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 | 13 | 7 | 7 | 7 | 6 | 6 | 3 | 6 | 7 | 6 |
N.S. |
1 | 0.54 | 0.54 | 0.54 | 0.46 | 0.46 | 0.23 | 0.46 | 0.54 | 0.46 |
time (sec) |
N/A | 0.172 | 0.001 | 0.021 | 0.026 | 0.063 | 0.030 | 0.120 | 0.305 | 0.019 |
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 | 24 | 24 | 24 | 23 | 23 | 24 | 23 | 24 | 23 |
N.S. |
1 | 1.26 | 1.26 | 1.26 | 1.21 | 1.21 | 1.26 | 1.21 | 1.26 | 1.21 |
time (sec) |
N/A | 0.878 | 0.837 | 0.209 | 0.032 | 0.065 | 0.092 | 0.114 | 0.235 | 0.434 |
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 | 24 | 21 | 22 | 22 | 19 | 27 | 22 | 28 |
N.S. |
1 | 0.00 | 0.92 | 0.81 | 0.85 | 0.85 | 0.73 | 1.04 | 0.85 | 1.08 |
time (sec) |
N/A | 0.000 | 0.151 | 0.170 | 0.103 | 0.072 | 0.108 | 0.122 | 0.270 | 0.568 |
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 | 37 | 38 | 35 | 34 | 31 | 32 | 37 | 38 | 31 |
N.S. |
1 | 1.32 | 1.36 | 1.25 | 1.21 | 1.11 | 1.14 | 1.32 | 1.36 | 1.11 |
time (sec) |
N/A | 0.796 | 0.025 | 0.152 | 0.033 | 0.065 | 1.018 | 0.128 | 0.262 | 0.565 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 64 | 41 | 59 | 172 | 77 | 61 | 0 | 105 | 28 |
N.S. |
1 | 3.37 | 2.16 | 3.11 | 9.05 | 4.05 | 3.21 | 0.00 | 5.53 | 1.47 |
time (sec) |
N/A | 0.908 | 0.054 | 0.537 | 0.080 | 0.066 | 0.148 | 0.000 | 0.286 | 0.531 |
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 | 15 | 12 | 15 | 12 | 14 | 13 |
N.S. |
1 | 1.00 | 0.92 | 1.00 | 1.15 | 0.92 | 1.15 | 0.92 | 1.08 | 1.00 |
time (sec) |
N/A | 0.150 | 0.003 | 0.121 | 0.025 | 0.059 | 0.061 | 0.115 | 0.264 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | B | C | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 186 | 42 | 82 | 165 | 82 | 83 | 112 | 85 | 74 |
N.S. |
1 | 8.45 | 1.91 | 3.73 | 7.50 | 3.73 | 3.77 | 5.09 | 3.86 | 3.36 |
time (sec) |
N/A | 1.278 | 1.401 | 133.193 | 0.111 | 0.067 | 0.069 | 0.131 | 0.259 | 0.550 |
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 | 19 | 13 | 16 | 15 | 10 | 16 | 14 | 16 |
N.S. |
1 | 0.82 | 0.86 | 0.59 | 0.73 | 0.68 | 0.45 | 0.73 | 0.64 | 0.73 |
time (sec) |
N/A | 0.191 | 0.006 | 0.069 | 0.029 | 0.055 | 0.035 | 0.115 | 0.228 | 0.024 |
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 | 24 | 23 | 29 | 20 | 39 | 42 | 37 |
N.S. |
1 | 0.93 | 0.93 | 0.86 | 0.82 | 1.04 | 0.71 | 1.39 | 1.50 | 1.32 |
time (sec) |
N/A | 0.666 | 0.143 | 0.222 | 0.117 | 0.071 | 0.101 | 0.125 | 0.241 | 0.154 |
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 | 23 | 23 | 22 | 23 | 23 | 24 | 23 | 23 | 26 |
N.S. |
1 | 1.21 | 1.21 | 1.16 | 1.21 | 1.21 | 1.26 | 1.21 | 1.21 | 1.37 |
time (sec) |
N/A | 0.221 | 0.007 | 0.040 | 0.047 | 0.058 | 0.067 | 0.113 | 0.282 | 0.131 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F(-2) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 34 | 53 | 37 | 45 | 34 | 0 | 51 | 52 | 0 |
N.S. |
1 | 1.31 | 2.04 | 1.42 | 1.73 | 1.31 | 0.00 | 1.96 | 2.00 | 0.00 |
time (sec) |
N/A | 2.313 | 0.055 | 1.455 | 0.087 | 0.077 | 0.000 | 0.188 | 0.298 | 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 | 21 | 0 | 24 | 21 | 24 | 24 | 20 | 26 | 27 | 34 |
N.S. |
1 | 0.00 | 1.14 | 1.00 | 1.14 | 1.14 | 0.95 | 1.24 | 1.29 | 1.62 |
time (sec) |
N/A | 0.000 | 0.190 | 0.326 | 0.086 | 0.067 | 0.119 | 0.118 | 0.242 | 0.533 |
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 | 29 | 20 | 20 | 19 | 23 | 17 | 25 | 27 | 23 |
N.S. |
1 | 1.38 | 0.95 | 0.95 | 0.90 | 1.10 | 0.81 | 1.19 | 1.29 | 1.10 |
time (sec) |
N/A | 0.891 | 0.091 | 0.186 | 0.074 | 0.067 | 0.089 | 0.113 | 0.222 | 0.482 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 36 | 31 | 29 | 28 | 28 | 31 | 0 | 639 | 32 |
N.S. |
1 | 1.20 | 1.03 | 0.97 | 0.93 | 0.93 | 1.03 | 0.00 | 21.30 | 1.07 |
time (sec) |
N/A | 2.416 | 0.099 | 3.252 | 0.151 | 0.068 | 0.637 | 0.000 | 0.466 | 0.691 |
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 | 23 | 22 | 22 | 21 | 20 | 21 | 32 | 24 |
N.S. |
1 | 0.00 | 0.92 | 0.88 | 0.88 | 0.84 | 0.80 | 0.84 | 1.28 | 0.96 |
time (sec) |
N/A | 0.000 | 0.250 | 0.898 | 0.122 | 0.064 | 0.123 | 0.131 | 0.248 | 0.504 |
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 | 14 | 19 | 19 | 10 | 11 | 11 | 8 | 13 | 11 | 8 |
N.S. |
1 | 1.36 | 1.36 | 0.71 | 0.79 | 0.79 | 0.57 | 0.93 | 0.79 | 0.57 |
time (sec) |
N/A | 0.165 | 0.003 | 0.049 | 0.025 | 0.069 | 0.049 | 0.108 | 0.289 | 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 | 29 | 12 | 13 | 14 | 16 | 13 | 12 | 16 | 18 | 11 |
N.S. |
1 | 0.41 | 0.45 | 0.48 | 0.55 | 0.45 | 0.41 | 0.55 | 0.62 | 0.38 |
time (sec) |
N/A | 0.155 | 0.010 | 0.049 | 0.031 | 0.060 | 0.044 | 0.112 | 0.270 | 0.042 |
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 | 19 | 20 | 19 | 19 | 15 | 19 | 51 | 18 |
N.S. |
1 | 0.00 | 0.73 | 0.77 | 0.73 | 0.73 | 0.58 | 0.73 | 1.96 | 0.69 |
time (sec) |
N/A | 0.000 | 0.507 | 0.780 | 0.081 | 0.065 | 0.089 | 0.122 | 0.235 | 0.484 |
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 | 23 | 23 | 21 | 18 | 19 | 22 | 18 | 22 | 19 |
N.S. |
1 | 0.82 | 0.82 | 0.75 | 0.64 | 0.68 | 0.79 | 0.64 | 0.79 | 0.68 |
time (sec) |
N/A | 0.316 | 0.006 | 0.038 | 0.038 | 0.062 | 0.052 | 0.111 | 0.229 | 0.028 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | A | F(-1) | F | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 51 | 281 | 52 | 50 | 0 | 0 | 57 | 50 |
N.S. |
1 | 0.00 | 1.82 | 10.04 | 1.86 | 1.79 | 0.00 | 0.00 | 2.04 | 1.79 |
time (sec) |
N/A | 0.000 | 0.211 | 0.046 | 0.619 | 0.070 | 0.000 | 0.000 | 0.323 | 1.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | B | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 54 | 54 | 62 | 54 | 56 | 0 | 58 | 57 |
N.S. |
1 | 0.00 | 1.80 | 1.80 | 2.07 | 1.80 | 1.87 | 0.00 | 1.93 | 1.90 |
time (sec) |
N/A | 0.000 | 0.090 | 1.350 | 0.199 | 0.075 | 0.203 | 0.000 | 0.401 | 0.737 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 20 | 21 | 21 | 21 | 0 | 28 | 21 | 20 |
N.S. |
1 | 0.00 | 0.91 | 0.95 | 0.95 | 0.95 | 0.00 | 1.27 | 0.95 | 0.91 |
time (sec) |
N/A | 0.000 | 0.168 | 3.130 | 0.162 | 0.067 | 0.000 | 0.176 | 10.539 | 0.721 |
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 | 39 | 35 | 35 | 30 | 47 | 32 | 33 | 44 | 32 |
N.S. |
1 | 1.22 | 1.09 | 1.09 | 0.94 | 1.47 | 1.00 | 1.03 | 1.38 | 1.00 |
time (sec) |
N/A | 0.419 | 0.016 | 0.090 | 0.025 | 0.060 | 0.087 | 0.112 | 0.244 | 0.061 |
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 | 12 | 12 | 13 | 19 | 19 | 8 | 12 | 21 | 12 |
N.S. |
1 | 0.80 | 0.80 | 0.87 | 1.27 | 1.27 | 0.53 | 0.80 | 1.40 | 0.80 |
time (sec) |
N/A | 0.559 | 0.054 | 0.200 | 0.068 | 0.075 | 0.044 | 0.113 | 0.259 | 0.562 |
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 | 27 | 20 | 20 | 16 | 22 | 20 | 17 | 20 | 23 | 18 |
N.S. |
1 | 0.74 | 0.74 | 0.59 | 0.81 | 0.74 | 0.63 | 0.74 | 0.85 | 0.67 |
time (sec) |
N/A | 0.217 | 0.086 | 0.146 | 0.059 | 0.067 | 0.060 | 0.112 | 0.235 | 0.041 |
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 | 34 | 32 | 42 | 33 | 29 | 34 | 35 | 37 |
N.S. |
1 | 0.00 | 1.26 | 1.19 | 1.56 | 1.22 | 1.07 | 1.26 | 1.30 | 1.37 |
time (sec) |
N/A | 0.000 | 0.270 | 0.517 | 0.159 | 0.063 | 0.230 | 0.121 | 0.284 | 0.659 |
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 | 18 | 6 | 6 | 5 | 4 | 4 | 3 | 5 | 4 | 4 |
N.S. |
1 | 0.33 | 0.33 | 0.28 | 0.22 | 0.22 | 0.17 | 0.28 | 0.22 | 0.22 |
time (sec) |
N/A | 0.212 | 0.000 | 0.014 | 0.040 | 0.059 | 0.020 | 0.108 | 0.250 | 0.035 |
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 | 22 | 16 | 15 | 14 | 18 | 14 | 14 | 16 | 14 |
N.S. |
1 | 0.92 | 0.67 | 0.62 | 0.58 | 0.75 | 0.58 | 0.58 | 0.67 | 0.58 |
time (sec) |
N/A | 0.345 | 0.011 | 0.101 | 0.062 | 0.068 | 0.056 | 0.123 | 0.273 | 0.435 |
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 | 21 | 21 | 14 | 9 | 14 | 7 | 16 | 10 | 11 |
N.S. |
1 | 1.75 | 1.75 | 1.17 | 0.75 | 1.17 | 0.58 | 1.33 | 0.83 | 0.92 |
time (sec) |
N/A | 0.275 | 0.011 | 0.021 | 0.024 | 0.066 | 0.032 | 0.108 | 0.270 | 0.391 |
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 | 34 | 33 | 27 | 27 | 27 | 26 | 30 | 29 | 24 |
N.S. |
1 | 1.36 | 1.32 | 1.08 | 1.08 | 1.08 | 1.04 | 1.20 | 1.16 | 0.96 |
time (sec) |
N/A | 0.442 | 0.010 | 0.124 | 0.025 | 0.060 | 0.152 | 0.114 | 0.236 | 0.074 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 193 | 33 | 41 | 395 | 40 | 32 | 36 | 47 | 43 |
N.S. |
1 | 6.89 | 1.18 | 1.46 | 14.11 | 1.43 | 1.14 | 1.29 | 1.68 | 1.54 |
time (sec) |
N/A | 1.604 | 0.024 | 16.827 | 0.057 | 0.065 | 0.103 | 0.140 | 0.226 | 0.519 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | F(-1) | F | B | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 24 | 627 | 33 | 24 | 0 | 0 | 27 | 0 |
N.S. |
1 | 0.00 | 0.96 | 25.08 | 1.32 | 0.96 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.000 | 5.085 | 0.088 | 0.163 | 0.073 | 0.000 | 0.000 | 0.246 | 0.000 |
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 | 25 | 22 | 18 | 22 | 27 | 19 | 17 | 21 | 23 | 16 |
N.S. |
1 | 0.88 | 0.72 | 0.88 | 1.08 | 0.76 | 0.68 | 0.84 | 0.92 | 0.64 |
time (sec) |
N/A | 0.257 | 0.028 | 0.131 | 0.055 | 0.065 | 0.075 | 0.116 | 0.271 | 0.051 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 13 | 11 | 9 | 8 | 8 | 7 | 8 | 9 | 8 |
N.S. |
1 | 0.72 | 0.61 | 0.50 | 0.44 | 0.44 | 0.39 | 0.44 | 0.50 | 0.44 |
time (sec) |
N/A | 0.148 | 0.001 | 0.027 | 0.038 | 0.069 | 0.035 | 0.105 | 0.250 | 0.386 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F(-1) | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 24 | 0 | 21 | 21 | 20 | 21 | 54 | 21 |
N.S. |
1 | 0.00 | 0.96 | 0.00 | 0.84 | 0.84 | 0.80 | 0.84 | 2.16 | 0.84 |
time (sec) |
N/A | 0.000 | 0.308 | 0.000 | 0.094 | 0.073 | 0.487 | 0.175 | 0.267 | 0.490 |
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 | 25 | 25 | 23 | 25 | 22 | 22 | 24 | 25 | 21 |
N.S. |
1 | 1.14 | 1.14 | 1.05 | 1.14 | 1.00 | 1.00 | 1.09 | 1.14 | 0.95 |
time (sec) |
N/A | 1.590 | 0.209 | 0.214 | 0.116 | 0.075 | 0.104 | 0.114 | 0.277 | 0.642 |
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 | 7 | 5 | 5 | 5 | 4 | 4 | 3 | 4 | 5 | 4 |
N.S. |
1 | 0.71 | 0.71 | 0.71 | 0.57 | 0.57 | 0.43 | 0.57 | 0.71 | 0.57 |
time (sec) |
N/A | 0.248 | 0.010 | 0.089 | 0.033 | 0.072 | 0.034 | 0.115 | 0.226 | 0.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 69 | 81 | 28 | 60 | 60 | 71 | 60 | 66 | 67 |
N.S. |
1 | 3.14 | 3.68 | 1.27 | 2.73 | 2.73 | 3.23 | 2.73 | 3.00 | 3.05 |
time (sec) |
N/A | 0.334 | 0.012 | 0.273 | 0.033 | 0.062 | 0.025 | 0.106 | 0.222 | 0.461 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 0 | 21 | 28 | 28 | 26 | 20 | 20 | 78 |
N.S. |
1 | 0.00 | 0.00 | 1.05 | 1.40 | 1.40 | 1.30 | 1.00 | 1.00 | 3.90 |
time (sec) |
N/A | 0.000 | 0.000 | 0.648 | 0.164 | 0.071 | 0.363 | 0.119 | 0.237 | 0.540 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 223 | 27 | 28 | 0 | 39 | 37 | 0 | 0 | 49 |
N.S. |
1 | 7.43 | 0.90 | 0.93 | 0.00 | 1.30 | 1.23 | 0.00 | 0.00 | 1.63 |
time (sec) |
N/A | 9.876 | 0.207 | 1.273 | 0.000 | 0.074 | 2.440 | 0.000 | 1.964 | 0.584 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 29 | 49 | 76 | 51 | 63 | 0 | 58 | 39 |
N.S. |
1 | 0.00 | 0.97 | 1.63 | 2.53 | 1.70 | 2.10 | 0.00 | 1.93 | 1.30 |
time (sec) |
N/A | 0.000 | 5.031 | 2.675 | 0.149 | 0.075 | 0.117 | 0.000 | 0.219 | 0.519 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 24 | 60 | 125 | 27 | 22 | 129 | 28 | 29 |
N.S. |
1 | 0.00 | 1.00 | 2.50 | 5.21 | 1.12 | 0.92 | 5.38 | 1.17 | 1.21 |
time (sec) |
N/A | 0.000 | 0.273 | 3.878 | 0.170 | 0.072 | 0.299 | 0.150 | 0.252 | 1.298 |
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 | 21 | 21 | 14 | 16 | 16 | 17 | 16 | 15 | 18 |
N.S. |
1 | 0.95 | 0.95 | 0.64 | 0.73 | 0.73 | 0.77 | 0.73 | 0.68 | 0.82 |
time (sec) |
N/A | 0.262 | 0.003 | 0.087 | 0.028 | 0.058 | 0.026 | 0.117 | 0.273 | 0.059 |
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 | 20 | 17 | 17 | 18 | 23 | 26 | 14 | 17 | 26 | 17 |
N.S. |
1 | 0.85 | 0.85 | 0.90 | 1.15 | 1.30 | 0.70 | 0.85 | 1.30 | 0.85 |
time (sec) |
N/A | 0.611 | 0.081 | 0.154 | 0.056 | 0.071 | 0.054 | 0.112 | 0.216 | 0.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | A | B | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 505 | 917 | 35 | 1585 | 32 | 37 | 1159 | 94 | 20 |
N.S. |
1 | 21.96 | 39.87 | 1.52 | 68.91 | 1.39 | 1.61 | 50.39 | 4.09 | 0.87 |
time (sec) |
N/A | 3.109 | 1.058 | 4.954 | 0.273 | 0.072 | 0.557 | 0.153 | 200.027 | 1.225 |
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 | 35 | 31 | 30 | 26 | 24 | 24 | 27 | 25 | 36 | 30 |
N.S. |
1 | 0.89 | 0.86 | 0.74 | 0.69 | 0.69 | 0.77 | 0.71 | 1.03 | 0.86 |
time (sec) |
N/A | 0.340 | 0.044 | 0.245 | 0.033 | 0.078 | 0.080 | 0.130 | 0.229 | 0.436 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 31 | 22 | 32 | 25 | 31 | 29 | 25 | 52 | 29 |
N.S. |
1 | 1.19 | 0.85 | 1.23 | 0.96 | 1.19 | 1.12 | 0.96 | 2.00 | 1.12 |
time (sec) |
N/A | 0.453 | 0.080 | 0.147 | 0.159 | 0.067 | 0.087 | 0.110 | 72.572 | 0.452 |
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 | 26 | 33 | 18 | 17 | 26 | 17 | 26 | 27 | 17 |
N.S. |
1 | 1.08 | 1.38 | 0.75 | 0.71 | 1.08 | 0.71 | 1.08 | 1.12 | 0.71 |
time (sec) |
N/A | 0.622 | 1.145 | 1.006 | 0.076 | 0.073 | 0.086 | 0.121 | 0.215 | 0.419 |
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 | 23 | 19 | 17 | 16 | 23 | 19 | 15 | 15 | 19 | 15 |
N.S. |
1 | 0.83 | 0.74 | 0.70 | 1.00 | 0.83 | 0.65 | 0.65 | 0.83 | 0.65 |
time (sec) |
N/A | 0.336 | 0.075 | 0.153 | 0.063 | 0.067 | 0.044 | 0.118 | 0.208 | 0.411 |
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 | 32 | 25 | 18 | 34 | 17 | 20 | 21 | 24 | 21 |
N.S. |
1 | 1.28 | 1.00 | 0.72 | 1.36 | 0.68 | 0.80 | 0.84 | 0.96 | 0.84 |
time (sec) |
N/A | 0.281 | 0.135 | 0.354 | 0.095 | 0.067 | 0.135 | 0.114 | 0.233 | 0.485 |
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 | 27 | 27 | 24 | 23 | 27 | 27 | 24 | 27 | 23 |
N.S. |
1 | 0.96 | 0.96 | 0.86 | 0.82 | 0.96 | 0.96 | 0.86 | 0.96 | 0.82 |
time (sec) |
N/A | 0.200 | 0.004 | 0.049 | 0.028 | 0.058 | 0.037 | 0.114 | 0.362 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 19 | 18 | 18 | 14 | 18 | 19 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.12 | 1.06 | 1.06 | 0.82 | 1.06 | 1.12 | 1.06 |
time (sec) |
N/A | 0.441 | 0.020 | 0.136 | 0.174 | 0.071 | 0.093 | 0.165 | 0.195 | 0.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 69 | 60 | 726 | 253 | 316 | 552 | 293 | 0 |
N.S. |
1 | 0.00 | 2.23 | 1.94 | 23.42 | 8.16 | 10.19 | 17.81 | 9.45 | 0.00 |
time (sec) |
N/A | 0.000 | 0.476 | 0.124 | 1.829 | 0.101 | 0.683 | 0.759 | 0.264 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | F | A | A | A | B | A | F | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 63 | 0 | 49 | 52 | 48 | 60 | 50 | 98 | 59 |
N.S. |
1 | 2.17 | 0.00 | 1.69 | 1.79 | 1.66 | 2.07 | 1.72 | 3.38 | 2.03 |
time (sec) |
N/A | 0.913 | 0.000 | 20.307 | 0.301 | 0.066 | 1.882 | 0.180 | 200.025 | 0.578 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | F(-2) | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 32 | 32 | 68 | 40 | 67 | 0 | 85 | 81 | 68 |
N.S. |
1 | 1.45 | 1.45 | 3.09 | 1.82 | 3.05 | 0.00 | 3.86 | 3.68 | 3.09 |
time (sec) |
N/A | 6.816 | 0.104 | 48.179 | 0.173 | 0.076 | 0.000 | 36.751 | 0.264 | 1.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | B | F(-2) | B | B | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 49 | 62 | 69 | 0 | 96 | 51 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.63 | 2.07 | 2.30 | 0.00 | 3.20 | 1.70 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.260 | 0.186 | 0.072 | 0.000 | 0.135 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 84 | 43 | 64 | 170 | 59 | 71 | 91 | 75 | 61 |
N.S. |
1 | 3.82 | 1.95 | 2.91 | 7.73 | 2.68 | 3.23 | 4.14 | 3.41 | 2.77 |
time (sec) |
N/A | 0.621 | 1.522 | 0.338 | 0.035 | 0.065 | 0.113 | 0.116 | 0.220 | 0.503 |
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 | 19 | 22 | 19 | 20 | 55 | 19 | 19 | 19 | 20 | 15 |
N.S. |
1 | 1.16 | 1.00 | 1.05 | 2.89 | 1.00 | 1.00 | 1.00 | 1.05 | 0.79 |
time (sec) |
N/A | 0.727 | 1.536 | 1.451 | 0.154 | 0.069 | 0.284 | 0.128 | 0.220 | 0.750 |
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 | 22 | 31 | 31 | 33 | 40 | 30 | 32 | 52 | 21 | 22 |
N.S. |
1 | 1.41 | 1.41 | 1.50 | 1.82 | 1.36 | 1.45 | 2.36 | 0.95 | 1.00 |
time (sec) |
N/A | 0.186 | 0.005 | 0.415 | 0.027 | 0.075 | 0.086 | 0.111 | 0.292 | 0.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 43 | 64 | 100 | 100 | 48 | 121 | 136 | 0 |
N.S. |
1 | 0.00 | 1.65 | 2.46 | 3.85 | 3.85 | 1.85 | 4.65 | 5.23 | 0.00 |
time (sec) |
N/A | 0.000 | 10.098 | 2.377 | 0.352 | 0.072 | 0.345 | 0.368 | 0.244 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 27 | 30 | 26 | 28 | 17 | 67 | 38 | 0 |
N.S. |
1 | 0.00 | 0.96 | 1.07 | 0.93 | 1.00 | 0.61 | 2.39 | 1.36 | 0.00 |
time (sec) |
N/A | 0.000 | 5.066 | 237.571 | 0.236 | 0.071 | 0.207 | 0.126 | 0.232 | 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 | 20 | 15 | 17 | 15 | 14 | 21 | 12 | 14 | 21 | 14 |
N.S. |
1 | 0.75 | 0.85 | 0.75 | 0.70 | 1.05 | 0.60 | 0.70 | 1.05 | 0.70 |
time (sec) |
N/A | 0.373 | 0.009 | 0.281 | 0.031 | 0.059 | 0.055 | 0.111 | 0.238 | 0.420 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 25 | 25 | 24 | 23 | 23 | 20 | 23 | 174 | 23 |
N.S. |
1 | 1.09 | 1.09 | 1.04 | 1.00 | 1.00 | 0.87 | 1.00 | 7.57 | 1.00 |
time (sec) |
N/A | 0.947 | 0.120 | 0.490 | 0.063 | 0.071 | 0.147 | 0.136 | 0.250 | 0.476 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | A | A | A | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 0 | 20 | 76 | 19 | 19 | 19 | 19 | 19 |
N.S. |
1 | 0.00 | 0.00 | 1.11 | 4.22 | 1.06 | 1.06 | 1.06 | 1.06 | 1.06 |
time (sec) |
N/A | 0.000 | 0.000 | 0.201 | 0.119 | 0.073 | 0.175 | 0.601 | 0.217 | 0.460 |
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 | 27 | 24 | 22 | 19 | 28 | 22 | 20 | 22 | 35 | 19 |
N.S. |
1 | 0.89 | 0.81 | 0.70 | 1.04 | 0.81 | 0.74 | 0.81 | 1.30 | 0.70 |
time (sec) |
N/A | 0.227 | 0.046 | 0.328 | 0.074 | 0.082 | 0.068 | 0.112 | 0.236 | 0.045 |
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 | 19 | 20 | 19 | 19 | 15 | 17 | 19 | 20 | 19 |
N.S. |
1 | 1.12 | 1.18 | 1.12 | 1.12 | 0.88 | 1.00 | 1.12 | 1.18 | 1.12 |
time (sec) |
N/A | 0.181 | 0.002 | 0.117 | 0.037 | 0.070 | 0.087 | 0.111 | 0.272 | 0.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 37 | 23 | 28 | 63 | 19 | 44 | 19 | 29 | 20 |
N.S. |
1 | 1.37 | 0.85 | 1.04 | 2.33 | 0.70 | 1.63 | 0.70 | 1.07 | 0.74 |
time (sec) |
N/A | 0.771 | 0.471 | 0.568 | 0.159 | 0.067 | 0.206 | 0.131 | 0.217 | 0.150 |
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 | 21 | 0 | 22 | 24 | 35 | 28 | 19 | 29 | 33 | 28 |
N.S. |
1 | 0.00 | 1.05 | 1.14 | 1.67 | 1.33 | 0.90 | 1.38 | 1.57 | 1.33 |
time (sec) |
N/A | 0.000 | 0.192 | 12.836 | 0.081 | 0.067 | 0.096 | 0.127 | 0.216 | 0.458 |
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 | 29 | 21 | 21 | 20 | 0 | 29 | 17 | 35 | 42 | 19 |
N.S. |
1 | 0.72 | 0.72 | 0.69 | 0.00 | 1.00 | 0.59 | 1.21 | 1.45 | 0.66 |
time (sec) |
N/A | 0.366 | 0.168 | 0.605 | 0.000 | 0.067 | 0.098 | 0.115 | 0.240 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 304 | 34 | 32 | 443 | 34 | 26 | 41 | 42 | 29 |
N.S. |
1 | 10.86 | 1.21 | 1.14 | 15.82 | 1.21 | 0.93 | 1.46 | 1.50 | 1.04 |
time (sec) |
N/A | 1.668 | 0.080 | 0.634 | 0.172 | 0.072 | 0.513 | 0.116 | 0.236 | 0.632 |
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 | 31 | 0 | 28 | 31 | 30 | 30 | 26 | 0 | 35 | 30 |
N.S. |
1 | 0.00 | 0.90 | 1.00 | 0.97 | 0.97 | 0.84 | 0.00 | 1.13 | 0.97 |
time (sec) |
N/A | 0.000 | 0.131 | 28.452 | 0.166 | 0.077 | 0.218 | 0.000 | 0.252 | 2.169 |
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 | 21 | 0 | 27 | 21 | 42 | 36 | 17 | 36 | 37 | 37 |
N.S. |
1 | 0.00 | 1.29 | 1.00 | 2.00 | 1.71 | 0.81 | 1.71 | 1.76 | 1.76 |
time (sec) |
N/A | 0.000 | 0.057 | 16.678 | 0.167 | 0.070 | 0.150 | 0.144 | 0.230 | 0.504 |
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 | 14 | 10 | 10 | 10 | 9 | 9 | 8 | 9 | 13 | 11 |
N.S. |
1 | 0.71 | 0.71 | 0.71 | 0.64 | 0.64 | 0.57 | 0.64 | 0.93 | 0.79 |
time (sec) |
N/A | 0.213 | 0.016 | 0.077 | 0.029 | 0.067 | 0.046 | 0.111 | 0.280 | 0.027 |
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 | 32 | 0 | 69 | 33 | 45 | 32 | 27 | 51 | 33 | 34 |
N.S. |
1 | 0.00 | 2.16 | 1.03 | 1.41 | 1.00 | 0.84 | 1.59 | 1.03 | 1.06 |
time (sec) |
N/A | 0.000 | 0.082 | 6.585 | 0.220 | 0.070 | 0.147 | 0.185 | 0.235 | 0.838 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-2) | B | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 55 | 30 | 45 | 41 | 0 | 79 | 445 | 93 |
N.S. |
1 | 0.00 | 1.96 | 1.07 | 1.61 | 1.46 | 0.00 | 2.82 | 15.89 | 3.32 |
time (sec) |
N/A | 0.000 | 3.863 | 0.511 | 0.116 | 0.069 | 0.000 | 0.125 | 0.260 | 0.600 |
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 | 17 | 12 | 13 | 15 | 11 | 8 | 11 | 15 | 13 |
N.S. |
1 | 1.42 | 1.00 | 1.08 | 1.25 | 0.92 | 0.67 | 0.92 | 1.25 | 1.08 |
time (sec) |
N/A | 0.165 | 0.041 | 0.056 | 0.029 | 0.065 | 0.046 | 0.107 | 0.276 | 0.389 |
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 | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 20 | 20 | 19 | 19 | 17 | 231 | 18 | 17 |
N.S. |
1 | 0.00 | 0.80 | 0.80 | 0.76 | 0.76 | 0.68 | 9.24 | 0.72 | 0.68 |
time (sec) |
N/A | 0.000 | 0.074 | 7.644 | 0.066 | 0.063 | 0.113 | 0.386 | 0.250 | 0.461 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 14 | 10 | 10 | 12 | 10 | 15 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 0.77 | 0.77 | 0.92 | 0.77 | 1.15 | 0.77 |
time (sec) |
N/A | 0.310 | 0.023 | 0.155 | 0.030 | 0.068 | 0.095 | 0.119 | 0.234 | 0.431 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 103 | 27 | 31 | 589 | 32 | 49 | 33 | 64 | 54 |
N.S. |
1 | 4.29 | 1.12 | 1.29 | 24.54 | 1.33 | 2.04 | 1.38 | 2.67 | 2.25 |
time (sec) |
N/A | 1.318 | 0.116 | 0.948 | 0.216 | 0.068 | 0.267 | 0.124 | 0.274 | 0.725 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | F(-2) | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 67 | 68 | 80 | 62 | 0 | 92 | 95 | 0 |
N.S. |
1 | 0.00 | 3.05 | 3.09 | 3.64 | 2.82 | 0.00 | 4.18 | 4.32 | 0.00 |
time (sec) |
N/A | 0.000 | 0.099 | 17.006 | 0.081 | 0.086 | 0.000 | 0.673 | 0.255 | 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 | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 40 | 29 | 29 | 28 | 28 | 58 | 28 | 29 | 29 |
N.S. |
1 | 1.82 | 1.32 | 1.32 | 1.27 | 1.27 | 2.64 | 1.27 | 1.32 | 1.32 |
time (sec) |
N/A | 0.188 | 0.019 | 0.196 | 0.047 | 0.070 | 0.082 | 0.116 | 0.244 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 16 | 16 | 14 | 31 | 47 | 31 | 31 | 35 | 31 |
N.S. |
1 | 0.89 | 0.89 | 0.78 | 1.72 | 2.61 | 1.72 | 1.72 | 1.94 | 1.72 |
time (sec) |
N/A | 5.860 | 0.161 | 0.613 | 0.086 | 0.067 | 0.090 | 0.120 | 0.257 | 0.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | F(-1) | A | B | B |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 67 | 23 | 31 | 0 | 31 | 32 | 54 |
N.S. |
1 | 0.00 | 1.00 | 2.91 | 1.00 | 1.35 | 0.00 | 1.35 | 1.39 | 2.35 |
time (sec) |
N/A | 0.000 | 0.160 | 0.200 | 0.298 | 0.084 | 0.000 | 21.635 | 0.521 | 1.508 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | A | F(-2) | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 26 | 24 | 0 | 26 | 0 | 26 | 27 | 26 |
N.S. |
1 | 0.00 | 0.90 | 0.83 | 0.00 | 0.90 | 0.00 | 0.90 | 0.93 | 0.90 |
time (sec) |
N/A | 0.000 | 2.033 | 1.723 | 0.000 | 0.063 | 0.000 | 0.185 | 0.241 | 0.825 |
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 | 25 | 0 | 26 | 57 | 32 | 47 | 39 | 39 | 44 | 39 |
N.S. |
1 | 0.00 | 1.04 | 2.28 | 1.28 | 1.88 | 1.56 | 1.56 | 1.76 | 1.56 |
time (sec) |
N/A | 0.000 | 0.218 | 133.696 | 0.085 | 0.075 | 0.271 | 0.186 | 0.260 | 0.507 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | F(-2) | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 49 | 45 | 62 | 55 | 60 | 0 | 0 | 153 | 59 |
N.S. |
1 | 1.40 | 1.29 | 1.77 | 1.57 | 1.71 | 0.00 | 0.00 | 4.37 | 1.69 |
time (sec) |
N/A | 18.881 | 0.247 | 5.866 | 0.392 | 0.071 | 0.000 | 0.000 | 200.023 | 0.561 |
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 | 28 | 0 | 28 | 35 | 38 | 38 | 34 | 0 | 158 | 41 |
N.S. |
1 | 0.00 | 1.00 | 1.25 | 1.36 | 1.36 | 1.21 | 0.00 | 5.64 | 1.46 |
time (sec) |
N/A | 0.000 | 0.154 | 5.020 | 0.101 | 0.070 | 0.291 | 0.000 | 37.463 | 0.704 |
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 | 23 | 21 | 21 | 20 | 21 | 21 | 20 | 23 | 21 | 19 |
N.S. |
1 | 0.91 | 0.91 | 0.87 | 0.91 | 0.91 | 0.87 | 1.00 | 0.91 | 0.83 |
time (sec) |
N/A | 0.377 | 0.007 | 0.064 | 0.038 | 0.059 | 0.072 | 0.109 | 0.227 | 0.416 |
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 | 29 | 29 | 26 | 25 | 26 | 26 | 26 | 28 | 24 |
N.S. |
1 | 1.21 | 1.21 | 1.08 | 1.04 | 1.08 | 1.08 | 1.08 | 1.17 | 1.00 |
time (sec) |
N/A | 0.230 | 0.006 | 0.245 | 0.022 | 0.066 | 0.087 | 0.112 | 0.206 | 0.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 48 | 39 | 41 | 0 | 40 | 49 | 45 | 49 | 45 |
N.S. |
1 | 2.18 | 1.77 | 1.86 | 0.00 | 1.82 | 2.23 | 2.05 | 2.23 | 2.05 |
time (sec) |
N/A | 0.325 | 0.074 | 39.574 | 0.000 | 0.066 | 0.209 | 0.119 | 0.201 | 0.496 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | F(-1) | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 35 | 42 | 94 | 90 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 1.46 | 1.75 | 3.92 | 3.75 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.123 | 33.358 | 2.379 | 0.078 | 0.000 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 16 | 17 | 0 | 13 | 19 | 30 | 16 | 15 |
N.S. |
1 | 1.00 | 0.94 | 1.00 | 0.00 | 0.76 | 1.12 | 1.76 | 0.94 | 0.88 |
time (sec) |
N/A | 0.302 | 0.014 | 0.253 | 0.000 | 0.061 | 0.108 | 0.116 | 0.207 | 0.043 |
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 | 21 | 0 | 32 | 17 | 14 | 14 | 14 | 14 | 22 | 15 |
N.S. |
1 | 0.00 | 1.52 | 0.81 | 0.67 | 0.67 | 0.67 | 0.67 | 1.05 | 0.71 |
time (sec) |
N/A | 0.000 | 0.077 | 0.270 | 0.079 | 0.064 | 0.102 | 0.105 | 0.205 | 0.638 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | F | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 75 | 0 | 28 | 26 | 28 | 22 | 31 | 30 | 0 |
N.S. |
1 | 2.42 | 0.00 | 0.90 | 0.84 | 0.90 | 0.71 | 1.00 | 0.97 | 0.00 |
time (sec) |
N/A | 2.482 | 0.000 | 1.202 | 0.168 | 0.066 | 0.241 | 0.162 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 25 | 22 | 62 | 41 | 39 | 108 | 33 | 58 |
N.S. |
1 | 0.00 | 1.09 | 0.96 | 2.70 | 1.78 | 1.70 | 4.70 | 1.43 | 2.52 |
time (sec) |
N/A | 0.000 | 5.033 | 1.251 | 0.156 | 0.063 | 0.107 | 0.139 | 0.209 | 0.758 |
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 | 6 | 4 | 5 | 4 | 4 | 3 | 5 | 4 | 4 |
N.S. |
1 | 0.35 | 0.24 | 0.29 | 0.24 | 0.24 | 0.18 | 0.29 | 0.24 | 0.24 |
time (sec) |
N/A | 0.136 | 0.000 | 0.125 | 0.023 | 0.061 | 0.017 | 0.111 | 0.201 | 0.012 |
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 | 31 | 31 | 23 | 22 | 22 | 20 | 22 | 25 | 21 |
N.S. |
1 | 1.19 | 1.19 | 0.88 | 0.85 | 0.85 | 0.77 | 0.85 | 0.96 | 0.81 |
time (sec) |
N/A | 1.130 | 0.127 | 0.159 | 0.083 | 0.075 | 0.120 | 0.121 | 0.203 | 0.586 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 87 | 87 | 24 | 35 | 41 | 48 | 0 | 37 | 27 |
N.S. |
1 | 4.83 | 4.83 | 1.33 | 1.94 | 2.28 | 2.67 | 0.00 | 2.06 | 1.50 |
time (sec) |
N/A | 2.525 | 0.424 | 2.274 | 0.180 | 0.069 | 0.142 | 0.000 | 0.245 | 0.638 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | B | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 43 | 81 | 44 | 43 | 49 | 47 | 74 | 0 |
N.S. |
1 | 0.00 | 1.34 | 2.53 | 1.38 | 1.34 | 1.53 | 1.47 | 2.31 | 0.00 |
time (sec) |
N/A | 0.000 | 5.117 | 3.357 | 0.135 | 0.079 | 0.299 | 0.751 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F(-1) | A | A | B | A | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 0 | 30 | 27 | 50 | 27 | 564 | 36 | 93 |
N.S. |
1 | 0.00 | 0.00 | 1.11 | 1.00 | 1.85 | 1.00 | 20.89 | 1.33 | 3.44 |
time (sec) |
N/A | 0.000 | 0.000 | 40.337 | 0.176 | 0.066 | 0.235 | 0.908 | 60.396 | 0.645 |