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 | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 21 | 19 | 23 | 22 | 22 | 51 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.79 | 0.96 | 0.92 | 0.92 | 2.12 | 0.88 |
time (sec) |
N/A | 0.551 | 0.105 | 0.175 | 0.127 | 0.064 | 0.206 | 0.120 | 34.114 | 1.807 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 21 | 71 | 57 | 31 | 0 | 100 | 75 |
N.S. |
1 | 0.00 | 1.00 | 0.84 | 2.84 | 2.28 | 1.24 | 0.00 | 4.00 | 3.00 |
time (sec) |
N/A | 0.000 | 5.059 | 55.316 | 0.362 | 0.074 | 5.338 | 0.000 | 200.028 | 1.966 |
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 | 38 | 34 | 34 | 42 | 34 | 35 | 35 |
N.S. |
1 | 1.36 | 1.36 | 1.36 | 1.21 | 1.21 | 1.50 | 1.21 | 1.25 | 1.25 |
time (sec) |
N/A | 0.224 | 0.019 | 0.215 | 0.031 | 0.068 | 0.095 | 0.119 | 0.178 | 1.800 |
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 | 69 | 63 | 61 | 60 | 66 | 70 | 66 | 66 | 55 |
N.S. |
1 | 2.46 | 2.25 | 2.18 | 2.14 | 2.36 | 2.50 | 2.36 | 2.36 | 1.96 |
time (sec) |
N/A | 1.768 | 0.290 | 0.046 | 0.160 | 0.070 | 0.178 | 0.125 | 0.174 | 1.857 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | C | F | B | F(-2) | F | B | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 65 | 356 | 0 | 59 | 0 | 0 | 71 | 109 |
N.S. |
1 | 0.00 | 2.24 | 12.28 | 0.00 | 2.03 | 0.00 | 0.00 | 2.45 | 3.76 |
time (sec) |
N/A | 0.000 | 0.229 | 0.198 | 0.000 | 0.072 | 0.000 | 0.000 | 0.202 | 4.219 |
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 | 21 | 19 | 24 | 18 | 20 | 18 | 19 | 20 |
N.S. |
1 | 0.00 | 0.84 | 0.76 | 0.96 | 0.72 | 0.80 | 0.72 | 0.76 | 0.80 |
time (sec) |
N/A | 0.000 | 0.063 | 9.286 | 0.220 | 0.067 | 1.752 | 0.164 | 0.203 | 2.297 |
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 | 14 | 12 | 12 | 12 | 19 | 14 | 12 | 11 | 15 | 11 |
N.S. |
1 | 0.86 | 0.86 | 0.86 | 1.36 | 1.00 | 0.86 | 0.79 | 1.07 | 0.79 |
time (sec) |
N/A | 0.181 | 0.053 | 0.112 | 0.065 | 0.064 | 0.040 | 0.118 | 0.211 | 0.065 |
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 | 9 | 9 | 10 | 7 | 9 | 8 | 12 | 9 | 9 |
N.S. |
1 | 0.43 | 0.43 | 0.48 | 0.33 | 0.43 | 0.38 | 0.57 | 0.43 | 0.43 |
time (sec) |
N/A | 0.158 | 0.030 | 0.042 | 0.030 | 0.057 | 0.052 | 0.115 | 0.185 | 1.872 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 290 | 13 | 82 | 18 | 15 | 71 | 17 | 17 |
N.S. |
1 | 1.00 | 26.36 | 1.18 | 7.45 | 1.64 | 1.36 | 6.45 | 1.55 | 1.55 |
time (sec) |
N/A | 0.371 | 0.116 | 0.266 | 0.109 | 0.064 | 0.071 | 0.128 | 0.190 | 2.225 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 16 | 14 | 28 | 21 | 21 | 36 | 21 | 25 | 11 |
N.S. |
1 | 0.89 | 0.78 | 1.56 | 1.17 | 1.17 | 2.00 | 1.17 | 1.39 | 0.61 |
time (sec) |
N/A | 0.140 | 0.002 | 0.049 | 0.031 | 0.061 | 0.026 | 0.111 | 0.174 | 0.056 |
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 | 17 | 0 | 29 | 31 | 32 | 29 | 29 | 33 | 32 | 29 |
N.S. |
1 | 0.00 | 1.71 | 1.82 | 1.88 | 1.71 | 1.71 | 1.94 | 1.88 | 1.71 |
time (sec) |
N/A | 0.000 | 0.046 | 95.013 | 0.131 | 0.064 | 1.527 | 0.299 | 0.190 | 3.112 |
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 | 18 | 18 | 21 | 17 | 18 | 26 | 27 | 26 | 20 |
N.S. |
1 | 0.90 | 0.90 | 1.05 | 0.85 | 0.90 | 1.30 | 1.35 | 1.30 | 1.00 |
time (sec) |
N/A | 0.282 | 0.034 | 0.207 | 0.121 | 0.062 | 0.081 | 0.119 | 0.178 | 1.003 |
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 | 27 | 318 | 73 | 54 | 221 | 221 | 282 | 221 | 303 | 207 |
N.S. |
1 | 11.78 | 2.70 | 2.00 | 8.19 | 8.19 | 10.44 | 8.19 | 11.22 | 7.67 |
time (sec) |
N/A | 0.420 | 0.022 | 1.593 | 0.041 | 0.065 | 0.054 | 0.121 | 0.205 | 2.081 |
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 | 23 | 23 | 22 | 28 | 26 | 22 | 23 | 20 |
N.S. |
1 | 0.00 | 0.88 | 0.88 | 0.85 | 1.08 | 1.00 | 0.85 | 0.88 | 0.77 |
time (sec) |
N/A | 0.000 | 0.179 | 0.188 | 0.153 | 0.067 | 0.120 | 0.122 | 0.166 | 1.943 |
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 | 14 | 14 | 15 | 14 | 14 | 14 | 14 | 11 | 11 |
N.S. |
1 | 0.78 | 0.78 | 0.83 | 0.78 | 0.78 | 0.78 | 0.78 | 0.61 | 0.61 |
time (sec) |
N/A | 0.147 | 0.001 | 0.054 | 0.034 | 0.058 | 0.039 | 0.113 | 0.191 | 1.770 |
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 | 27 | 59 | 37 | 33 | 50 | 25 | 41 | 25 | 31 | 31 |
N.S. |
1 | 2.19 | 1.37 | 1.22 | 1.85 | 0.93 | 1.52 | 0.93 | 1.15 | 1.15 |
time (sec) |
N/A | 0.564 | 1.126 | 0.675 | 0.090 | 0.066 | 0.127 | 0.114 | 0.187 | 0.252 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 55 | 24 | 22 | 176 | 21 | 22 | 26 | 23 | 21 |
N.S. |
1 | 2.20 | 0.96 | 0.88 | 7.04 | 0.84 | 0.88 | 1.04 | 0.92 | 0.84 |
time (sec) |
N/A | 0.382 | 0.117 | 0.344 | 0.082 | 0.069 | 0.142 | 0.114 | 0.186 | 1.797 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 39 | 18 | 119 | 30 | 12 | 39 | 18 | 42 |
N.S. |
1 | 0.00 | 2.05 | 0.95 | 6.26 | 1.58 | 0.63 | 2.05 | 0.95 | 2.21 |
time (sec) |
N/A | 0.000 | 0.071 | 0.155 | 0.044 | 0.069 | 0.105 | 0.114 | 0.187 | 1.897 |
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 | 24 | 24 | 24 | 23 | 47 | 22 | 24 | 52 | 24 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 1.96 | 0.92 | 1.00 | 2.17 | 1.00 | 0.92 |
time (sec) |
N/A | 0.184 | 0.009 | 0.384 | 0.034 | 0.063 | 0.083 | 0.114 | 0.185 | 1.840 |
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 | 26 | 0 | 24 | 32 | 22 | 31 | 29 | 56 | 26 | 59 |
N.S. |
1 | 0.00 | 0.92 | 1.23 | 0.85 | 1.19 | 1.12 | 2.15 | 1.00 | 2.27 |
time (sec) |
N/A | 0.000 | 0.042 | 0.737 | 0.277 | 0.064 | 0.183 | 0.248 | 0.425 | 2.360 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | B | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 21 | 51 | 26 | 43 | 15 | 0 | 46 | 31 |
N.S. |
1 | 0.00 | 0.88 | 2.12 | 1.08 | 1.79 | 0.62 | 0.00 | 1.92 | 1.29 |
time (sec) |
N/A | 0.000 | 0.167 | 0.974 | 0.039 | 0.068 | 0.171 | 0.000 | 0.194 | 2.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 11 | 5 | 6 | 5 | 5 | 3 | 5 | 5 | 5 |
N.S. |
1 | 0.69 | 0.31 | 0.38 | 0.31 | 0.31 | 0.19 | 0.31 | 0.31 | 0.31 |
time (sec) |
N/A | 0.132 | 0.000 | 0.029 | 0.033 | 0.049 | 0.015 | 0.113 | 0.176 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | A | F(-2) | F(-1) | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 30 | 80 | 35 | 43 | 0 | 0 | 1342 | 36 |
N.S. |
1 | 0.00 | 1.00 | 2.67 | 1.17 | 1.43 | 0.00 | 0.00 | 44.73 | 1.20 |
time (sec) |
N/A | 0.000 | 0.107 | 237.583 | 0.163 | 0.074 | 0.000 | 0.000 | 0.479 | 3.648 |
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 | 20 | 17 | 17 | 22 | 22 | 26 | 18 | 25 | 17 |
N.S. |
1 | 1.00 | 0.85 | 0.85 | 1.10 | 1.10 | 1.30 | 0.90 | 1.25 | 0.85 |
time (sec) |
N/A | 0.225 | 0.030 | 0.080 | 0.028 | 0.067 | 0.054 | 0.121 | 0.201 | 0.136 |
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 | 18 | 0 | 19 | 38 | 43 | 44 | 63 | 65 | 70 | 0 |
N.S. |
1 | 0.00 | 1.06 | 2.11 | 2.39 | 2.44 | 3.50 | 3.61 | 3.89 | 0.00 |
time (sec) |
N/A | 0.000 | 0.291 | 1.112 | 0.084 | 0.072 | 0.211 | 0.162 | 0.198 | 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 | 32 | 0 | 35 | 32 | 35 | 31 | 27 | 31 | 41 | 49 |
N.S. |
1 | 0.00 | 1.09 | 1.00 | 1.09 | 0.97 | 0.84 | 0.97 | 1.28 | 1.53 |
time (sec) |
N/A | 0.000 | 0.089 | 0.213 | 0.093 | 0.065 | 0.146 | 0.121 | 0.199 | 1.862 |
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 | 24 | 23 | 20 | 41 | 19 | 17 | 19 | 39 | 15 |
N.S. |
1 | 1.26 | 1.21 | 1.05 | 2.16 | 1.00 | 0.89 | 1.00 | 2.05 | 0.79 |
time (sec) |
N/A | 0.293 | 0.028 | 0.265 | 0.152 | 0.063 | 0.079 | 0.115 | 0.195 | 1.891 |
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 | 17 | 15 | 14 | 13 | 13 | 14 | 13 | 14 | 13 |
N.S. |
1 | 1.13 | 1.00 | 0.93 | 0.87 | 0.87 | 0.93 | 0.87 | 0.93 | 0.87 |
time (sec) |
N/A | 0.155 | 0.003 | 0.082 | 0.031 | 0.063 | 0.046 | 0.110 | 0.193 | 1.814 |
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 | 38 | 0 | 34 | 67 | 45 | 39 | 26 | 37 | 65 | 35 |
N.S. |
1 | 0.00 | 0.89 | 1.76 | 1.18 | 1.03 | 0.68 | 0.97 | 1.71 | 0.92 |
time (sec) |
N/A | 0.000 | 0.079 | 2.573 | 0.168 | 0.067 | 0.333 | 0.212 | 0.194 | 2.530 |
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 | 25 | 25 | 19 | 37 | 34 | 17 | 34 | 34 | 18 |
N.S. |
1 | 0.89 | 0.89 | 0.68 | 1.32 | 1.21 | 0.61 | 1.21 | 1.21 | 0.64 |
time (sec) |
N/A | 0.832 | 0.303 | 0.266 | 0.060 | 0.067 | 0.065 | 0.110 | 0.180 | 0.093 |
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 | 24 | 24 | 23 | 22 | 22 | 19 | 24 | 22 | 35 |
N.S. |
1 | 0.83 | 0.83 | 0.79 | 0.76 | 0.76 | 0.66 | 0.83 | 0.76 | 1.21 |
time (sec) |
N/A | 0.373 | 0.099 | 0.343 | 0.056 | 0.072 | 0.083 | 0.112 | 0.188 | 1.963 |
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 | 18 | 0 | 29 | 17 | 26 | 26 | 15 | 0 | 19 | 26 |
N.S. |
1 | 0.00 | 1.61 | 0.94 | 1.44 | 1.44 | 0.83 | 0.00 | 1.06 | 1.44 |
time (sec) |
N/A | 0.000 | 0.153 | 4.487 | 0.278 | 0.070 | 0.198 | 0.000 | 0.208 | 2.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | B | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 58 | 54 | 57 | 54 | 53 | 57 | 61 | 51 |
N.S. |
1 | 0.00 | 2.00 | 1.86 | 1.97 | 1.86 | 1.83 | 1.97 | 2.10 | 1.76 |
time (sec) |
N/A | 0.000 | 0.381 | 27.085 | 0.097 | 0.071 | 0.170 | 0.124 | 0.192 | 1.931 |
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 | 21 | 21 | 19 | 20 | 23 | 62 | 24 | 25 | 73 | 17 |
N.S. |
1 | 1.00 | 0.90 | 0.95 | 1.10 | 2.95 | 1.14 | 1.19 | 3.48 | 0.81 |
time (sec) |
N/A | 0.790 | 0.146 | 1.161 | 0.084 | 0.065 | 0.083 | 0.291 | 0.182 | 1.912 |
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 | 14 | 14 | 14 | 12 | 30 | 11 | 12 | 11 | 12 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 2.14 | 0.79 | 0.86 | 0.79 | 0.86 | 0.79 |
time (sec) |
N/A | 0.217 | 0.005 | 0.062 | 0.034 | 0.077 | 0.047 | 0.116 | 0.175 | 1.763 |
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 | 27 | 27 | 22 | 34 | 38 | 22 | 40 | 44 | 31 |
N.S. |
1 | 1.08 | 1.08 | 0.88 | 1.36 | 1.52 | 0.88 | 1.60 | 1.76 | 1.24 |
time (sec) |
N/A | 0.620 | 0.131 | 0.487 | 0.072 | 0.065 | 0.056 | 0.118 | 0.171 | 1.934 |
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 | 38 | 27 | 26 | 33 | 23 | 27 | 26 | 29 | 24 |
N.S. |
1 | 1.58 | 1.12 | 1.08 | 1.38 | 0.96 | 1.12 | 1.08 | 1.21 | 1.00 |
time (sec) |
N/A | 0.274 | 0.183 | 0.171 | 0.067 | 0.061 | 0.071 | 0.119 | 0.187 | 1.779 |
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 | 49 | 24 | 31 | 35 | 28 | 31 | 42 | 48 | 42 |
N.S. |
1 | 1.75 | 0.86 | 1.11 | 1.25 | 1.00 | 1.11 | 1.50 | 1.71 | 1.50 |
time (sec) |
N/A | 0.297 | 0.215 | 0.397 | 0.162 | 0.069 | 0.101 | 0.122 | 0.208 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | C | A | B | A | A | A | B | B |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 3581 | 173773 | 32 | 165 | 42 | 26 | 30 | 38 | 25 |
N.S. |
1 | 115.52 | 5605.58 | 1.03 | 5.32 | 1.35 | 0.84 | 0.97 | 1.23 | 0.81 |
time (sec) |
N/A | 18.429 | 40.003 | 9.017 | 3.569 | 0.071 | 0.176 | 0.304 | 0.190 | 2.023 |
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 | 26 | 71 | 22 | 22 | 35 | 34 | 32 | 66 | 39 | 66 |
N.S. |
1 | 2.73 | 0.85 | 0.85 | 1.35 | 1.31 | 1.23 | 2.54 | 1.50 | 2.54 |
time (sec) |
N/A | 0.350 | 0.067 | 0.339 | 0.037 | 0.065 | 0.634 | 0.124 | 0.183 | 0.183 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | C | B | B | F(-1) | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 24 | 80 | 74 | 56 | 129 | 0 | 99 | 94 |
N.S. |
1 | 0.00 | 0.92 | 3.08 | 2.85 | 2.15 | 4.96 | 0.00 | 3.81 | 3.62 |
time (sec) |
N/A | 0.000 | 5.065 | 0.655 | 0.097 | 0.072 | 0.330 | 0.000 | 0.174 | 2.202 |
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 | 26 | 0 | 26 | 20 | 19 | 28 | 20 | 0 | 246 | 21 |
N.S. |
1 | 0.00 | 1.00 | 0.77 | 0.73 | 1.08 | 0.77 | 0.00 | 9.46 | 0.81 |
time (sec) |
N/A | 0.000 | 0.734 | 0.647 | 0.554 | 0.066 | 6.933 | 0.000 | 0.439 | 1.947 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 24 | 26 | 21 | 20 | 20 | 22 | 20 | 45 | 21 |
N.S. |
1 | 0.89 | 0.96 | 0.78 | 0.74 | 0.74 | 0.81 | 0.74 | 1.67 | 0.78 |
time (sec) |
N/A | 0.305 | 0.013 | 0.138 | 0.037 | 0.060 | 0.284 | 0.112 | 0.179 | 0.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 24 | 20 | 38 | 24 | 24 | 24 | 37 | 877 | 0 |
N.S. |
1 | 1.09 | 0.91 | 1.73 | 1.09 | 1.09 | 1.09 | 1.68 | 39.86 | 0.00 |
time (sec) |
N/A | 6.263 | 0.342 | 0.450 | 0.105 | 0.064 | 0.127 | 0.198 | 0.194 | 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 | 25 | 23 | 23 | 19 | 18 | 22 | 19 | 27 | 28 | 18 |
N.S. |
1 | 0.92 | 0.92 | 0.76 | 0.72 | 0.88 | 0.76 | 1.08 | 1.12 | 0.72 |
time (sec) |
N/A | 0.622 | 0.021 | 0.451 | 0.033 | 0.070 | 0.115 | 0.118 | 0.195 | 1.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | F(-2) | F(-1) | F | B | B |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 24 | 24 | 0 | 17 | 0 | 0 | 0 | 21 | 16 |
N.S. |
1 | 0.96 | 0.96 | 0.00 | 0.68 | 0.00 | 0.00 | 0.00 | 0.84 | 0.64 |
time (sec) |
N/A | 0.306 | 0.034 | 0.000 | 0.241 | 0.000 | 0.000 | 0.000 | 0.185 | 2.064 |
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 | 27 | 33 | 17 | 21 | 24 | 19 | 17 | 26 | 18 |
N.S. |
1 | 1.35 | 1.65 | 0.85 | 1.05 | 1.20 | 0.95 | 0.85 | 1.30 | 0.90 |
time (sec) |
N/A | 0.347 | 0.397 | 0.091 | 0.087 | 0.067 | 0.124 | 0.118 | 0.176 | 0.207 |
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 | 16 | 16 | 15 | 18 | 16 | 16 | 14 | 16 | 37 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.12 | 1.00 | 1.00 | 0.88 | 1.00 | 2.31 | 0.00 |
time (sec) |
N/A | 0.385 | 0.015 | 0.566 | 0.162 | 0.067 | 0.097 | 0.123 | 0.168 | 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 | 27 | 31 | 29 | 24 | 26 | 26 | 31 | 26 | 31 | 24 |
N.S. |
1 | 1.15 | 1.07 | 0.89 | 0.96 | 0.96 | 1.15 | 0.96 | 1.15 | 0.89 |
time (sec) |
N/A | 0.175 | 0.020 | 0.227 | 0.039 | 0.064 | 0.079 | 0.114 | 0.160 | 1.798 |
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 | 20 | 15 | 19 | 17 | 15 | 19 | 33 | 20 |
N.S. |
1 | 1.00 | 1.18 | 0.88 | 1.12 | 1.00 | 0.88 | 1.12 | 1.94 | 1.18 |
time (sec) |
N/A | 0.307 | 0.073 | 0.240 | 0.102 | 0.064 | 0.089 | 0.117 | 0.203 | 1.831 |
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 | 33 | 0 | 157 | 28 | 47 | 47 | 22 | 47 | 54 | 47 |
N.S. |
1 | 0.00 | 4.76 | 0.85 | 1.42 | 1.42 | 0.67 | 1.42 | 1.64 | 1.42 |
time (sec) |
N/A | 0.000 | 0.104 | 0.439 | 0.169 | 0.083 | 0.074 | 0.124 | 0.180 | 1.921 |
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 | 19 | 27 | 17 | 24 | 16 | 17 | 20 | 19 | 16 |
N.S. |
1 | 1.06 | 1.50 | 0.94 | 1.33 | 0.89 | 0.94 | 1.11 | 1.06 | 0.89 |
time (sec) |
N/A | 0.798 | 1.060 | 0.217 | 0.084 | 0.070 | 0.065 | 0.111 | 0.166 | 1.885 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | F | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 32 | 90 | 0 | 94 | 704 | 107 | 105 | 657 |
N.S. |
1 | 0.00 | 1.39 | 3.91 | 0.00 | 4.09 | 30.61 | 4.65 | 4.57 | 28.57 |
time (sec) |
N/A | 0.000 | 0.070 | 0.471 | 0.000 | 0.070 | 0.335 | 0.135 | 0.180 | 2.202 |
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 | 31 | 24 | 32 | 33 | 33 | 32 | 33 | 33 | 31 |
N.S. |
1 | 1.41 | 1.09 | 1.45 | 1.50 | 1.50 | 1.45 | 1.50 | 1.50 | 1.41 |
time (sec) |
N/A | 0.209 | 0.011 | 0.164 | 0.029 | 0.069 | 0.230 | 0.138 | 0.172 | 0.118 |
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 | 28 | 44 | 42 | 39 | 39 | 43 | 44 | 43 |
N.S. |
1 | 0.00 | 0.85 | 1.33 | 1.27 | 1.18 | 1.18 | 1.30 | 1.33 | 1.30 |
time (sec) |
N/A | 0.000 | 0.034 | 14.131 | 0.151 | 0.064 | 0.109 | 0.130 | 0.184 | 1.992 |
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 | 17 | 17 | 16 | 17 | 27 | 12 | 18 | 26 | 17 |
N.S. |
1 | 0.71 | 0.71 | 0.67 | 0.71 | 1.12 | 0.50 | 0.75 | 1.08 | 0.71 |
time (sec) |
N/A | 0.234 | 0.008 | 0.060 | 0.032 | 0.073 | 0.044 | 0.113 | 0.176 | 1.759 |
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 | 25 | 0 | 31 | 34 | 35 | 34 | 44 | 36 | 33 | 33 |
N.S. |
1 | 0.00 | 1.24 | 1.36 | 1.40 | 1.36 | 1.76 | 1.44 | 1.32 | 1.32 |
time (sec) |
N/A | 0.000 | 0.453 | 1.020 | 0.169 | 0.073 | 0.263 | 0.148 | 0.178 | 2.581 |
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 | 33 | 41 | 43 | 28 | 31 | 37 | 24 | 36 | 56 | 32 |
N.S. |
1 | 1.24 | 1.30 | 0.85 | 0.94 | 1.12 | 0.73 | 1.09 | 1.70 | 0.97 |
time (sec) |
N/A | 0.482 | 0.205 | 0.323 | 0.131 | 0.069 | 0.091 | 0.113 | 0.197 | 0.112 |
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 | 21 | 21 | 20 | 19 | 33 | 17 | 35 | 50 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 1.57 | 0.81 | 1.67 | 2.38 | 0.90 |
time (sec) |
N/A | 0.218 | 0.018 | 0.080 | 0.027 | 0.069 | 0.080 | 0.112 | 0.177 | 1.815 |
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 | 21 | 17 | 18 | 15 | 16 | 16 | 24 | 14 | 16 | 14 |
N.S. |
1 | 0.81 | 0.86 | 0.71 | 0.76 | 0.76 | 1.14 | 0.67 | 0.76 | 0.67 |
time (sec) |
N/A | 0.161 | 0.004 | 1.290 | 0.026 | 0.058 | 0.172 | 0.110 | 0.179 | 0.107 |
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 | 11 | 11 | 11 | 12 | 11 | 11 | 12 | 11 | 13 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 1.00 | 1.09 | 1.00 | 1.18 | 1.00 |
time (sec) |
N/A | 0.421 | 0.026 | 0.233 | 0.165 | 0.070 | 0.062 | 0.111 | 0.180 | 1.864 |
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 | 40 | 21 | 21 | 23 | 23 | 22 | 23 | 26 | 23 |
N.S. |
1 | 1.60 | 0.84 | 0.84 | 0.92 | 0.92 | 0.88 | 0.92 | 1.04 | 0.92 |
time (sec) |
N/A | 0.451 | 0.012 | 0.472 | 0.148 | 0.065 | 0.353 | 0.110 | 0.173 | 1.888 |
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 | 19 | 19 | 19 | 16 | 21 | 31 | 14 | 19 | 30 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 1.11 | 1.63 | 0.74 | 1.00 | 1.58 | 0.79 |
time (sec) |
N/A | 0.373 | 0.140 | 0.246 | 0.074 | 0.075 | 0.057 | 0.115 | 0.168 | 0.091 |
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 | 18 | 18 | 16 | 15 | 22 | 17 | 16 | 25 | 15 |
N.S. |
1 | 0.78 | 0.78 | 0.70 | 0.65 | 0.96 | 0.74 | 0.70 | 1.09 | 0.65 |
time (sec) |
N/A | 0.176 | 0.006 | 0.069 | 0.030 | 0.059 | 0.051 | 0.112 | 0.176 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | B | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 17 | 21 | 84 | 19 | 42 | 20 | 55 | 18 |
N.S. |
1 | 1.00 | 0.89 | 1.11 | 4.42 | 1.00 | 2.21 | 1.05 | 2.89 | 0.95 |
time (sec) |
N/A | 0.366 | 0.060 | 0.694 | 0.127 | 0.068 | 0.254 | 0.142 | 0.179 | 1.990 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 28 | 33 | 46 | 86 | 26 | 0 | 803 | 60 |
N.S. |
1 | 0.00 | 1.17 | 1.38 | 1.92 | 3.58 | 1.08 | 0.00 | 33.46 | 2.50 |
time (sec) |
N/A | 0.000 | 0.137 | 26.869 | 0.773 | 0.069 | 0.381 | 0.000 | 0.229 | 2.035 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 35 | 11 | 12 | 11 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 2.69 | 0.85 | 0.92 | 0.85 | 0.85 | 0.85 |
time (sec) |
N/A | 0.191 | 0.005 | 0.165 | 0.035 | 0.062 | 0.059 | 0.113 | 0.179 | 1.768 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F(-1) | B | B | B | B | F | B |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 26 | 0 | 183 | 144 | 175 | 180 | 297 | 230 |
N.S. |
1 | 0.00 | 0.79 | 0.00 | 5.55 | 4.36 | 5.30 | 5.45 | 9.00 | 6.97 |
time (sec) |
N/A | 0.000 | 1.824 | 0.000 | 0.973 | 0.076 | 1.646 | 1.596 | 200.028 | 2.947 |
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 | 34 | 0 | 26 | 38 | 24 | 34 | 34 | 27 | 43 | 26 |
N.S. |
1 | 0.00 | 0.76 | 1.12 | 0.71 | 1.00 | 1.00 | 0.79 | 1.26 | 0.76 |
time (sec) |
N/A | 0.000 | 0.151 | 3.849 | 0.278 | 0.064 | 0.169 | 1.724 | 0.220 | 2.404 |
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 | 19 | 13 | 17 | 16 | 16 | 17 | 16 | 24 | 18 |
N.S. |
1 | 1.27 | 0.87 | 1.13 | 1.07 | 1.07 | 1.13 | 1.07 | 1.60 | 1.20 |
time (sec) |
N/A | 0.305 | 0.053 | 0.151 | 0.112 | 0.064 | 0.097 | 0.122 | 0.210 | 1.849 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 17 | 30 | 35 | 29 | 27 | 35 | 29 | 25 |
N.S. |
1 | 0.00 | 0.89 | 1.58 | 1.84 | 1.53 | 1.42 | 1.84 | 1.53 | 1.32 |
time (sec) |
N/A | 0.000 | 0.235 | 4.080 | 0.145 | 0.068 | 0.742 | 0.171 | 0.209 | 2.215 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 44 | 12 | 36 | 11 | 10 | 19 | 12 | 10 |
N.S. |
1 | 1.00 | 3.67 | 1.00 | 3.00 | 0.92 | 0.83 | 1.58 | 1.00 | 0.83 |
time (sec) |
N/A | 0.216 | 0.036 | 0.279 | 0.036 | 0.062 | 0.078 | 0.108 | 0.200 | 1.944 |
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 | 30 | 0 | 26 | 33 | 22 | 31 | 27 | 0 | 25 | 36 |
N.S. |
1 | 0.00 | 0.87 | 1.10 | 0.73 | 1.03 | 0.90 | 0.00 | 0.83 | 1.20 |
time (sec) |
N/A | 0.000 | 2.857 | 0.813 | 0.099 | 0.066 | 0.190 | 0.000 | 0.211 | 2.271 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 27 | 30 | 42 | 42 | 24 | 24 | 52 | 77 |
N.S. |
1 | 0.00 | 1.04 | 1.15 | 1.62 | 1.62 | 0.92 | 0.92 | 2.00 | 2.96 |
time (sec) |
N/A | 0.000 | 0.957 | 3.748 | 0.164 | 0.065 | 0.088 | 0.277 | 0.232 | 2.021 |
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 | 18 | 16 | 15 | 14 | 17 | 10 | 14 | 17 | 15 |
N.S. |
1 | 0.69 | 0.62 | 0.58 | 0.54 | 0.65 | 0.38 | 0.54 | 0.65 | 0.58 |
time (sec) |
N/A | 0.177 | 0.001 | 0.038 | 0.032 | 0.053 | 0.034 | 0.114 | 0.203 | 0.030 |
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 | 23 | 0 | 29 | 27 | 34 | 34 | 19 | 28 | 32 | 26 |
N.S. |
1 | 0.00 | 1.26 | 1.17 | 1.48 | 1.48 | 0.83 | 1.22 | 1.39 | 1.13 |
time (sec) |
N/A | 0.000 | 0.152 | 0.713 | 0.071 | 0.065 | 0.079 | 0.121 | 0.197 | 2.160 |
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 | 35 | 0 | 44 | 36 | 38 | 36 | 39 | 1093 | 48 | 0 |
N.S. |
1 | 0.00 | 1.26 | 1.03 | 1.09 | 1.03 | 1.11 | 31.23 | 1.37 | 0.00 |
time (sec) |
N/A | 0.000 | 0.068 | 1.072 | 0.194 | 0.065 | 0.160 | 0.229 | 0.209 | 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 | 21 | 20 | 20 | 22 | 27 | 27 | 17 | 27 | 26 | 21 |
N.S. |
1 | 0.95 | 0.95 | 1.05 | 1.29 | 1.29 | 0.81 | 1.29 | 1.24 | 1.00 |
time (sec) |
N/A | 0.510 | 0.100 | 0.444 | 0.080 | 0.066 | 0.054 | 0.113 | 0.202 | 1.970 |
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 | 22 | 0 | 22 | 29 | 23 | 27 | 29 | 51 | 22 | 20 |
N.S. |
1 | 0.00 | 1.00 | 1.32 | 1.05 | 1.23 | 1.32 | 2.32 | 1.00 | 0.91 |
time (sec) |
N/A | 0.000 | 0.625 | 1.562 | 0.071 | 0.071 | 0.226 | 0.133 | 0.193 | 2.214 |
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 | 16 | 26 | 15 | 14 | 14 | 10 | 16 | 14 | 12 |
N.S. |
1 | 0.89 | 1.44 | 0.83 | 0.78 | 0.78 | 0.56 | 0.89 | 0.78 | 0.67 |
time (sec) |
N/A | 0.203 | 0.004 | 0.154 | 0.038 | 0.057 | 0.045 | 0.113 | 0.236 | 1.848 |
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 | 25 | 26 | 28 | 22 | 46 | 16 | 22 | 22 | 16 | 16 |
N.S. |
1 | 1.04 | 1.12 | 0.88 | 1.84 | 0.64 | 0.88 | 0.88 | 0.64 | 0.64 |
time (sec) |
N/A | 0.269 | 0.025 | 0.309 | 0.029 | 0.064 | 0.073 | 0.114 | 0.210 | 2.022 |
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 | 16 | 55 | 29 | 28 | 242 | 27 | 27 | 27 | 27 | 15 |
N.S. |
1 | 3.44 | 1.81 | 1.75 | 15.12 | 1.69 | 1.69 | 1.69 | 1.69 | 0.94 |
time (sec) |
N/A | 0.614 | 0.049 | 1.082 | 0.045 | 0.064 | 0.078 | 0.118 | 0.216 | 2.338 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | B | B | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 35 | 65 | 75 | 90 | 81 | 85 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.52 | 2.83 | 3.26 | 3.91 | 3.52 | 3.70 | 0.00 |
time (sec) |
N/A | 1.042 | 0.048 | 0.214 | 0.401 | 0.078 | 0.317 | 1.083 | 0.428 | 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 | 27 | 26 | 27 | 34 | 24 | 29 | 26 | 29 | 34 | 24 |
N.S. |
1 | 0.96 | 1.00 | 1.26 | 0.89 | 1.07 | 0.96 | 1.07 | 1.26 | 0.89 |
time (sec) |
N/A | 1.039 | 0.215 | 0.419 | 0.092 | 0.072 | 0.165 | 0.131 | 0.212 | 2.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | B | A | A | F | B | B |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 26 | 0 | 71 | 28 | 24 | 0 | 49 | 29 |
N.S. |
1 | 0.00 | 0.90 | 0.00 | 2.45 | 0.97 | 0.83 | 0.00 | 1.69 | 1.00 |
time (sec) |
N/A | 0.000 | 0.100 | 0.000 | 0.394 | 0.069 | 72.378 | 0.000 | 0.208 | 2.486 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 43 | 41 | 34 | 31 | 41 | 34 | 41 | 44 | 32 |
N.S. |
1 | 2.05 | 1.95 | 1.62 | 1.48 | 1.95 | 1.62 | 1.95 | 2.10 | 1.52 |
time (sec) |
N/A | 0.262 | 0.127 | 0.333 | 0.041 | 0.066 | 0.079 | 0.119 | 0.226 | 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 | 20 | 27 | 24 | 25 | 19 | 24 | 24 | 19 | 29 | 23 |
N.S. |
1 | 1.35 | 1.20 | 1.25 | 0.95 | 1.20 | 1.20 | 0.95 | 1.45 | 1.15 |
time (sec) |
N/A | 0.435 | 0.054 | 0.141 | 0.147 | 0.057 | 0.079 | 0.110 | 0.443 | 2.038 |
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 | 27 | 29 | 22 | 22 | 22 | 22 | 20 | 22 | 22 | 20 |
N.S. |
1 | 1.07 | 0.81 | 0.81 | 0.81 | 0.81 | 0.74 | 0.81 | 0.81 | 0.74 |
time (sec) |
N/A | 0.390 | 0.016 | 0.289 | 0.028 | 0.060 | 0.618 | 0.118 | 0.197 | 2.152 |
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 | 16 | 0 | 21 | 21 | 20 | 20 | 20 | 39 | 24 | 20 |
N.S. |
1 | 0.00 | 1.31 | 1.31 | 1.25 | 1.25 | 1.25 | 2.44 | 1.50 | 1.25 |
time (sec) |
N/A | 0.000 | 1.416 | 0.296 | 0.088 | 0.060 | 0.054 | 0.119 | 0.201 | 2.329 |
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 | 19 | 17 | 25 | 25 | 19 | 27 | 28 | 16 |
N.S. |
1 | 1.22 | 0.83 | 0.74 | 1.09 | 1.09 | 0.83 | 1.17 | 1.22 | 0.70 |
time (sec) |
N/A | 0.193 | 0.009 | 0.246 | 0.041 | 0.066 | 0.069 | 0.112 | 0.195 | 2.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 46 | 53 | 49 | 49 | 51 | 52 | 0 | 0 |
N.S. |
1 | 0.00 | 1.48 | 1.71 | 1.58 | 1.58 | 1.65 | 1.68 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.100 | 0.776 | 0.108 | 0.080 | 0.219 | 0.260 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | F(-1) | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 33 | 32 | 33 | 35 | 60 | 0 | 78 | 31 |
N.S. |
1 | 0.00 | 1.06 | 1.03 | 1.06 | 1.13 | 1.94 | 0.00 | 2.52 | 1.00 |
time (sec) |
N/A | 0.000 | 0.058 | 28.395 | 0.129 | 0.073 | 1.388 | 0.000 | 0.205 | 2.543 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 32 | 40 | 58 | 53 | 56 | 58 | 58 | 64 | 55 |
N.S. |
1 | 1.68 | 2.11 | 3.05 | 2.79 | 2.95 | 3.05 | 3.05 | 3.37 | 2.89 |
time (sec) |
N/A | 0.212 | 0.014 | 0.108 | 0.037 | 0.053 | 0.086 | 0.109 | 0.179 | 0.116 |
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 | 35 | 0 | 34 | 28 | 46 | 46 | 27 | 49 | 54 | 28 |
N.S. |
1 | 0.00 | 0.97 | 0.80 | 1.31 | 1.31 | 0.77 | 1.40 | 1.54 | 0.80 |
time (sec) |
N/A | 0.000 | 1.848 | 0.774 | 0.038 | 0.065 | 0.098 | 0.115 | 0.185 | 2.358 |
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 | 17 | 17 | 17 | 14 | 13 | 19 | 15 | 14 | 19 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 1.12 | 0.88 | 0.82 | 1.12 | 0.76 |
time (sec) |
N/A | 0.169 | 0.001 | 0.051 | 0.046 | 0.054 | 0.039 | 0.104 | 0.185 | 0.030 |
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 | 10 | 10 | 11 | 10 | 10 | 10 | 10 | 10 | 10 |
N.S. |
1 | 0.56 | 0.56 | 0.61 | 0.56 | 0.56 | 0.56 | 0.56 | 0.56 | 0.56 |
time (sec) |
N/A | 0.332 | 0.042 | 0.113 | 0.073 | 0.064 | 0.057 | 0.105 | 0.184 | 2.277 |
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 | 13 | 35 | 29 | 27 | 30 | 30 | 27 | 30 | 31 | 26 |
N.S. |
1 | 2.69 | 2.23 | 2.08 | 2.31 | 2.31 | 2.08 | 2.31 | 2.38 | 2.00 |
time (sec) |
N/A | 0.165 | 0.004 | 0.089 | 0.029 | 0.058 | 0.031 | 0.105 | 0.192 | 0.079 |
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 | 33 | 0 | 28 | 29 | 25 | 28 | 24 | 0 | 56 | 25 |
N.S. |
1 | 0.00 | 0.85 | 0.88 | 0.76 | 0.85 | 0.73 | 0.00 | 1.70 | 0.76 |
time (sec) |
N/A | 0.000 | 0.260 | 0.619 | 0.125 | 0.066 | 1.133 | 0.000 | 0.231 | 2.134 |
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 | 37 | 24 | 28 | 33 | 33 | 37 | 40 | 27 | 41 |
N.S. |
1 | 1.54 | 1.00 | 1.17 | 1.38 | 1.38 | 1.54 | 1.67 | 1.12 | 1.71 |
time (sec) |
N/A | 0.277 | 0.006 | 0.242 | 0.027 | 0.065 | 0.345 | 0.110 | 0.198 | 0.176 |
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 | 16 | 16 | 15 | 34 | 14 | 14 | 14 | 25 | 16 |
N.S. |
1 | 0.94 | 0.94 | 0.88 | 2.00 | 0.82 | 0.82 | 0.82 | 1.47 | 0.94 |
time (sec) |
N/A | 0.291 | 0.070 | 0.154 | 0.034 | 0.067 | 0.052 | 0.115 | 0.214 | 2.057 |