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 | F | A | A | A | A | F(-1) | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 22 | 30 | 19 | 24 | 0 | 0 | 23 | 18 |
N.S. |
1 | 0.00 | 1.05 | 1.43 | 0.90 | 1.14 | 0.00 | 0.00 | 1.10 | 0.86 |
time (sec) |
N/A | 0.000 | 0.451 | 5.207 | 0.209 | 0.077 | 0.000 | 0.000 | 0.193 | 3.859 |
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 | 23 | 19 | 18 | 34 | 19 | 34 | 29 | 18 |
N.S. |
1 | 1.12 | 0.96 | 0.79 | 0.75 | 1.42 | 0.79 | 1.42 | 1.21 | 0.75 |
time (sec) |
N/A | 0.360 | 0.139 | 0.165 | 0.072 | 0.086 | 0.142 | 0.124 | 0.229 | 3.588 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | A | A | A | F | F | B |
verified | N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 0 | 18 | 17 | 25 | 17 | 0 | 130 | 21 |
N.S. |
1 | 1.00 | 0.00 | 0.95 | 0.89 | 1.32 | 0.89 | 0.00 | 6.84 | 1.11 |
time (sec) |
N/A | 0.276 | 0.000 | 0.150 | 0.238 | 0.092 | 0.135 | 0.000 | 0.220 | 0.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 25 | 23 | 47 | 97 | 22 | 0 | 62 | 68 |
N.S. |
1 | 0.00 | 0.93 | 0.85 | 1.74 | 3.59 | 0.81 | 0.00 | 2.30 | 2.52 |
time (sec) |
N/A | 0.000 | 1.667 | 242.086 | 0.420 | 0.103 | 1.111 | 0.000 | 0.227 | 3.675 |
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 | 29 | 0 | 27 | 28 | 33 | 26 | 22 | 150 | 30 | 0 |
N.S. |
1 | 0.00 | 0.93 | 0.97 | 1.14 | 0.90 | 0.76 | 5.17 | 1.03 | 0.00 |
time (sec) |
N/A | 0.000 | 0.054 | 1.349 | 0.173 | 0.077 | 0.280 | 0.199 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 24 | 20 | 17 | 59 | 20 | 0 | 25 | 20 |
N.S. |
1 | 0.00 | 1.09 | 0.91 | 0.77 | 2.68 | 0.91 | 0.00 | 1.14 | 0.91 |
time (sec) |
N/A | 0.000 | 0.136 | 0.320 | 0.148 | 0.090 | 0.122 | 0.000 | 0.237 | 3.723 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 23 | 32 | 31 | 48 | 29 | 0 | 36 | 33 |
N.S. |
1 | 0.00 | 1.10 | 1.52 | 1.48 | 2.29 | 1.38 | 0.00 | 1.71 | 1.57 |
time (sec) |
N/A | 0.000 | 0.230 | 0.462 | 0.214 | 0.107 | 0.127 | 0.000 | 0.213 | 3.780 |
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 | 19 | 47 | 19 | 20 | 19 | 19 | 19 | 21 | 19 | 14 |
N.S. |
1 | 2.47 | 1.00 | 1.05 | 1.00 | 1.00 | 1.00 | 1.11 | 1.00 | 0.74 |
time (sec) |
N/A | 0.285 | 0.008 | 0.151 | 0.036 | 0.089 | 0.114 | 0.127 | 0.195 | 0.095 |
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 | 25 | 0 | 25 | 25 | 60 | 60 | 78 | 70 | 71 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 2.40 | 2.40 | 3.12 | 2.80 | 2.84 | 0.00 |
time (sec) |
N/A | 0.000 | 0.376 | 3.727 | 0.097 | 0.103 | 0.247 | 0.154 | 0.197 | 0.000 |
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 | 16 | 26 | 18 | 23 | 45 | 22 | 20 | 22 | 15 | 16 |
N.S. |
1 | 1.62 | 1.12 | 1.44 | 2.81 | 1.38 | 1.25 | 1.38 | 0.94 | 1.00 |
time (sec) |
N/A | 0.272 | 0.114 | 0.064 | 0.038 | 0.090 | 0.054 | 0.124 | 0.223 | 3.450 |
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 | 27 | 24 | 25 | 25 | 36 | 24 | 25 | 36 | 53 |
N.S. |
1 | 0.84 | 0.75 | 0.78 | 0.78 | 1.12 | 0.75 | 0.78 | 1.12 | 1.66 |
time (sec) |
N/A | 0.295 | 0.023 | 0.068 | 0.038 | 0.084 | 0.137 | 0.121 | 0.210 | 0.116 |
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 | 19 | 21 | 20 | 22 | 21 | 22 | 23 | 21 | 19 |
N.S. |
1 | 0.95 | 1.05 | 1.00 | 1.10 | 1.05 | 1.10 | 1.15 | 1.05 | 0.95 |
time (sec) |
N/A | 0.269 | 0.009 | 0.054 | 0.045 | 0.075 | 0.217 | 0.132 | 0.193 | 0.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 16 | 16 | 17 | 16 | 20 | 14 | 16 | 21 | 17 |
N.S. |
1 | 0.70 | 0.70 | 0.74 | 0.70 | 0.87 | 0.61 | 0.70 | 0.91 | 0.74 |
time (sec) |
N/A | 0.166 | 0.001 | 0.081 | 0.032 | 0.083 | 0.052 | 0.119 | 0.195 | 3.477 |
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 | 27 | 22 | 18 | 20 | 20 | 17 | 20 | 20 | 17 |
N.S. |
1 | 1.42 | 1.16 | 0.95 | 1.05 | 1.05 | 0.89 | 1.05 | 1.05 | 0.89 |
time (sec) |
N/A | 0.158 | 0.004 | 0.036 | 0.030 | 0.079 | 0.023 | 0.124 | 0.215 | 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 | 24 | 35 | 24 | 21 | 30 | 33 | 17 | 21 | 36 | 33 |
N.S. |
1 | 1.46 | 1.00 | 0.88 | 1.25 | 1.38 | 0.71 | 0.88 | 1.50 | 1.38 |
time (sec) |
N/A | 0.650 | 0.111 | 0.332 | 0.076 | 0.083 | 0.055 | 0.134 | 0.199 | 3.598 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 29 | 26 | 23 | 0 | 43 | 24 | 94 | 35 | 42 |
N.S. |
1 | 1.21 | 1.08 | 0.96 | 0.00 | 1.79 | 1.00 | 3.92 | 1.46 | 1.75 |
time (sec) |
N/A | 0.511 | 0.100 | 0.309 | 0.000 | 0.100 | 0.050 | 0.142 | 0.182 | 3.702 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F(-1) | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 38 | 28 | 30 | 27 | 0 | 0 | 101 | 27 |
N.S. |
1 | 0.00 | 1.41 | 1.04 | 1.11 | 1.00 | 0.00 | 0.00 | 3.74 | 1.00 |
time (sec) |
N/A | 0.000 | 0.216 | 41.162 | 0.291 | 0.083 | 0.000 | 0.000 | 200.033 | 4.186 |
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 | 30 | 0 | 20 | 19 | 20 | 20 | 17 | 20 | 20 | 18 |
N.S. |
1 | 0.00 | 0.67 | 0.63 | 0.67 | 0.67 | 0.57 | 0.67 | 0.67 | 0.60 |
time (sec) |
N/A | 0.000 | 0.069 | 0.138 | 0.084 | 0.074 | 0.062 | 0.114 | 0.173 | 3.663 |
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 | 31 | 26 | 40 | 33 | 27 | 23 | 31 | 23 |
N.S. |
1 | 0.00 | 1.19 | 1.00 | 1.54 | 1.27 | 1.04 | 0.88 | 1.19 | 0.88 |
time (sec) |
N/A | 0.000 | 2.319 | 0.485 | 0.108 | 0.087 | 0.145 | 0.120 | 0.174 | 3.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 238 | 54 | 44 | 40 | 40 | 73 | 0 | 32 | 58 |
N.S. |
1 | 6.26 | 1.42 | 1.16 | 1.05 | 1.05 | 1.92 | 0.00 | 0.84 | 1.53 |
time (sec) |
N/A | 0.740 | 0.035 | 0.303 | 0.040 | 0.078 | 1.011 | 0.000 | 0.177 | 4.150 |
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 | 34 | 116 | 152 | 104 | 97 | 94 | 107 | 110 | 122 | 94 |
N.S. |
1 | 3.41 | 4.47 | 3.06 | 2.85 | 2.76 | 3.15 | 3.24 | 3.59 | 2.76 |
time (sec) |
N/A | 0.405 | 0.011 | 0.232 | 0.033 | 0.077 | 0.448 | 0.118 | 0.172 | 3.448 |
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 | 24 | 0 | 20 | 18 | 27 | 20 | 22 | 0 | 41 | 29 |
N.S. |
1 | 0.00 | 0.83 | 0.75 | 1.12 | 0.83 | 0.92 | 0.00 | 1.71 | 1.21 |
time (sec) |
N/A | 0.000 | 1.327 | 0.777 | 0.281 | 0.107 | 1.509 | 0.000 | 0.188 | 3.759 |
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 | 6 | 6 | 7 | 6 | 6 | 5 | 7 | 6 | 6 |
N.S. |
1 | 0.67 | 0.67 | 0.78 | 0.67 | 0.67 | 0.56 | 0.78 | 0.67 | 0.67 |
time (sec) |
N/A | 0.142 | 0.001 | 0.019 | 0.024 | 0.065 | 0.031 | 0.118 | 0.175 | 0.016 |
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 | 26 | 47 | 25 | 22 | 28 | 28 | 34 | 145 | 38 | 22 |
N.S. |
1 | 1.81 | 0.96 | 0.85 | 1.08 | 1.08 | 1.31 | 5.58 | 1.46 | 0.85 |
time (sec) |
N/A | 0.751 | 0.072 | 0.322 | 0.172 | 0.080 | 0.160 | 0.135 | 1.462 | 3.755 |
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 | 16 | 17 | 14 | 12 | 13 | 10 | 14 | 14 | 13 |
N.S. |
1 | 0.67 | 0.71 | 0.58 | 0.50 | 0.54 | 0.42 | 0.58 | 0.58 | 0.54 |
time (sec) |
N/A | 0.156 | 0.002 | 0.032 | 0.032 | 0.072 | 0.037 | 0.123 | 0.168 | 0.031 |
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 | 36 | 31 | 30 | 30 | 30 | 31 | 30 | 31 | 29 |
N.S. |
1 | 1.44 | 1.24 | 1.20 | 1.20 | 1.20 | 1.24 | 1.20 | 1.24 | 1.16 |
time (sec) |
N/A | 0.333 | 0.020 | 0.137 | 0.031 | 0.081 | 0.352 | 0.124 | 0.173 | 0.122 |
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 | 72 | 25 | 28 | 17 | 22 | 19 | 18 | 18 | 0 |
N.S. |
1 | 2.88 | 1.00 | 1.12 | 0.68 | 0.88 | 0.76 | 0.72 | 0.72 | 0.00 |
time (sec) |
N/A | 1.103 | 0.167 | 3.544 | 0.092 | 0.102 | 0.246 | 0.127 | 0.174 | 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 | 13 | 12 | 16 | 15 | 13 | 13 | 15 | 13 | 15 | 17 |
N.S. |
1 | 0.92 | 1.23 | 1.15 | 1.00 | 1.00 | 1.15 | 1.00 | 1.15 | 1.31 |
time (sec) |
N/A | 0.143 | 0.001 | 0.036 | 0.031 | 0.061 | 0.018 | 0.117 | 0.164 | 3.394 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-2) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 22 | 22 | 21 | 64 | 39 | 0 | 0 | 22 | 18 |
N.S. |
1 | 0.92 | 0.92 | 0.88 | 2.67 | 1.62 | 0.00 | 0.00 | 0.92 | 0.75 |
time (sec) |
N/A | 0.267 | 0.174 | 7.258 | 0.193 | 0.087 | 0.000 | 0.000 | 0.178 | 3.678 |
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 | 51 | 23 | 23 | 19 | 28 | 31 | 19 | 32 | 21 |
N.S. |
1 | 1.76 | 0.79 | 0.79 | 0.66 | 0.97 | 1.07 | 0.66 | 1.10 | 0.72 |
time (sec) |
N/A | 0.250 | 0.094 | 3.491 | 0.215 | 0.092 | 0.140 | 0.125 | 0.175 | 3.575 |
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 | 18 | 21 | 17 | 18 | 16 | 19 | 16 | 16 | 15 |
N.S. |
1 | 1.00 | 1.17 | 0.94 | 1.00 | 0.89 | 1.06 | 0.89 | 0.89 | 0.83 |
time (sec) |
N/A | 0.352 | 0.047 | 0.214 | 0.061 | 0.079 | 0.046 | 0.126 | 0.177 | 3.575 |
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 | 24 | 23 | 22 | 22 | 19 | 22 | 42 | 25 |
N.S. |
1 | 0.00 | 0.89 | 0.85 | 0.81 | 0.81 | 0.70 | 0.81 | 1.56 | 0.93 |
time (sec) |
N/A | 0.000 | 0.227 | 0.245 | 0.127 | 0.080 | 0.122 | 0.143 | 2.645 | 3.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 24 | 24 | 370 | 264 | 167 | 236 | 183 | 359 | 187 |
N.S. |
1 | 0.83 | 0.83 | 12.76 | 9.10 | 5.76 | 8.14 | 6.31 | 12.38 | 6.45 |
time (sec) |
N/A | 0.984 | 0.051 | 2.230 | 0.192 | 0.092 | 0.522 | 1.657 | 0.183 | 4.406 |
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 | 28 | 20 | 17 | 16 | 16 | 14 | 16 | 27 | 17 |
N.S. |
1 | 1.22 | 0.87 | 0.74 | 0.70 | 0.70 | 0.61 | 0.70 | 1.17 | 0.74 |
time (sec) |
N/A | 0.194 | 0.019 | 0.061 | 0.035 | 0.071 | 0.065 | 0.113 | 0.177 | 3.407 |
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 | 21 | 23 | 20 | 19 | 19 | 19 | 20 | 19 | 19 |
N.S. |
1 | 1.11 | 1.21 | 1.05 | 1.00 | 1.00 | 1.00 | 1.05 | 1.00 | 1.00 |
time (sec) |
N/A | 0.201 | 0.017 | 0.100 | 0.032 | 0.068 | 0.048 | 0.117 | 0.190 | 0.052 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 33 | 34 | 0 | 68 | 27 | 68 | 37 | 36 |
N.S. |
1 | 0.00 | 1.03 | 1.06 | 0.00 | 2.12 | 0.84 | 2.12 | 1.16 | 1.12 |
time (sec) |
N/A | 0.000 | 0.041 | 42.254 | 0.000 | 0.087 | 0.286 | 0.162 | 0.184 | 4.353 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 50 | 50 | 24 | 24 | 42 | 26 | 24 | 37 | 24 |
N.S. |
1 | 2.08 | 2.08 | 1.00 | 1.00 | 1.75 | 1.08 | 1.00 | 1.54 | 1.00 |
time (sec) |
N/A | 0.223 | 0.314 | 0.313 | 0.039 | 0.085 | 0.059 | 0.123 | 0.182 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 60 | 70 | 72 | 70 | 48 | 85 | 86 | 109 |
N.S. |
1 | 0.00 | 1.88 | 2.19 | 2.25 | 2.19 | 1.50 | 2.66 | 2.69 | 3.41 |
time (sec) |
N/A | 0.000 | 0.073 | 0.022 | 0.089 | 0.095 | 0.091 | 0.166 | 0.194 | 3.822 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | A | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 74 | 61 | 56 | 55 | 57 | 53 | 61 | 62 | 55 |
N.S. |
1 | 2.55 | 2.10 | 1.93 | 1.90 | 1.97 | 1.83 | 2.10 | 2.14 | 1.90 |
time (sec) |
N/A | 0.283 | 0.015 | 0.599 | 0.031 | 0.086 | 0.110 | 0.125 | 0.169 | 3.450 |
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 | 13 | 13 | 10 | 9 | 10 | 10 | 9 | 12 | 10 |
N.S. |
1 | 0.57 | 0.57 | 0.43 | 0.39 | 0.43 | 0.43 | 0.39 | 0.52 | 0.43 |
time (sec) |
N/A | 0.153 | 0.001 | 0.022 | 0.034 | 0.065 | 0.030 | 0.128 | 0.172 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | F(-2) | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 80 | 36 | 59 | 59 | 0 | 35 | 35 | 49468 |
N.S. |
1 | 0.00 | 3.48 | 1.57 | 2.57 | 2.57 | 0.00 | 1.52 | 1.52 | 2150.78 |
time (sec) |
N/A | 0.000 | 0.324 | 0.346 | 0.154 | 0.090 | 0.000 | 0.136 | 0.173 | 9.962 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 37 | 37 | 51 | 41 | 47 | 39 | 50 | 50 | 42 |
N.S. |
1 | 1.42 | 1.42 | 1.96 | 1.58 | 1.81 | 1.50 | 1.92 | 1.92 | 1.62 |
time (sec) |
N/A | 14.815 | 0.186 | 0.368 | 0.047 | 0.091 | 79.981 | 0.537 | 0.167 | 0.567 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 226 | 29 | 27 | 104 | 123 | 110 | 528 | 152 | 25 |
N.S. |
1 | 7.53 | 0.97 | 0.90 | 3.47 | 4.10 | 3.67 | 17.60 | 5.07 | 0.83 |
time (sec) |
N/A | 1.086 | 0.171 | 2.542 | 0.230 | 0.093 | 15.459 | 0.270 | 0.500 | 0.781 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | B | A | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 20 | 27 | 0 | 41 | 31 | 40 | 138 | 16 |
N.S. |
1 | 0.00 | 1.00 | 1.35 | 0.00 | 2.05 | 1.55 | 2.00 | 6.90 | 0.80 |
time (sec) |
N/A | 0.000 | 0.316 | 0.333 | 0.000 | 0.080 | 0.137 | 0.119 | 0.172 | 3.486 |
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 | 25 | 12 | 10 | 12 | 12 | 14 | 12 | 25 | 12 |
N.S. |
1 | 1.79 | 0.86 | 0.71 | 0.86 | 0.86 | 1.00 | 0.86 | 1.79 | 0.86 |
time (sec) |
N/A | 0.177 | 0.044 | 0.068 | 0.031 | 0.078 | 0.051 | 0.119 | 0.177 | 0.094 |
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 | 21 | 17 | 18 | 20 | 22 | 12 | 23 | 25 | 17 |
N.S. |
1 | 0.88 | 0.71 | 0.75 | 0.83 | 0.92 | 0.50 | 0.96 | 1.04 | 0.71 |
time (sec) |
N/A | 0.179 | 0.042 | 0.114 | 0.036 | 0.079 | 0.053 | 0.120 | 0.167 | 0.067 |
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 | 21 | 21 | 22 | 21 | 20 | 37 | 79 | 23 | 20 |
N.S. |
1 | 0.95 | 0.95 | 1.00 | 0.95 | 0.91 | 1.68 | 3.59 | 1.05 | 0.91 |
time (sec) |
N/A | 0.639 | 0.207 | 0.278 | 0.071 | 0.082 | 0.435 | 0.142 | 0.165 | 3.724 |
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 | 9 | 8 | 7 | 7 | 7 | 7 | 11 | 7 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.78 | 0.78 | 0.78 | 0.78 | 1.22 | 0.78 |
time (sec) |
N/A | 0.174 | 0.031 | 0.024 | 0.036 | 0.075 | 0.051 | 0.118 | 0.174 | 0.059 |
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 | 27 | 0 | 27 | 29 | 53 | 49 | 26 | 28 | 51 | 28 |
N.S. |
1 | 0.00 | 1.00 | 1.07 | 1.96 | 1.81 | 0.96 | 1.04 | 1.89 | 1.04 |
time (sec) |
N/A | 0.000 | 0.248 | 0.734 | 0.180 | 0.094 | 0.103 | 0.137 | 0.177 | 3.561 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | F(-1) | F | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 0 | 22 | 25 | 21 | 0 | 0 | 22 | 21 |
N.S. |
1 | 0.00 | 0.00 | 0.88 | 1.00 | 0.84 | 0.00 | 0.00 | 0.88 | 0.84 |
time (sec) |
N/A | 0.000 | 0.000 | 59.033 | 0.209 | 0.088 | 0.000 | 0.000 | 0.184 | 3.800 |
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 | 21 | 24 | 21 | 23 | 20 | 22 | 23 | 23 |
N.S. |
1 | 1.14 | 0.95 | 1.09 | 0.95 | 1.05 | 0.91 | 1.00 | 1.05 | 1.05 |
time (sec) |
N/A | 1.041 | 0.133 | 1.536 | 0.089 | 0.088 | 0.349 | 0.190 | 0.164 | 3.935 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 25 | 20 | 0 | 36 | 24 | 0 | 42 | 21 |
N.S. |
1 | 0.00 | 1.09 | 0.87 | 0.00 | 1.57 | 1.04 | 0.00 | 1.83 | 0.91 |
time (sec) |
N/A | 0.000 | 0.485 | 0.141 | 0.000 | 0.084 | 0.116 | 0.000 | 0.170 | 3.596 |
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 | 36 | 0 | 40 | 36 | 111 | 106 | 54 | 120 | 155 | 0 |
N.S. |
1 | 0.00 | 1.11 | 1.00 | 3.08 | 2.94 | 1.50 | 3.33 | 4.31 | 0.00 |
time (sec) |
N/A | 0.000 | 0.069 | 1.376 | 0.217 | 0.101 | 0.121 | 0.203 | 0.170 | 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 | 27 | 24 | 24 | 21 | 32 | 20 | 26 | 20 | 22 | 21 |
N.S. |
1 | 0.89 | 0.89 | 0.78 | 1.19 | 0.74 | 0.96 | 0.74 | 0.81 | 0.78 |
time (sec) |
N/A | 5.673 | 0.124 | 0.818 | 0.117 | 0.076 | 0.101 | 0.138 | 0.165 | 3.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 43 | 28 | 23 | 41 | 72 | 46 | 48 | 20 | 43 |
N.S. |
1 | 2.15 | 1.40 | 1.15 | 2.05 | 3.60 | 2.30 | 2.40 | 1.00 | 2.15 |
time (sec) |
N/A | 0.266 | 0.018 | 0.206 | 0.029 | 0.077 | 0.155 | 0.126 | 0.167 | 3.561 |
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 | 23 | 19 | 22 | 16 | 28 | 17 | 28 | 40 | 17 |
N.S. |
1 | 0.88 | 0.73 | 0.85 | 0.62 | 1.08 | 0.65 | 1.08 | 1.54 | 0.65 |
time (sec) |
N/A | 0.277 | 0.056 | 0.242 | 0.111 | 0.095 | 0.072 | 0.125 | 0.778 | 3.532 |
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 | 30 | 0 | 30 | 33 | 55 | 55 | 27 | 59 | 60 | 60 |
N.S. |
1 | 0.00 | 1.00 | 1.10 | 1.83 | 1.83 | 0.90 | 1.97 | 2.00 | 2.00 |
time (sec) |
N/A | 0.000 | 0.121 | 151.189 | 0.165 | 0.090 | 0.207 | 0.151 | 0.222 | 3.815 |
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 | 9 | 9 | 9 | 8 | 8 | 7 | 8 | 9 | 8 |
N.S. |
1 | 0.90 | 0.90 | 0.90 | 0.80 | 0.80 | 0.70 | 0.80 | 0.90 | 0.80 |
time (sec) |
N/A | 0.143 | 0.002 | 0.026 | 0.025 | 0.071 | 0.029 | 0.124 | 0.225 | 3.505 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 59 | 49 | 23 | 29 | 29 | 20 | 0 | 45 | 22 |
N.S. |
1 | 2.11 | 1.75 | 0.82 | 1.04 | 1.04 | 0.71 | 0.00 | 1.61 | 0.79 |
time (sec) |
N/A | 1.549 | 0.074 | 0.840 | 0.152 | 0.088 | 0.112 | 0.000 | 0.237 | 0.232 |
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 | 34 | 0 | 42 | 33 | 53 | 53 | 20 | 2098 | 87 | 74 |
N.S. |
1 | 0.00 | 1.24 | 0.97 | 1.56 | 1.56 | 0.59 | 61.71 | 2.56 | 2.18 |
time (sec) |
N/A | 0.000 | 0.070 | 1.082 | 0.119 | 0.090 | 0.134 | 0.195 | 0.229 | 3.713 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | C | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 65 | 56 | 72 | 61 | 48 | 55 | 76 | 58 |
N.S. |
1 | 0.00 | 2.03 | 1.75 | 2.25 | 1.91 | 1.50 | 1.72 | 2.38 | 1.81 |
time (sec) |
N/A | 0.000 | 0.099 | 1.500 | 0.064 | 0.089 | 0.082 | 0.134 | 0.202 | 3.664 |
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 | 22 | 76 | 57 | 56 | 103 | 63 | 65 | 74 | 83 | 68 |
N.S. |
1 | 3.45 | 2.59 | 2.55 | 4.68 | 2.86 | 2.95 | 3.36 | 3.77 | 3.09 |
time (sec) |
N/A | 0.390 | 0.040 | 14.059 | 0.036 | 0.092 | 0.112 | 0.125 | 0.210 | 3.763 |
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 | 24 | 288 | 242 | 244 | 322 | 216 | 226 | 0 | 271 | 223 |
N.S. |
1 | 12.00 | 10.08 | 10.17 | 13.42 | 9.00 | 9.42 | 0.00 | 11.29 | 9.29 |
time (sec) |
N/A | 0.918 | 0.059 | 0.008 | 0.051 | 0.109 | 0.725 | 0.000 | 0.223 | 4.395 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 0 | 13 | 12 | 14 | 50 | 14 | 0 | 17 | 14 |
N.S. |
1 | 0.00 | 0.87 | 0.80 | 0.93 | 3.33 | 0.93 | 0.00 | 1.13 | 0.93 |
time (sec) |
N/A | 0.000 | 0.176 | 0.111 | 0.126 | 0.077 | 0.086 | 0.000 | 0.201 | 3.570 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 25 | 29 | 24 | 66 | 24 | 26 | 26 |
N.S. |
1 | 0.00 | 1.00 | 1.09 | 1.26 | 1.04 | 2.87 | 1.04 | 1.13 | 1.13 |
time (sec) |
N/A | 0.000 | 0.038 | 2.804 | 0.151 | 0.102 | 0.557 | 0.423 | 0.174 | 3.851 |
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 | 25 | 0 | 31 | 21 | 24 | 37 | 26 | 0 | 28 | 24 |
N.S. |
1 | 0.00 | 1.24 | 0.84 | 0.96 | 1.48 | 1.04 | 0.00 | 1.12 | 0.96 |
time (sec) |
N/A | 0.000 | 1.545 | 4.123 | 0.240 | 0.080 | 0.284 | 0.000 | 0.176 | 3.666 |
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 | 21 | 23 | 34 | 38 | 90 | 90 | 100 | 207 | 32 | 1277 |
N.S. |
1 | 1.10 | 1.62 | 1.81 | 4.29 | 4.29 | 4.76 | 9.86 | 1.52 | 60.81 |
time (sec) |
N/A | 0.497 | 0.186 | 1.224 | 0.168 | 0.086 | 0.136 | 0.138 | 0.167 | 3.990 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 44 | 31 | 0 | 30 | 24 | 55 | 128 | 44 |
N.S. |
1 | 0.00 | 1.83 | 1.29 | 0.00 | 1.25 | 1.00 | 2.29 | 5.33 | 1.83 |
time (sec) |
N/A | 0.000 | 0.082 | 1.092 | 0.000 | 0.089 | 0.250 | 0.281 | 200.016 | 3.708 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 37 | 22 | 30 | 0 | 95 | 54 | 147 | 156 | 52 |
N.S. |
1 | 1.32 | 0.79 | 1.07 | 0.00 | 3.39 | 1.93 | 5.25 | 5.57 | 1.86 |
time (sec) |
N/A | 0.455 | 0.024 | 0.379 | 0.000 | 0.086 | 0.260 | 0.130 | 0.179 | 3.741 |
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 | 12 | 12 | 13 | 12 | 15 | 8 | 13 | 19 | 12 |
N.S. |
1 | 0.38 | 0.38 | 0.41 | 0.38 | 0.47 | 0.25 | 0.41 | 0.59 | 0.38 |
time (sec) |
N/A | 0.193 | 0.005 | 0.031 | 0.036 | 0.071 | 0.038 | 0.121 | 0.164 | 3.499 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 26 | 21 | 25 | 22 | 25 | 27 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.13 | 0.91 | 1.09 | 0.96 | 1.09 | 1.17 | 0.00 |
time (sec) |
N/A | 0.000 | 0.282 | 10.947 | 0.086 | 0.079 | 1.194 | 0.200 | 0.173 | 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 | 13 | 11 | 12 | 11 | 15 | 5 | 11 | 12 | 11 |
N.S. |
1 | 0.59 | 0.50 | 0.55 | 0.50 | 0.68 | 0.23 | 0.50 | 0.55 | 0.50 |
time (sec) |
N/A | 0.169 | 0.005 | 0.063 | 0.030 | 0.072 | 0.029 | 0.125 | 0.169 | 3.731 |
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 | 20 | 37 | 18 | 16 | 15 | 15 | 14 | 0 | 19 | 15 |
N.S. |
1 | 1.85 | 0.90 | 0.80 | 0.75 | 0.75 | 0.70 | 0.00 | 0.95 | 0.75 |
time (sec) |
N/A | 0.197 | 0.021 | 0.155 | 0.095 | 0.085 | 0.162 | 0.000 | 0.173 | 3.632 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 28 | 24 | 25 | 36 | 21 | 24 | 32 | 27 | 21 |
N.S. |
1 | 1.75 | 1.50 | 1.56 | 2.25 | 1.31 | 1.50 | 2.00 | 1.69 | 1.31 |
time (sec) |
N/A | 0.185 | 0.035 | 0.076 | 0.039 | 0.077 | 0.055 | 0.119 | 0.170 | 3.562 |
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 | 48 | 21 | 20 | 28 | 19 | 17 | 19 | 21 | 19 |
N.S. |
1 | 1.71 | 0.75 | 0.71 | 1.00 | 0.68 | 0.61 | 0.68 | 0.75 | 0.68 |
time (sec) |
N/A | 0.625 | 0.063 | 0.645 | 0.079 | 0.078 | 0.163 | 0.131 | 0.168 | 3.813 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 570 | 32 | 24 | 255 | 24 | 26 | 34 | 23 | 19 |
N.S. |
1 | 22.80 | 1.28 | 0.96 | 10.20 | 0.96 | 1.04 | 1.36 | 0.92 | 0.76 |
time (sec) |
N/A | 1.932 | 0.566 | 0.361 | 0.287 | 0.080 | 0.189 | 0.128 | 0.172 | 0.279 |
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 | 17 | 22 | 17 | 21 | 50 | 20 | 20 | 20 | 17 | 15 |
N.S. |
1 | 1.29 | 1.00 | 1.24 | 2.94 | 1.18 | 1.18 | 1.18 | 1.00 | 0.88 |
time (sec) |
N/A | 0.236 | 0.037 | 0.102 | 0.033 | 0.095 | 0.058 | 0.118 | 0.164 | 3.564 |
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 | 24 | 192 | 21 | 22 | 73 | 21 | 20 | 34 | 50 | 23 |
N.S. |
1 | 8.00 | 0.88 | 0.92 | 3.04 | 0.88 | 0.83 | 1.42 | 2.08 | 0.96 |
time (sec) |
N/A | 1.164 | 0.247 | 0.262 | 0.167 | 0.102 | 0.079 | 0.128 | 0.157 | 3.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 24 | 23 | 42 | 22 | 0 | 24 | 27 | 24 |
N.S. |
1 | 0.00 | 0.86 | 0.82 | 1.50 | 0.79 | 0.00 | 0.86 | 0.96 | 0.86 |
time (sec) |
N/A | 0.000 | 0.036 | 96.330 | 0.277 | 0.084 | 0.000 | 0.200 | 0.181 | 4.022 |
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 | 16 | 16 | 18 | 17 | 17 | 15 | 17 | 16 | 17 |
N.S. |
1 | 0.62 | 0.62 | 0.69 | 0.65 | 0.65 | 0.58 | 0.65 | 0.62 | 0.65 |
time (sec) |
N/A | 1.275 | 0.153 | 0.528 | 0.157 | 0.082 | 0.090 | 0.169 | 0.162 | 0.361 |
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 | 19 | 0 | 19 | 16 | 48 | 15 | 15 | 23 | 15 | 15 |
N.S. |
1 | 0.00 | 1.00 | 0.84 | 2.53 | 0.79 | 0.79 | 1.21 | 0.79 | 0.79 |
time (sec) |
N/A | 0.000 | 0.156 | 0.657 | 0.142 | 0.086 | 0.171 | 0.257 | 0.169 | 3.852 |
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 | 18 | 18 | 28 | 23 | 23 | 27 | 23 | 27 | 23 |
N.S. |
1 | 1.00 | 1.00 | 1.56 | 1.28 | 1.28 | 1.50 | 1.28 | 1.50 | 1.28 |
time (sec) |
N/A | 0.164 | 0.014 | 0.069 | 0.031 | 0.087 | 0.044 | 0.121 | 0.166 | 0.046 |
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 | 26 | 0 | 22 | 25 | 92 | 24 | 22 | 36 | 22 | 21 |
N.S. |
1 | 0.00 | 0.85 | 0.96 | 3.54 | 0.92 | 0.85 | 1.38 | 0.85 | 0.81 |
time (sec) |
N/A | 0.000 | 0.190 | 0.322 | 0.156 | 0.074 | 0.086 | 0.126 | 0.176 | 3.654 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | C | B | A | F(-1) | F | B | F(-1) |
verified | N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 174 | 33 | 1142 | 103 | 41 | 0 | 0 | 48 | 0 |
N.S. |
1 | 4.83 | 0.92 | 31.72 | 2.86 | 1.14 | 0.00 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 1.090 | 0.105 | 0.066 | 0.290 | 0.098 | 0.000 | 0.000 | 0.216 | 0.000 |
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 | 13 | 13 | 13 | 13 | 12 | 16 | 14 | 12 | 36 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.92 | 1.23 | 1.08 | 0.92 | 2.77 | 1.00 |
time (sec) |
N/A | 0.184 | 0.013 | 0.049 | 0.034 | 0.076 | 0.075 | 0.119 | 0.174 | 3.705 |
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 | 39 | 256 | 252 | 195 | 491 | 201 | 192 | 0 | 264 | 246 |
N.S. |
1 | 6.56 | 6.46 | 5.00 | 12.59 | 5.15 | 4.92 | 0.00 | 6.77 | 6.31 |
time (sec) |
N/A | 1.416 | 0.074 | 156.868 | 0.046 | 0.103 | 0.326 | 0.000 | 0.173 | 6.244 |
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 | 19 | 21 | 19 | 16 | 19 | 19 | 17 | 42 | 35 | 15 |
N.S. |
1 | 1.11 | 1.00 | 0.84 | 1.00 | 1.00 | 0.89 | 2.21 | 1.84 | 0.79 |
time (sec) |
N/A | 0.753 | 0.035 | 0.332 | 0.168 | 0.077 | 0.057 | 0.146 | 0.181 | 3.825 |
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 | 31 | 22 | 16 | 31 | 19 | 22 | 19 | 25 | 21 |
N.S. |
1 | 1.48 | 1.05 | 0.76 | 1.48 | 0.90 | 1.05 | 0.90 | 1.19 | 1.00 |
time (sec) |
N/A | 0.300 | 0.140 | 0.120 | 0.027 | 0.085 | 0.067 | 0.121 | 0.174 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 267 | 64 | 67 | 68 | 71 | 65 | 110 | 104 | 93 |
N.S. |
1 | 8.34 | 2.00 | 2.09 | 2.12 | 2.22 | 2.03 | 3.44 | 3.25 | 2.91 |
time (sec) |
N/A | 1.323 | 0.490 | 260.783 | 0.143 | 0.086 | 0.079 | 0.150 | 0.195 | 4.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 24 | 25 | 20 | 24 | 23 | 20 | 0 | 22 | 0 |
N.S. |
1 | 0.96 | 1.00 | 0.80 | 0.96 | 0.92 | 0.80 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.284 | 0.020 | 1.591 | 0.034 | 0.083 | 0.421 | 0.000 | 0.187 | 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 | 22 | 0 | 26 | 25 | 24 | 23 | 22 | 24 | 37 | 26 |
N.S. |
1 | 0.00 | 1.18 | 1.14 | 1.09 | 1.05 | 1.00 | 1.09 | 1.68 | 1.18 |
time (sec) |
N/A | 0.000 | 0.968 | 0.116 | 0.124 | 0.077 | 0.104 | 0.148 | 0.203 | 0.114 |
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 | 32 | 0 | 32 | 32 | 26 | 109 | 366 | 108 | 47 | 28 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.81 | 3.41 | 11.44 | 3.38 | 1.47 | 0.88 |
time (sec) |
N/A | 0.000 | 6.738 | 1.322 | 0.088 | 0.099 | 0.330 | 0.150 | 0.196 | 0.275 |
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 | 23 | 24 | 23 | 35 | 20 | 23 | 35 | 72 |
N.S. |
1 | 0.00 | 0.85 | 0.89 | 0.85 | 1.30 | 0.74 | 0.85 | 1.30 | 2.67 |
time (sec) |
N/A | 0.000 | 0.120 | 0.645 | 0.080 | 0.076 | 0.062 | 0.167 | 0.189 | 0.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | B | B | B | B | B | F | B |
verified | N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 0 | 43 | 87 | 42 | 58 | 50 | 140 | 47 |
N.S. |
1 | 1.00 | 0.00 | 1.95 | 3.95 | 1.91 | 2.64 | 2.27 | 6.36 | 2.14 |
time (sec) |
N/A | 5.580 | 0.000 | 1.595 | 0.318 | 0.094 | 0.996 | 0.480 | 200.021 | 4.269 |
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 | 28 | 53 | 51 | 38 | 41 | 37 | 39 | 37 | 70 | 44 |
N.S. |
1 | 1.89 | 1.82 | 1.36 | 1.46 | 1.32 | 1.39 | 1.32 | 2.50 | 1.57 |
time (sec) |
N/A | 0.195 | 0.050 | 0.226 | 0.106 | 0.072 | 0.066 | 0.121 | 0.177 | 3.871 |
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 | 31 | 31 | 36 | 44 | 33 | 27 | 34 | 50 | 32 |
N.S. |
1 | 1.00 | 1.00 | 1.16 | 1.42 | 1.06 | 0.87 | 1.10 | 1.61 | 1.03 |
time (sec) |
N/A | 1.624 | 0.156 | 24.412 | 0.250 | 0.084 | 0.475 | 0.879 | 0.192 | 4.453 |
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 | 21 | 26 | 16 | 17 | 0 | 20 | 22 | 19 | 17 | 16 |
N.S. |
1 | 1.24 | 0.76 | 0.81 | 0.00 | 0.95 | 1.05 | 0.90 | 0.81 | 0.76 |
time (sec) |
N/A | 0.778 | 0.075 | 0.151 | 0.000 | 0.084 | 0.074 | 0.122 | 0.179 | 3.887 |
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 | 22 | 22 | 19 | 20 | 46 | 17 | 46 | 24 | 17 |
N.S. |
1 | 0.79 | 0.79 | 0.68 | 0.71 | 1.64 | 0.61 | 1.64 | 0.86 | 0.61 |
time (sec) |
N/A | 0.352 | 0.048 | 0.161 | 0.279 | 0.089 | 0.110 | 0.129 | 0.171 | 3.873 |
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 | 26 | 30 | 26 | 31 | 43 | 28 | 26 |
N.S. |
1 | 1.00 | 1.00 | 1.44 | 1.67 | 1.44 | 1.72 | 2.39 | 1.56 | 1.44 |
time (sec) |
N/A | 0.823 | 0.039 | 1.609 | 0.162 | 0.103 | 0.265 | 0.813 | 0.193 | 6.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 24 | 0 | 36 | 22 | 0 | 310 | 27 |
N.S. |
1 | 0.00 | 1.00 | 0.83 | 0.00 | 1.24 | 0.76 | 0.00 | 10.69 | 0.93 |
time (sec) |
N/A | 0.000 | 1.089 | 0.385 | 0.000 | 0.075 | 0.194 | 0.000 | 0.283 | 3.811 |