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 | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 16 | 10 | 15 | 9 | 14 | 10 | 9 | 14 | 11 |
N.S. |
1 | 1.60 | 1.00 | 1.50 | 0.90 | 1.40 | 1.00 | 0.90 | 1.40 | 1.10 |
time (sec) |
N/A | 0.286 | 0.021 | 0.105 | 0.090 | 0.087 | 0.053 | 0.111 | 0.670 | 3.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 62 | 32 | 53 | 49 | 24 | 49 | 44 | 129 |
N.S. |
1 | 0.00 | 2.21 | 1.14 | 1.89 | 1.75 | 0.86 | 1.75 | 1.57 | 4.61 |
time (sec) |
N/A | 0.000 | 0.126 | 3.526 | 0.147 | 0.106 | 0.084 | 0.171 | 0.165 | 3.826 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 110 | 19 | 16 | 19 | 28 | 15 | 0 | 331 | 20 |
N.S. |
1 | 5.79 | 1.00 | 0.84 | 1.00 | 1.47 | 0.79 | 0.00 | 17.42 | 1.05 |
time (sec) |
N/A | 0.709 | 0.391 | 0.657 | 0.210 | 0.115 | 6.845 | 0.000 | 0.263 | 3.369 |
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 | 22 | 38 | 38 | 38 | 37 | 41 | 42 | 37 | 38 | 37 |
N.S. |
1 | 1.73 | 1.73 | 1.73 | 1.68 | 1.86 | 1.91 | 1.68 | 1.73 | 1.68 |
time (sec) |
N/A | 0.261 | 0.005 | 0.116 | 0.027 | 0.108 | 0.036 | 0.111 | 0.164 | 3.311 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | F(-2) | B | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 22 | 20 | 21 | 69 | 0 | 157 | 1136 | 0 |
N.S. |
1 | 0.00 | 0.88 | 0.80 | 0.84 | 2.76 | 0.00 | 6.28 | 45.44 | 0.00 |
time (sec) |
N/A | 0.000 | 1.192 | 4.335 | 0.311 | 0.094 | 0.000 | 1.409 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 73 | 34 | 21 | 21 | 21 | 20 | 21 | 21 | 0 |
N.S. |
1 | 2.92 | 1.36 | 0.84 | 0.84 | 0.84 | 0.80 | 0.84 | 0.84 | 0.00 |
time (sec) |
N/A | 0.850 | 0.118 | 0.211 | 0.141 | 0.093 | 0.082 | 0.119 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | B | B | B | B | F | F(-1) |
verified | N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 41 | 0 | 37 | 220 | 96 | 94 | 137 | 0 | 0 |
N.S. |
1 | 1.64 | 0.00 | 1.48 | 8.80 | 3.84 | 3.76 | 5.48 | 0.00 | 0.00 |
time (sec) |
N/A | 2.666 | 0.000 | 53.864 | 0.387 | 0.128 | 1.538 | 1.882 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | C | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 183 | 141 | 145 | 327 | 147 | 163 | 178 | 194 | 142 |
N.S. |
1 | 6.10 | 4.70 | 4.83 | 10.90 | 4.90 | 5.43 | 5.93 | 6.47 | 4.73 |
time (sec) |
N/A | 0.992 | 5.753 | 16.737 | 0.083 | 0.100 | 0.160 | 0.118 | 0.165 | 0.124 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 33 | 33 | 30 | 33 | 48 | 27 | 33 | 33 | 29 |
N.S. |
1 | 1.38 | 1.38 | 1.25 | 1.38 | 2.00 | 1.12 | 1.38 | 1.38 | 1.21 |
time (sec) |
N/A | 10.706 | 0.293 | 46.786 | 0.109 | 0.095 | 2.094 | 0.252 | 0.161 | 3.409 |
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 | 28 | 19 | 26 | 17 | 18 | 20 | 19 | 18 | 19 | 18 |
N.S. |
1 | 0.68 | 0.93 | 0.61 | 0.64 | 0.71 | 0.68 | 0.64 | 0.68 | 0.64 |
time (sec) |
N/A | 1.376 | 0.505 | 0.073 | 0.062 | 0.091 | 0.074 | 0.130 | 0.157 | 0.065 |
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 | 21 | 30 | 21 | 18 | 17 | 42 | 15 | 44 | 24 | 17 |
N.S. |
1 | 1.43 | 1.00 | 0.86 | 0.81 | 2.00 | 0.71 | 2.10 | 1.14 | 0.81 |
time (sec) |
N/A | 0.376 | 0.021 | 0.093 | 0.025 | 0.087 | 0.081 | 0.116 | 0.153 | 3.273 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 20 | 18 | 20 | 20 | 20 | 20 | 22 | 24 |
N.S. |
1 | 0.00 | 0.80 | 0.72 | 0.80 | 0.80 | 0.80 | 0.80 | 0.88 | 0.96 |
time (sec) |
N/A | 0.000 | 0.403 | 0.096 | 0.069 | 0.087 | 0.063 | 0.116 | 0.151 | 3.323 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | B | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 24 | 0 | 46 | 24 | 0 | 310 | 23 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 0.00 | 1.84 | 0.96 | 0.00 | 12.40 | 0.92 |
time (sec) |
N/A | 0.000 | 0.898 | 2.077 | 0.000 | 0.122 | 0.179 | 0.000 | 0.346 | 3.442 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | A | F(-2) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 63 | 33 | 33 | 39 | 35 | 0 | 39 | 97 | 34 |
N.S. |
1 | 2.17 | 1.14 | 1.14 | 1.34 | 1.21 | 0.00 | 1.34 | 3.34 | 1.17 |
time (sec) |
N/A | 1.923 | 0.318 | 12.883 | 0.095 | 0.094 | 0.000 | 0.940 | 0.186 | 3.655 |
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 | 27 | 47 | 51 | 44 | 43 | 64 | 44 | 0 | 55 | 44 |
N.S. |
1 | 1.74 | 1.89 | 1.63 | 1.59 | 2.37 | 1.63 | 0.00 | 2.04 | 1.63 |
time (sec) |
N/A | 0.323 | 0.625 | 0.329 | 0.113 | 0.088 | 0.152 | 0.000 | 0.178 | 3.292 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | F(-1) | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 20 | 37 | 53 | 0 | 37 | 21 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.87 | 1.61 | 2.30 | 0.00 | 1.61 | 0.91 | 0.00 |
time (sec) |
N/A | 0.000 | 1.342 | 0.807 | 0.180 | 0.091 | 0.000 | 0.132 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 27 | 32 | 28 | 30 | 24 | 28 | 31 | 30 |
N.S. |
1 | 0.00 | 1.00 | 1.19 | 1.04 | 1.11 | 0.89 | 1.04 | 1.15 | 1.11 |
time (sec) |
N/A | 0.000 | 0.103 | 4.172 | 0.077 | 0.088 | 0.464 | 0.224 | 0.158 | 3.640 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 171 | 47 | 32 | 152 | 52 | 26 | 34 | 124 | 34 |
N.S. |
1 | 7.43 | 2.04 | 1.39 | 6.61 | 2.26 | 1.13 | 1.48 | 5.39 | 1.48 |
time (sec) |
N/A | 2.334 | 0.054 | 1.111 | 0.085 | 0.091 | 0.088 | 0.119 | 0.151 | 3.364 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 22 | 18 | 15 | 23 | 15 | 15 | 15 | 16 | 15 |
N.S. |
1 | 0.92 | 0.75 | 0.62 | 0.96 | 0.62 | 0.62 | 0.62 | 0.67 | 0.62 |
time (sec) |
N/A | 0.351 | 0.016 | 0.095 | 0.051 | 0.074 | 0.058 | 0.110 | 0.152 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 23 | 23 | 22 | 22 | 20 | 0 | 504 | 209 |
N.S. |
1 | 0.00 | 0.92 | 0.92 | 0.88 | 0.88 | 0.80 | 0.00 | 20.16 | 8.36 |
time (sec) |
N/A | 0.000 | 0.071 | 33.962 | 0.106 | 0.108 | 0.174 | 0.000 | 0.174 | 3.517 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 23 | 35 | 22 | 20 | 35 | 22 | 22 |
N.S. |
1 | 0.00 | 1.00 | 0.88 | 1.35 | 0.85 | 0.77 | 1.35 | 0.85 | 0.85 |
time (sec) |
N/A | 0.000 | 0.048 | 1.806 | 0.162 | 0.085 | 0.139 | 0.180 | 0.152 | 3.477 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 291 | 124 | 140 | 112 | 109 | 134 | 109 | 118 | 26 |
N.S. |
1 | 10.39 | 4.43 | 5.00 | 4.00 | 3.89 | 4.79 | 3.89 | 4.21 | 0.93 |
time (sec) |
N/A | 0.949 | 10.115 | 0.076 | 0.104 | 0.082 | 0.176 | 0.151 | 0.155 | 3.415 |
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 | 21 | 11 | 11 | 8 | 9 | 9 | 7 | 9 | 10 | 9 |
N.S. |
1 | 0.52 | 0.52 | 0.38 | 0.43 | 0.43 | 0.33 | 0.43 | 0.48 | 0.43 |
time (sec) |
N/A | 0.135 | 0.001 | 0.037 | 0.030 | 0.068 | 0.034 | 0.113 | 0.149 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 107 | 89 | 129 | 119 | 144 | 0 | 124 | 137 |
N.S. |
1 | 0.00 | 4.46 | 3.71 | 5.38 | 4.96 | 6.00 | 0.00 | 5.17 | 5.71 |
time (sec) |
N/A | 0.000 | 0.234 | 0.349 | 0.469 | 0.128 | 1.568 | 0.000 | 0.221 | 3.905 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F(-2) | A | F(-2) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 94 | 26 | 27 | 0 | 26 | 0 | 30 | 27 | 31 |
N.S. |
1 | 3.76 | 1.04 | 1.08 | 0.00 | 1.04 | 0.00 | 1.20 | 1.08 | 1.24 |
time (sec) |
N/A | 1.617 | 0.038 | 1.380 | 0.000 | 0.085 | 0.000 | 0.257 | 0.155 | 3.354 |
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 | 26 | 26 | 16 | 16 | 16 | 15 | 17 | 21 | 15 |
N.S. |
1 | 0.90 | 0.90 | 0.55 | 0.55 | 0.55 | 0.52 | 0.59 | 0.72 | 0.52 |
time (sec) |
N/A | 0.164 | 0.006 | 0.087 | 0.024 | 0.075 | 0.062 | 0.110 | 0.151 | 0.049 |
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 | 22 | 18 | 18 | 17 | 16 | 16 | 12 | 16 | 18 | 16 |
N.S. |
1 | 0.82 | 0.82 | 0.77 | 0.73 | 0.73 | 0.55 | 0.73 | 0.82 | 0.73 |
time (sec) |
N/A | 0.292 | 0.092 | 0.154 | 0.065 | 0.088 | 2.279 | 0.131 | 0.149 | 3.354 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 75 | 33 | 30 | 38 | 41 | 29 | 119 | 42 | 29 |
N.S. |
1 | 2.42 | 1.06 | 0.97 | 1.23 | 1.32 | 0.94 | 3.84 | 1.35 | 0.94 |
time (sec) |
N/A | 3.509 | 0.130 | 19.069 | 0.118 | 0.097 | 0.244 | 0.156 | 0.156 | 3.503 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 30 | 30 | 31 | 55 | 56 | 27 | 30 | 592 | 32 |
N.S. |
1 | 1.20 | 1.20 | 1.24 | 2.20 | 2.24 | 1.08 | 1.20 | 23.68 | 1.28 |
time (sec) |
N/A | 0.682 | 0.050 | 0.466 | 0.076 | 0.085 | 0.183 | 0.320 | 0.166 | 3.358 |
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 | 28 | 38 | 38 | 35 | 34 | 34 | 34 | 36 | 34 | 34 |
N.S. |
1 | 1.36 | 1.36 | 1.25 | 1.21 | 1.21 | 1.21 | 1.29 | 1.21 | 1.21 |
time (sec) |
N/A | 0.304 | 0.009 | 0.045 | 0.025 | 0.082 | 0.062 | 0.116 | 0.152 | 3.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 105 | 39 | 34 | 36 | 36 | 0 | 0 | 45 | 39 |
N.S. |
1 | 4.77 | 1.77 | 1.55 | 1.64 | 1.64 | 0.00 | 0.00 | 2.05 | 1.77 |
time (sec) |
N/A | 0.365 | 0.076 | 0.490 | 0.114 | 0.086 | 0.000 | 0.000 | 0.177 | 0.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 36 | 39 | 15 | 33 | 13 | 14 | 19 | 17 | 15 |
N.S. |
1 | 1.89 | 2.05 | 0.79 | 1.74 | 0.68 | 0.74 | 1.00 | 0.89 | 0.79 |
time (sec) |
N/A | 0.460 | 0.031 | 0.108 | 0.069 | 0.088 | 0.063 | 0.112 | 0.151 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | F | A | A | F | B | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 28 | 1052 | 0 | 39 | 39 | 0 | 45 | 43 |
N.S. |
1 | 0.00 | 0.85 | 31.88 | 0.00 | 1.18 | 1.18 | 0.00 | 1.36 | 1.30 |
time (sec) |
N/A | 0.000 | 0.033 | 6.483 | 0.000 | 0.099 | 0.266 | 0.000 | 0.151 | 4.086 |
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 | 21 | 26 | 21 | 25 | 25 | 25 | 24 | 26 | 27 | 25 |
N.S. |
1 | 1.24 | 1.00 | 1.19 | 1.19 | 1.19 | 1.14 | 1.24 | 1.29 | 1.19 |
time (sec) |
N/A | 0.627 | 2.158 | 0.261 | 0.079 | 0.091 | 0.139 | 0.674 | 0.156 | 3.362 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 35 | 37 | 139 | 35 | 32 | 35 | 36 | 26 |
N.S. |
1 | 0.00 | 1.17 | 1.23 | 4.63 | 1.17 | 1.07 | 1.17 | 1.20 | 0.87 |
time (sec) |
N/A | 0.000 | 0.020 | 0.808 | 0.041 | 0.082 | 0.096 | 0.147 | 0.150 | 3.772 |
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 | 29 | 29 | 27 | 26 | 26 | 24 | 28 | 27 | 26 |
N.S. |
1 | 0.97 | 0.97 | 0.90 | 0.87 | 0.87 | 0.80 | 0.93 | 0.90 | 0.87 |
time (sec) |
N/A | 3.466 | 0.053 | 2.841 | 0.183 | 0.102 | 0.226 | 0.166 | 0.157 | 0.355 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 134 | 135 | 39 | 106 | 21 | 41 | 39 | 145 | 41 |
N.S. |
1 | 6.09 | 6.14 | 1.77 | 4.82 | 0.95 | 1.86 | 1.77 | 6.59 | 1.86 |
time (sec) |
N/A | 0.652 | 0.057 | 0.401 | 0.216 | 0.093 | 0.150 | 0.138 | 0.150 | 3.378 |
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 | 12 | 9 | 9 | 8 | 8 | 5 | 8 | 9 | 8 |
N.S. |
1 | 1.33 | 1.00 | 1.00 | 0.89 | 0.89 | 0.56 | 0.89 | 1.00 | 0.89 |
time (sec) |
N/A | 0.141 | 0.000 | 0.016 | 0.025 | 0.074 | 0.013 | 0.109 | 0.152 | 0.001 |
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 | 14 | 14 | 15 | 14 | 14 | 12 | 14 | 11 | 10 |
N.S. |
1 | 0.93 | 0.93 | 1.00 | 0.93 | 0.93 | 0.80 | 0.93 | 0.73 | 0.67 |
time (sec) |
N/A | 0.150 | 0.001 | 0.037 | 0.024 | 0.089 | 0.039 | 0.111 | 0.153 | 3.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 28 | 28 | 58 | 58 | 54 | 60 | 55 | 0 |
N.S. |
1 | 0.00 | 0.90 | 0.90 | 1.87 | 1.87 | 1.74 | 1.94 | 1.77 | 0.00 |
time (sec) |
N/A | 0.000 | 0.322 | 0.429 | 0.084 | 0.095 | 0.123 | 0.177 | 0.165 | 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 | 22 | 38 | 19 | 19 | 18 | 18 | 19 | 18 | 25 | 18 |
N.S. |
1 | 1.73 | 0.86 | 0.86 | 0.82 | 0.82 | 0.86 | 0.82 | 1.14 | 0.82 |
time (sec) |
N/A | 0.206 | 0.064 | 0.227 | 0.030 | 0.117 | 0.082 | 0.109 | 0.148 | 3.471 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 20 | 19 | 19 | 20 | 19 | 20 | 19 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.95 | 0.95 | 1.00 | 0.95 | 1.00 | 0.95 |
time (sec) |
N/A | 0.000 | 0.231 | 0.993 | 0.066 | 0.087 | 0.130 | 0.117 | 0.153 | 3.466 |
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 | 19 | 31 | 16 | 16 | 25 | 18 | 14 | 18 | 19 | 15 |
N.S. |
1 | 1.63 | 0.84 | 0.84 | 1.32 | 0.95 | 0.74 | 0.95 | 1.00 | 0.79 |
time (sec) |
N/A | 0.195 | 0.008 | 0.092 | 0.031 | 0.078 | 0.043 | 0.108 | 0.149 | 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 | 26 | 33 | 24 | 19 | 26 | 35 | 19 | 26 | 37 | 20 |
N.S. |
1 | 1.27 | 0.92 | 0.73 | 1.00 | 1.35 | 0.73 | 1.00 | 1.42 | 0.77 |
time (sec) |
N/A | 0.226 | 0.016 | 0.138 | 0.025 | 0.093 | 0.075 | 0.107 | 0.149 | 0.054 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 18 | 16 | 17 | 15 | 14 | 17 | 16 | 77 |
N.S. |
1 | 0.00 | 1.00 | 0.89 | 0.94 | 0.83 | 0.78 | 0.94 | 0.89 | 4.28 |
time (sec) |
N/A | 0.000 | 0.180 | 0.823 | 0.151 | 0.078 | 0.305 | 0.122 | 0.151 | 3.439 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F(-1) | B | B | B | B | B | B |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 47 | 0 | 140 | 108 | 90 | 116 | 124 | 212 |
N.S. |
1 | 0.00 | 1.38 | 0.00 | 4.12 | 3.18 | 2.65 | 3.41 | 3.65 | 6.24 |
time (sec) |
N/A | 0.000 | 0.674 | 0.000 | 2.647 | 0.111 | 1.851 | 57.272 | 0.247 | 3.613 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 57 | 19 | 19 | 20 | 20 | 17 | 20 | 19 | 18 |
N.S. |
1 | 2.19 | 0.73 | 0.73 | 0.77 | 0.77 | 0.65 | 0.77 | 0.73 | 0.69 |
time (sec) |
N/A | 0.452 | 0.016 | 0.155 | 0.032 | 0.078 | 0.292 | 0.120 | 0.163 | 3.167 |
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 | 18 | 32 | 16 | 17 | 15 | 16 | 0 | 16 | 18 | 15 |
N.S. |
1 | 1.78 | 0.89 | 0.94 | 0.83 | 0.89 | 0.00 | 0.89 | 1.00 | 0.83 |
time (sec) |
N/A | 0.242 | 0.011 | 0.245 | 0.090 | 0.077 | 0.000 | 0.117 | 1.055 | 3.198 |
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 | 20 | 15 | 17 | 16 | 16 | 15 | 16 | 13 | 11 |
N.S. |
1 | 1.54 | 1.15 | 1.31 | 1.23 | 1.23 | 1.15 | 1.23 | 1.00 | 0.85 |
time (sec) |
N/A | 0.163 | 0.002 | 0.048 | 0.030 | 0.083 | 0.042 | 0.112 | 0.162 | 3.201 |
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 | 37 | 41 | 38 | 38 | 38 | 36 | 38 | 36 | 39 |
N.S. |
1 | 1.28 | 1.41 | 1.31 | 1.31 | 1.31 | 1.24 | 1.31 | 1.24 | 1.34 |
time (sec) |
N/A | 0.192 | 0.002 | 0.066 | 0.026 | 0.091 | 0.022 | 0.108 | 0.166 | 3.178 |
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 | 7 | 7 | 7 | 6 | 6 | 5 | 6 | 9 | 6 |
N.S. |
1 | 0.78 | 0.78 | 0.78 | 0.67 | 0.67 | 0.56 | 0.67 | 1.00 | 0.67 |
time (sec) |
N/A | 0.145 | 0.001 | 0.025 | 0.024 | 0.077 | 0.030 | 0.111 | 0.162 | 0.011 |
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 | 28 | 39 | 24 | 21 | 32 | 26 | 22 | 28 | 32 | 24 |
N.S. |
1 | 1.39 | 0.86 | 0.75 | 1.14 | 0.93 | 0.79 | 1.00 | 1.14 | 0.86 |
time (sec) |
N/A | 0.217 | 0.031 | 0.155 | 0.034 | 0.099 | 0.065 | 0.111 | 0.163 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 48 | 47 | 41 | 34 | 44 | 104 | 98 | 61 |
N.S. |
1 | 0.00 | 1.92 | 1.88 | 1.64 | 1.36 | 1.76 | 4.16 | 3.92 | 2.44 |
time (sec) |
N/A | 0.000 | 0.543 | 16.555 | 0.128 | 0.097 | 0.336 | 127.402 | 0.164 | 3.410 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 31 | 36 | 30 | 30 | 76 | 35 | 30 | 0 |
N.S. |
1 | 0.00 | 0.89 | 1.03 | 0.86 | 0.86 | 2.17 | 1.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.000 | 5.060 | 1.167 | 0.093 | 0.104 | 0.135 | 0.153 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | C | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 74 | 62 | 73 | 83 | 63 | 71 | 64 | 71 | 53 |
N.S. |
1 | 2.55 | 2.14 | 2.52 | 2.86 | 2.17 | 2.45 | 2.21 | 2.45 | 1.83 |
time (sec) |
N/A | 0.600 | 0.100 | 4.561 | 0.078 | 0.088 | 0.119 | 0.112 | 0.164 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | C | A | A | A | A | B | B |
verified | N/A | N/A | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 0 | 142 | 30 | 40 | 32 | 40 | 36 | 68 |
N.S. |
1 | 0.00 | 0.00 | 4.44 | 0.94 | 1.25 | 1.00 | 1.25 | 1.12 | 2.12 |
time (sec) |
N/A | 0.000 | 0.000 | 0.220 | 0.299 | 0.084 | 0.763 | 1.576 | 0.188 | 3.737 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 58 | 34 | 27 | 29 | 29 | 27 | 43 | 86 |
N.S. |
1 | 0.00 | 2.07 | 1.21 | 0.96 | 1.04 | 1.04 | 0.96 | 1.54 | 3.07 |
time (sec) |
N/A | 0.000 | 5.066 | 34.310 | 0.149 | 0.083 | 0.123 | 0.125 | 0.163 | 3.660 |
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 | 8 | 6 | 6 | 7 | 17 | 6 | 5 | 6 | 6 | 6 |
N.S. |
1 | 0.75 | 0.75 | 0.88 | 2.12 | 0.75 | 0.62 | 0.75 | 0.75 | 0.75 |
time (sec) |
N/A | 0.151 | 0.001 | 0.043 | 0.026 | 0.080 | 0.039 | 0.109 | 0.160 | 3.399 |
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 | 22 | 28 | 28 | 39 | 74 | 59 | 24 | 26 | 29 | 21 |
N.S. |
1 | 1.27 | 1.27 | 1.77 | 3.36 | 2.68 | 1.09 | 1.18 | 1.32 | 0.95 |
time (sec) |
N/A | 0.640 | 0.046 | 0.309 | 0.037 | 0.099 | 0.065 | 0.114 | 0.154 | 3.397 |
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 | 22 | 30 | 22 | 19 | 26 | 26 | 27 | 26 | 47 | 29 |
N.S. |
1 | 1.36 | 1.00 | 0.86 | 1.18 | 1.18 | 1.23 | 1.18 | 2.14 | 1.32 |
time (sec) |
N/A | 0.221 | 0.024 | 0.085 | 0.039 | 0.101 | 0.081 | 0.130 | 0.210 | 3.454 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | B | A | B | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 0 | 28 | 53 | 59 | 27 | 10848 | 64 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.85 | 1.61 | 1.79 | 0.82 | 328.73 | 1.94 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 3.669 | 0.157 | 0.119 | 0.116 | 0.297 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 35 | 63 | 44 | 82 | 66 | 107 | 56 | 0 |
N.S. |
1 | 0.00 | 1.09 | 1.97 | 1.38 | 2.56 | 2.06 | 3.34 | 1.75 | 0.00 |
time (sec) |
N/A | 0.000 | 0.184 | 2.241 | 0.170 | 0.110 | 0.197 | 1.717 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 25 | 29 | 0 | 25 | 32 | 45 | 31 | 18 |
N.S. |
1 | 0.00 | 0.96 | 1.12 | 0.00 | 0.96 | 1.23 | 1.73 | 1.19 | 0.69 |
time (sec) |
N/A | 0.000 | 0.035 | 0.173 | 0.000 | 0.121 | 0.124 | 0.122 | 0.151 | 0.050 |
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 | 34 | 54 | 55 | 50 | 41 | 47 | 46 | 49 | 51 | 43 |
N.S. |
1 | 1.59 | 1.62 | 1.47 | 1.21 | 1.38 | 1.35 | 1.44 | 1.50 | 1.26 |
time (sec) |
N/A | 0.676 | 0.011 | 0.181 | 0.027 | 0.131 | 0.094 | 0.110 | 0.149 | 0.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 22 | 21 | 20 | 40 | 17 | 0 | 27 | 20 |
N.S. |
1 | 0.00 | 0.96 | 0.91 | 0.87 | 1.74 | 0.74 | 0.00 | 1.17 | 0.87 |
time (sec) |
N/A | 0.000 | 1.038 | 0.457 | 0.193 | 0.159 | 0.166 | 0.000 | 0.150 | 3.580 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 84 | 27 | 27 | 0 | 26 | 29 | 0 | 49 | 31 |
N.S. |
1 | 2.62 | 0.84 | 0.84 | 0.00 | 0.81 | 0.91 | 0.00 | 1.53 | 0.97 |
time (sec) |
N/A | 2.044 | 1.907 | 11.438 | 0.000 | 0.097 | 0.115 | 0.000 | 0.155 | 3.574 |
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 | 27 | 17 | 16 | 27 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.69 | 1.06 | 1.00 | 1.69 | 1.00 |
time (sec) |
N/A | 1.740 | 0.129 | 0.448 | 0.067 | 0.120 | 0.089 | 0.125 | 0.149 | 3.549 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 24 | 24 | 22 | 19 | 22 | 22 | 22 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.00 | 0.92 | 0.79 | 0.92 | 0.92 | 0.92 |
time (sec) |
N/A | 0.000 | 0.062 | 2.244 | 0.083 | 0.101 | 0.310 | 0.253 | 0.160 | 3.786 |
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 | 5 | 5 | 6 | 5 | 5 | 2 | 5 | 5 | 5 |
N.S. |
1 | 0.21 | 0.21 | 0.25 | 0.21 | 0.21 | 0.08 | 0.21 | 0.21 | 0.21 |
time (sec) |
N/A | 0.204 | 0.000 | 0.012 | 0.029 | 0.076 | 0.018 | 0.110 | 0.145 | 0.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | F(-1) | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 32 | 25 | 37 | 43 | 48 | 0 | 45 | 42 |
N.S. |
1 | 0.00 | 1.78 | 1.39 | 2.06 | 2.39 | 2.67 | 0.00 | 2.50 | 2.33 |
time (sec) |
N/A | 0.000 | 2.109 | 2.326 | 0.165 | 0.119 | 0.467 | 0.000 | 0.156 | 3.737 |
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 | 28 | 26 | 26 | 26 | 25 | 25 | 24 | 25 | 27 | 27 |
N.S. |
1 | 0.93 | 0.93 | 0.93 | 0.89 | 0.89 | 0.86 | 0.89 | 0.96 | 0.96 |
time (sec) |
N/A | 0.556 | 0.184 | 0.169 | 0.062 | 0.095 | 0.202 | 0.134 | 0.167 | 3.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 20 | 22 | 26 | 22 | 20 | 0 | 25 | 20 |
N.S. |
1 | 0.00 | 0.87 | 0.96 | 1.13 | 0.96 | 0.87 | 0.00 | 1.09 | 0.87 |
time (sec) |
N/A | 0.000 | 0.312 | 85.910 | 0.180 | 0.094 | 0.447 | 0.000 | 0.166 | 3.805 |
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 | 27 | 24 | 26 | 28 | 28 | 26 | 23 | 39 | 25 |
N.S. |
1 | 1.12 | 1.00 | 1.08 | 1.17 | 1.17 | 1.08 | 0.96 | 1.62 | 1.04 |
time (sec) |
N/A | 0.310 | 0.132 | 0.065 | 0.026 | 0.095 | 0.051 | 0.111 | 0.151 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 27 | 16 | 23 | 23 | 12 | 23 | 25 | 15 |
N.S. |
1 | 0.00 | 1.35 | 0.80 | 1.15 | 1.15 | 0.60 | 1.15 | 1.25 | 0.75 |
time (sec) |
N/A | 0.000 | 0.839 | 0.058 | 0.054 | 0.088 | 0.059 | 0.120 | 0.150 | 0.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 68 | 52 | 60 | 0 | 59 | 60 | 71 | 81 | 140 |
N.S. |
1 | 1.94 | 1.49 | 1.71 | 0.00 | 1.69 | 1.71 | 2.03 | 2.31 | 4.00 |
time (sec) |
N/A | 2.667 | 0.080 | 51.076 | 0.000 | 0.104 | 0.128 | 0.125 | 0.148 | 3.703 |
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 | 18 | 13 | 13 | 12 | 12 | 10 | 12 | 10 | 9 |
N.S. |
1 | 1.12 | 0.81 | 0.81 | 0.75 | 0.75 | 0.62 | 0.75 | 0.62 | 0.56 |
time (sec) |
N/A | 0.182 | 0.003 | 0.050 | 0.025 | 0.080 | 0.036 | 0.115 | 0.146 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | A | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 53 | 27 | 34 | 30 | 36 | 26 | 36 | 24 | 31 |
N.S. |
1 | 3.53 | 1.80 | 2.27 | 2.00 | 2.40 | 1.73 | 2.40 | 1.60 | 2.07 |
time (sec) |
N/A | 10.618 | 0.019 | 0.174 | 0.033 | 0.086 | 0.704 | 0.126 | 0.150 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 37 | 34 | 83 | 39 | 30 | 31 | 32 | 576 | 33 |
N.S. |
1 | 1.19 | 1.10 | 2.68 | 1.26 | 0.97 | 1.00 | 1.03 | 18.58 | 1.06 |
time (sec) |
N/A | 2.228 | 0.063 | 0.542 | 0.140 | 0.105 | 0.390 | 0.165 | 1.295 | 3.384 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 22 | 55 | 18 | 20 | 19 | 21 | 19 | 20 |
N.S. |
1 | 0.00 | 1.16 | 2.89 | 0.95 | 1.05 | 1.00 | 1.11 | 1.00 | 1.05 |
time (sec) |
N/A | 0.000 | 0.052 | 1.568 | 0.069 | 0.090 | 0.374 | 0.145 | 0.153 | 3.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 0 | 15 | 16 | 15 | 15 | 14 | 15 | 13 | 13 |
N.S. |
1 | 0.00 | 1.00 | 1.07 | 1.00 | 1.00 | 0.93 | 1.00 | 0.87 | 0.87 |
time (sec) |
N/A | 0.000 | 0.084 | 0.365 | 0.190 | 0.093 | 0.170 | 0.490 | 0.149 | 3.298 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | F(-1) | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 30 | 66 | 67 | 58 | 0 | 0 | 58 | 27 |
N.S. |
1 | 0.00 | 1.00 | 2.20 | 2.23 | 1.93 | 0.00 | 0.00 | 1.93 | 0.90 |
time (sec) |
N/A | 0.000 | 0.105 | 4.555 | 0.180 | 0.094 | 0.000 | 0.000 | 0.154 | 3.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 22 | 22 | 21 | 20 | 20 | 20 | 20 | 23 | 0 |
N.S. |
1 | 0.92 | 0.92 | 0.88 | 0.83 | 0.83 | 0.83 | 0.83 | 0.96 | 0.00 |
time (sec) |
N/A | 0.520 | 0.024 | 1.061 | 0.065 | 0.080 | 0.099 | 0.135 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 0 | 57 | 53 | 68 | 68 | 49 | 70 | 46 | 0 |
N.S. |
1 | 0.00 | 1.54 | 1.43 | 1.84 | 1.84 | 1.32 | 1.89 | 1.24 | 0.00 |
time (sec) |
N/A | 0.000 | 6.768 | 0.406 | 0.092 | 0.091 | 0.185 | 0.135 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 25 | 39 | 46 | 50 | 49 | 54 | 63 | 46 |
N.S. |
1 | 0.00 | 0.96 | 1.50 | 1.77 | 1.92 | 1.88 | 2.08 | 2.42 | 1.77 |
time (sec) |
N/A | 0.000 | 0.075 | 16.762 | 0.121 | 0.103 | 0.148 | 0.165 | 13.024 | 3.312 |
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 | 17 | 16 | 16 | 13 | 12 | 12 | 14 | 0 | 19 | 13 |
N.S. |
1 | 0.94 | 0.94 | 0.76 | 0.71 | 0.71 | 0.82 | 0.00 | 1.12 | 0.76 |
time (sec) |
N/A | 0.264 | 0.021 | 0.189 | 0.115 | 0.087 | 20.040 | 0.000 | 0.172 | 3.303 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 55 | 26 | 25 | 32 | 25 | 24 | 25 | 28 | 35 |
N.S. |
1 | 2.04 | 0.96 | 0.93 | 1.19 | 0.93 | 0.89 | 0.93 | 1.04 | 1.30 |
time (sec) |
N/A | 0.583 | 0.126 | 0.127 | 0.209 | 0.094 | 0.093 | 0.115 | 0.171 | 3.331 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 24 | 23 | 33 | 37 | 17 | 20 | 58 | 25 |
N.S. |
1 | 0.00 | 0.96 | 0.92 | 1.32 | 1.48 | 0.68 | 0.80 | 2.32 | 1.00 |
time (sec) |
N/A | 0.000 | 0.071 | 0.538 | 0.053 | 0.079 | 0.052 | 0.126 | 0.165 | 3.317 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 23 | 21 | 28 | 20 | 19 | 54 | 23 | 20 |
N.S. |
1 | 0.00 | 1.05 | 0.95 | 1.27 | 0.91 | 0.86 | 2.45 | 1.05 | 0.91 |
time (sec) |
N/A | 0.000 | 0.274 | 0.114 | 0.086 | 0.094 | 0.094 | 0.113 | 0.150 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 36 | 36 | 31 | 38 | 31 | 43 | 51 | 33 |
N.S. |
1 | 0.00 | 1.09 | 1.09 | 0.94 | 1.15 | 0.94 | 1.30 | 1.55 | 1.00 |
time (sec) |
N/A | 0.000 | 0.259 | 8.835 | 0.089 | 0.084 | 0.346 | 0.196 | 0.157 | 3.423 |
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 | 27 | 33 | 25 | 26 | 32 | 17 | 26 | 43 | 26 |
N.S. |
1 | 0.79 | 0.97 | 0.74 | 0.76 | 0.94 | 0.50 | 0.76 | 1.26 | 0.76 |
time (sec) |
N/A | 0.784 | 0.063 | 0.375 | 0.080 | 0.080 | 0.106 | 0.117 | 0.153 | 3.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 39 | 24 | 73 | 27 | 26 | 44 | 55 | 45 |
N.S. |
1 | 0.00 | 1.70 | 1.04 | 3.17 | 1.17 | 1.13 | 1.91 | 2.39 | 1.96 |
time (sec) |
N/A | 0.000 | 0.151 | 4.074 | 0.253 | 0.099 | 0.635 | 0.170 | 0.152 | 3.388 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | F(-2) | B | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 44 | 45 | 43 | 0 | 109 | 137 | 42 |
N.S. |
1 | 0.00 | 0.00 | 1.47 | 1.50 | 1.43 | 0.00 | 3.63 | 4.57 | 1.40 |
time (sec) |
N/A | 0.000 | 0.000 | 10.123 | 0.189 | 0.087 | 0.000 | 0.619 | 0.192 | 3.599 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 76 | 171 | 485 | 90 | 165 | 358 | 70 | 170 |
N.S. |
1 | 0.00 | 2.92 | 6.58 | 18.65 | 3.46 | 6.35 | 13.77 | 2.69 | 6.54 |
time (sec) |
N/A | 0.000 | 3.089 | 0.278 | 0.210 | 0.103 | 0.464 | 0.167 | 0.151 | 3.467 |
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 | 22 | 28 | 28 | 20 | 21 | 29 | 19 | 20 | 21 | 20 |
N.S. |
1 | 1.27 | 1.27 | 0.91 | 0.95 | 1.32 | 0.86 | 0.91 | 0.95 | 0.91 |
time (sec) |
N/A | 0.240 | 0.020 | 0.098 | 0.025 | 0.087 | 0.061 | 0.121 | 0.153 | 3.229 |
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 | 27 | 26 | 29 | 26 | 26 | 30 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.90 | 1.00 | 0.90 | 0.90 | 1.03 | 0.90 |
time (sec) |
N/A | 0.207 | 0.008 | 0.113 | 0.027 | 0.076 | 0.037 | 0.113 | 0.146 | 3.218 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | B | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 131 | 34 | 36 | 36 | 62 | 34 | 34 | 117 | 55 |
N.S. |
1 | 4.68 | 1.21 | 1.29 | 1.29 | 2.21 | 1.21 | 1.21 | 4.18 | 1.96 |
time (sec) |
N/A | 0.716 | 0.035 | 0.436 | 0.028 | 0.080 | 0.353 | 0.128 | 0.152 | 3.347 |
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 | 10 | 10 | 10 | 8 | 8 | 7 | 9 | 10 | 8 |
N.S. |
1 | 0.62 | 0.62 | 0.62 | 0.50 | 0.50 | 0.44 | 0.56 | 0.62 | 0.50 |
time (sec) |
N/A | 0.132 | 0.000 | 0.021 | 0.041 | 0.070 | 0.020 | 0.111 | 0.150 | 0.020 |
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 | 19 | 16 | 16 | 14 | 11 | 11 | 12 | 11 | 17 | 15 |
N.S. |
1 | 0.84 | 0.84 | 0.74 | 0.58 | 0.58 | 0.63 | 0.58 | 0.89 | 0.79 |
time (sec) |
N/A | 0.158 | 0.001 | 0.032 | 0.028 | 0.078 | 0.017 | 0.113 | 0.149 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | C | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 129 | 34 | 47 | 565 | 85 | 68 | 84 | 152 | 82 |
N.S. |
1 | 5.61 | 1.48 | 2.04 | 24.57 | 3.70 | 2.96 | 3.65 | 6.61 | 3.57 |
time (sec) |
N/A | 1.706 | 0.241 | 1.310 | 0.354 | 0.088 | 0.107 | 0.160 | 0.165 | 3.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | B | B | A | B | B | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 0 | 67 | 528 | 55 | 53 | 256 | 78 | 55 |
N.S. |
1 | 0.00 | 0.00 | 2.31 | 18.21 | 1.90 | 1.83 | 8.83 | 2.69 | 1.90 |
time (sec) |
N/A | 0.000 | 0.000 | 15.311 | 0.214 | 0.086 | 0.151 | 0.247 | 0.150 | 3.515 |