | 54 | 43 | 42 | 42 | 48 | 43 | 50 | 56 |
N.S. |
1 | 1.22 | 1.00 | 0.80 | 0.78 | 0.78 | 0.89 | 0.80 | 0.93 | 1.04 |
time (sec) |
N/A | 0.236 | 0.022 | 0.145 | 0.025 | 0.070 | 0.081 | 0.116 | 0.153 | 27.082 |
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 | 33 | 33 | 30 | 52 | 42 | 41 | 31 | 55 | 46 |
N.S. |
1 | 0.94 | 0.94 | 0.86 | 1.49 | 1.20 | 1.17 | 0.89 | 1.57 | 1.31 |
time (sec) |
N/A | 0.195 | 0.034 | 0.088 | 0.032 | 0.067 | 0.102 | 0.124 | 0.155 | 26.965 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 33 | 44 | 30 | 74 | 64 | 63 | 31 | 83 | 73 |
N.S. |
1 | 0.94 | 1.26 | 0.86 | 2.11 | 1.83 | 1.80 | 0.89 | 2.37 | 2.09 |
time (sec) |
N/A | 0.202 | 0.027 | 0.223 | 0.026 | 0.068 | 0.118 | 0.136 | 0.164 | 25.986 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 14 | 13 | 13 | 10 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 0.67 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.197 | 0.006 | 0.309 | 0.029 | 0.069 | 0.052 | 0.116 | 0.150 | 26.469 |
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 | 31 | 29 | 21 | 26 | 31 | 21 | 26 | 32 | 27 | 25 |
N.S. |
1 | 0.94 | 0.68 | 0.84 | 1.00 | 0.68 | 0.84 | 1.03 | 0.87 | 0.81 |
time (sec) |
N/A | 0.203 | 0.016 | 0.293 | 0.037 | 0.076 | 0.115 | 0.136 | 0.158 | 26.100 |
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 | 44 | 42 | 30 | 61 | 44 | 47 | 185 | 44 | 65 | 52 |
N.S. |
1 | 0.95 | 0.68 | 1.39 | 1.00 | 1.07 | 4.20 | 1.00 | 1.48 | 1.18 |
time (sec) |
N/A | 0.213 | 0.025 | 0.340 | 0.032 | 0.078 | 0.421 | 0.110 | 0.148 | 26.202 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 19 | 24 | 19 | 31 | 45 | 18 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.33 | 1.06 | 1.72 | 2.50 | 1.00 | 1.00 |
time (sec) |
N/A | 0.184 | 0.078 | 0.146 | 0.035 | 0.073 | 0.422 | 0.130 | 0.152 | 26.356 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 24 | 0 | 121 | 99 | 26 | 31 | 71 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.00 | 3.78 | 3.09 | 0.81 | 0.97 | 2.22 |
time (sec) |
N/A | 0.190 | 0.088 | 0.369 | 0.000 | 0.079 | 2.355 | 0.110 | 0.152 | 26.449 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | A | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 135 | 112 | 112 | 0 | 480 | 175 | 239 | 90 | 153 |
N.S. |
1 | 0.94 | 0.78 | 0.78 | 0.00 | 3.33 | 1.22 | 1.66 | 0.62 | 1.06 |
time (sec) |
N/A | 0.345 | 0.118 | 0.468 | 0.000 | 0.097 | 27.908 | 0.122 | 0.155 | 28.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 234 | 167 | 113 | 0 | 160 | 133 | 170 | 145 | 95 |
N.S. |
1 | 1.44 | 1.02 | 0.69 | 0.00 | 0.98 | 0.82 | 1.04 | 0.89 | 0.58 |
time (sec) |
N/A | 0.487 | 0.133 | 1.029 | 0.000 | 0.080 | 15.315 | 0.116 | 0.159 | 28.218 |
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 | 27 | 32 | 34 | 29 | 33 | 28 | 116 | 53 | 27 | 27 |
N.S. |
1 | 1.19 | 1.26 | 1.07 | 1.22 | 1.04 | 4.30 | 1.96 | 1.00 | 1.00 |
time (sec) |
N/A | 0.225 | 0.075 | 0.172 | 0.036 | 0.076 | 1.859 | 0.113 | 0.160 | 27.476 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 45 | 40 | 41 | 0 | 143 | 204 | 38 | 36 | 45 |
N.S. |
1 | 1.12 | 1.00 | 1.02 | 0.00 | 3.58 | 5.10 | 0.95 | 0.90 | 1.12 |
time (sec) |
N/A | 0.208 | 0.051 | 0.305 | 0.000 | 0.087 | 4.250 | 0.112 | 0.148 | 26.377 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | A | B | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 152 | 129 | 118 | 0 | 149 | 245 | 257 | 105 | 174 |
N.S. |
1 | 1.02 | 0.87 | 0.79 | 0.00 | 1.00 | 1.64 | 1.72 | 0.70 | 1.17 |
time (sec) |
N/A | 0.360 | 0.099 | 0.509 | 0.000 | 0.083 | 30.168 | 0.132 | 0.157 | 28.488 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 251 | 208 | 118 | 0 | 156 | 228 | 178 | 179 | 176 |
N.S. |
1 | 1.49 | 1.23 | 0.70 | 0.00 | 0.92 | 1.35 | 1.05 | 1.06 | 1.04 |
time (sec) |
N/A | 0.478 | 0.113 | 0.936 | 0.000 | 0.094 | 16.894 | 0.136 | 0.155 | 29.194 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 20 | 0 | 21 | 22 | 0 | 18 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.91 | 0.00 | 0.95 | 1.00 | 0.00 | 0.82 | 0.86 |
time (sec) |
N/A | 0.198 | 0.087 | 0.141 | 0.000 | 0.069 | 0.103 | 0.000 | 0.148 | 27.382 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 42 | 42 | 38 | 37 | 39 | 22 | 0 | 36 | 37 |
N.S. |
1 | 1.02 | 1.02 | 0.93 | 0.90 | 0.95 | 0.54 | 0.00 | 0.88 | 0.90 |
time (sec) |
N/A | 0.267 | 0.131 | 0.092 | 0.112 | 0.071 | 0.105 | 0.000 | 0.156 | 27.466 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 42 | 42 | 38 | 0 | 39 | 22 | 0 | 36 | 37 |
N.S. |
1 | 1.02 | 1.02 | 0.93 | 0.00 | 0.95 | 0.54 | 0.00 | 0.88 | 0.90 |
time (sec) |
N/A | 0.239 | 0.252 | 0.154 | 0.000 | 0.069 | 0.102 | 0.000 | 0.162 | 27.442 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 44 | 44 | 40 | 0 | 41 | 19 | 0 | 36 | 37 |
N.S. |
1 | 1.05 | 1.05 | 0.95 | 0.00 | 0.98 | 0.45 | 0.00 | 0.86 | 0.88 |
time (sec) |
N/A | 0.257 | 0.109 | 0.159 | 0.000 | 0.074 | 0.095 | 0.000 | 0.158 | 27.126 |
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 | 37 | 32 | 21 | 17 | 21 | 27 | 22 | 17 | 21 |
N.S. |
1 | 1.16 | 1.00 | 0.66 | 0.53 | 0.66 | 0.84 | 0.69 | 0.53 | 0.66 |
time (sec) |
N/A | 0.208 | 0.006 | 0.106 | 0.029 | 0.069 | 0.065 | 0.108 | 0.160 | 26.438 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 59 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 1.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.240 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 60 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 1.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.236 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 62 | 0 | 0 | 0 | 0 | 32 | 21 | 0 |
N.S. |
1 | 1.00 | 1.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.49 | 0.00 |
time (sec) |
N/A | 0.245 | 0.018 | 0.000 | 0.000 | 0.000 | 0.000 | 0.111 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 121 | 121 | 102 | 0 | 0 | 0 | 0 | 212 | 0 |
N.S. |
1 | 1.07 | 1.07 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 1.88 | 0.00 |
time (sec) |
N/A | 0.391 | 0.114 | 0.173 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 73 | 109 | 111 | 0 | 0 | 0 | 119 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.35 | 1.37 | 0.00 | 0.00 | 0.00 | 1.47 | 0.00 |
time (sec) |
N/A | 0.337 | 0.065 | 0.907 | 0.034 | 0.000 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 5 | 12 | 8 | 10 | 0 | 21 | 4 |
N.S. |
1 | 1.00 | 1.00 | 0.56 | 1.33 | 0.89 | 1.11 | 0.00 | 2.33 | 0.44 |
time (sec) |
N/A | 0.168 | 0.008 | 0.266 | 0.027 | 0.071 | 1.093 | 0.000 | 0.158 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 35 | 47 | 82 | 0 | 0 | 0 | 106 | 59 |
N.S. |
1 | 1.00 | 0.81 | 1.09 | 1.91 | 0.00 | 0.00 | 0.00 | 2.47 | 1.37 |
time (sec) |
N/A | 0.279 | 0.025 | 0.392 | 0.029 | 0.000 | 0.000 | 0.000 | 0.154 | 27.576 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 31 | 31 | 49 | 0 | 228 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 1.03 | 1.03 | 1.63 | 0.00 | 7.60 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.288 | 0.018 | 0.352 | 0.028 | 0.000 | 62.562 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 7 | 7 | 7 | 8 | 7 | 7 | 0 | 7 | 7 | 7 |
N.S. |
1 | 1.00 | 1.00 | 1.14 | 1.00 | 1.00 | 0.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.179 | 0.328 | 0.329 | 0.077 | 0.070 | 0.000 | 0.121 | 0.168 | 28.253 |
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 | 68 | 77 | 63 | 57 | 57 | 58 | 46 | 59 | 60 | 59 |
N.S. |
1 | 1.13 | 0.93 | 0.84 | 0.84 | 0.85 | 0.68 | 0.87 | 0.88 | 0.87 |
time (sec) |
N/A | 0.333 | 0.044 | 0.575 | 0.108 | 0.074 | 0.124 | 0.124 | 0.151 | 28.227 |
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 | 29 | 29 | 29 | 24 | 23 | 31 | 37 | 23 | 23 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.79 | 1.07 | 1.28 | 0.79 | 0.79 | 0.79 |
time (sec) |
N/A | 0.217 | 0.017 | 0.047 | 0.027 | 0.081 | 2.347 | 0.112 | 0.152 | 0.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 19 | 18 | 18 | 14 | 47 | 25 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.00 | 0.78 | 2.61 | 1.39 | 1.00 |
time (sec) |
N/A | 0.166 | 0.005 | 0.145 | 0.027 | 0.080 | 0.053 | 0.122 | 0.157 | 27.111 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 21 | 22 | 25 | 21 | 15 | 55 | 29 | 21 |
N.S. |
1 | 1.00 | 0.78 | 0.81 | 0.93 | 0.78 | 0.56 | 2.04 | 1.07 | 0.78 |
time (sec) |
N/A | 0.181 | 0.006 | 0.174 | 0.027 | 0.072 | 0.069 | 0.128 | 0.152 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 64 | 60 | 56 | 54 | 54 | 41 | 56 | 80 | 55 |
N.S. |
1 | 1.12 | 1.05 | 0.98 | 0.95 | 0.95 | 0.72 | 0.98 | 1.40 | 0.96 |
time (sec) |
N/A | 0.284 | 0.059 | 0.725 | 0.117 | 0.080 | 0.106 | 0.249 | 0.161 | 27.835 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 65 | 62 | 129 | 0 | 0 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.08 | 1.03 | 2.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.425 | 0.014 | 0.507 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 73 | 239 | 146 | 0 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.20 | 3.92 | 2.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.416 | 0.063 | 0.532 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 175 | 373 | 121 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.06 | 2.26 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.588 | 0.245 | 0.553 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 134 | 0 | 0 | 37 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 4.62 | 0.00 | 0.00 | 1.28 | 0.00 | 0.00 | 1.45 | 0.00 |
time (sec) |
N/A | 0.205 | 0.996 | 0.000 | 0.000 | 0.106 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 134 | 0 | 0 | 36 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.00 | 4.62 | 0.00 | 0.00 | 1.24 | 0.00 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.212 | 0.896 | 0.000 | 0.000 | 0.078 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 15 | 10 | 10 | 8 | 10 | 10 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.59 | 0.59 | 0.47 | 0.59 | 0.59 | 1.00 |
time (sec) |
N/A | 0.164 | 0.006 | 0.138 | 0.030 | 0.052 | 0.040 | 0.111 | 0.160 | 0.071 |
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 | 27 | 27 | 25 | 26 | 16 | 20 | 65 | 16 | 17 | 49 |
N.S. |
1 | 1.00 | 0.93 | 0.96 | 0.59 | 0.74 | 2.41 | 0.59 | 0.63 | 1.81 |
time (sec) |
N/A | 0.173 | 0.032 | 0.067 | 0.027 | 0.075 | 0.502 | 0.108 | 0.157 | 27.449 |
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 | 25 | 38 | 25 | 28 | 26 | 25 | 0 | 26 | 34 | 27 |
N.S. |
1 | 1.52 | 1.00 | 1.12 | 1.04 | 1.00 | 0.00 | 1.04 | 1.36 | 1.08 |
time (sec) |
N/A | 0.261 | 0.023 | 0.118 | 0.026 | 0.069 | 0.000 | 0.115 | 0.152 | 27.711 |
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 | 26 | 26 | 22 | 26 | 24 | 23 | 26 | 24 | 22 | 20 |
N.S. |
1 | 1.00 | 0.85 | 1.00 | 0.92 | 0.88 | 1.00 | 0.92 | 0.85 | 0.77 |
time (sec) |
N/A | 0.227 | 0.027 | 0.169 | 0.074 | 0.069 | 3.321 | 0.116 | 0.159 | 27.526 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.221 | 22.208 | 0.128 | 0.055 | 0.060 | 0.259 | 0.110 | 0.152 | 27.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 10 | 8 | 10 | 10 | 7 | 10 | 15 | 10 |
N.S. |
1 | 1.00 | 1.25 | 1.00 | 1.25 | 1.25 | 0.88 | 1.25 | 1.88 | 1.25 |
time (sec) |
N/A | 0.209 | 16.527 | 0.127 | 0.050 | 0.071 | 0.245 | 0.117 | 0.168 | 26.877 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 8 | 6 | 8 | 8 | 7 | 8 | 20 | 8 |
N.S. |
1 | 1.00 | 1.33 | 1.00 | 1.33 | 1.33 | 1.17 | 1.33 | 3.33 | 1.33 |
time (sec) |
N/A | 0.185 | 0.013 | 0.121 | 0.051 | 0.063 | 0.283 | 0.099 | 0.243 | 28.355 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.215 | 0.094 | 0.125 | 0.056 | 0.063 | 0.616 | 0.106 | 0.187 | 27.395 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 14 | 10 | 12 | 14 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.40 | 1.00 | 1.20 | 1.40 | 1.20 |
time (sec) |
N/A | 0.212 | 24.092 | 0.128 | 0.055 | 0.063 | 0.517 | 0.102 | 0.162 | 27.240 |
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 | 13 | 13 | 13 | 10 | 9 | 11 | 10 | 11 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.69 | 0.85 | 0.77 | 0.85 | 0.85 | 0.85 |
time (sec) |
N/A | 0.186 | 0.018 | 0.069 | 0.058 | 0.066 | 0.053 | 0.112 | 0.154 | 26.822 |
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 | 9 | 9 | 10 | 11 | 10 | 10 | 8 | 14 | 10 | 10 |
N.S. |
1 | 1.00 | 1.11 | 1.22 | 1.11 | 1.11 | 0.89 | 1.56 | 1.11 | 1.11 |
time (sec) |
N/A | 0.251 | 0.105 | 0.299 | 0.059 | 0.076 | 0.065 | 0.111 | 0.168 | 27.415 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 20 | 0 | 13 | 15 | 0 | 29 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.54 | 0.00 | 1.00 | 1.15 | 0.00 | 2.23 | 1.00 |
time (sec) |
N/A | 0.348 | 0.079 | 0.338 | 0.000 | 0.069 | 1.387 | 0.000 | 0.167 | 26.863 |
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 | 67 | 73 | 53 | 107 | 67 | 48 | 53 | 88 | 87 | 63 |
N.S. |
1 | 1.09 | 0.79 | 1.60 | 1.00 | 0.72 | 0.79 | 1.31 | 1.30 | 0.94 |
time (sec) |
N/A | 0.337 | 0.045 | 0.159 | 0.026 | 0.082 | 26.761 | 0.141 | 0.165 | 0.398 |
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 | 52 | 53 | 81 | 68 | 49 | 53 | 53 | 50 | 38 |
N.S. |
1 | 1.04 | 1.06 | 1.62 | 1.36 | 0.98 | 1.06 | 1.06 | 1.00 | 0.76 |
time (sec) |
N/A | 0.299 | 0.051 | 0.175 | 0.036 | 0.078 | 26.710 | 0.135 | 0.166 | 26.895 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 17 | 19 | 18 | 18 | 17 | 47 | 26 | 18 |
N.S. |
1 | 1.00 | 0.81 | 0.90 | 0.86 | 0.86 | 0.81 | 2.24 | 1.24 | 0.86 |
time (sec) |
N/A | 0.192 | 0.007 | 0.153 | 0.026 | 0.069 | 0.052 | 0.119 | 0.157 | 0.062 |
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 | 50 | 53 | 80 | 68 | 49 | 53 | 53 | 35 | 38 |
N.S. |
1 | 1.00 | 1.06 | 1.60 | 1.36 | 0.98 | 1.06 | 1.06 | 0.70 | 0.76 |
time (sec) |
N/A | 0.297 | 0.045 | 0.162 | 0.027 | 0.082 | 26.921 | 0.131 | 0.164 | 26.295 |
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 | 69 | 69 | 64 | 108 | 67 | 48 | 53 | 88 | 89 | 63 |
N.S. |
1 | 1.00 | 0.93 | 1.57 | 0.97 | 0.70 | 0.77 | 1.28 | 1.29 | 0.91 |
time (sec) |
N/A | 0.307 | 0.038 | 0.119 | 0.032 | 0.081 | 25.822 | 0.134 | 0.164 | 0.382 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 10 | 9 | 9 | 10 | 0 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.00 | 1.00 | 1.11 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.171 | 0.019 | 0.070 | 0.057 | 0.072 | 0.079 | 0.000 | 0.152 | 26.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 0 | 0 | 17 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.65 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.272 | 0.046 | 0.000 | 0.000 | 0.071 | 0.000 | 0.000 | 0.165 | 0.000 |