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 | 22 | 21 | 21 | 22 | 20 | 30 | 19 | 35 | 37 | 17 |
N.S. |
1 | 0.95 | 0.95 | 1.00 | 0.91 | 1.36 | 0.86 | 1.59 | 1.68 | 0.77 |
time (sec) |
N/A | 0.472 | 0.015 | 0.796 | 0.147 | 0.135 | 0.123 | 0.109 | 0.220 | 2.817 |
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 | 29 | 0 | 44 | 81 | 76 | 81 | 75 | 93 | 95 | 53 |
N.S. |
1 | 0.00 | 1.52 | 2.79 | 2.62 | 2.79 | 2.59 | 3.21 | 3.28 | 1.83 |
time (sec) |
N/A | 0.000 | 0.201 | 150.480 | 0.337 | 0.154 | 2.180 | 1.254 | 0.278 | 3.166 |
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 | 30 | 0 | 23 | 28 | 25 | 25 | 31 | 44 | 27 | 0 |
N.S. |
1 | 0.00 | 0.77 | 0.93 | 0.83 | 0.83 | 1.03 | 1.47 | 0.90 | 0.00 |
time (sec) |
N/A | 0.000 | 0.421 | 0.799 | 0.066 | 0.093 | 0.125 | 0.123 | 0.233 | 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 | 24 | 48 | 28 | 27 | 21 | 31 | 29 | 33 | 28 | 21 |
N.S. |
1 | 2.00 | 1.17 | 1.12 | 0.88 | 1.29 | 1.21 | 1.38 | 1.17 | 0.88 |
time (sec) |
N/A | 0.724 | 3.143 | 1.230 | 0.070 | 0.118 | 0.098 | 0.111 | 0.224 | 0.107 |
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 | 20 | 56 | 41 | 54 | 52 | 37 | 54 | 50 | 65 | 49 |
N.S. |
1 | 2.80 | 2.05 | 2.70 | 2.60 | 1.85 | 2.70 | 2.50 | 3.25 | 2.45 |
time (sec) |
N/A | 0.265 | 0.018 | 0.479 | 0.048 | 0.101 | 0.073 | 0.110 | 0.212 | 2.720 |
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 | 25 | 52 | 49 | 36 | 39 | 39 | 39 | 39 | 45 | 35 |
N.S. |
1 | 2.08 | 1.96 | 1.44 | 1.56 | 1.56 | 1.56 | 1.56 | 1.80 | 1.40 |
time (sec) |
N/A | 0.193 | 0.008 | 0.175 | 0.024 | 0.090 | 0.028 | 0.123 | 0.255 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 36 | 26 | 26 | 25 | 24 | 25 | 31 | 16 |
N.S. |
1 | 0.00 | 1.50 | 1.08 | 1.08 | 1.04 | 1.00 | 1.04 | 1.29 | 0.67 |
time (sec) |
N/A | 0.000 | 2.789 | 0.483 | 0.153 | 0.146 | 0.121 | 0.147 | 0.276 | 2.789 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 18 | 23 | 98 | 24 | 19 | 24 | 16 | 15 |
N.S. |
1 | 0.00 | 1.00 | 1.28 | 5.44 | 1.33 | 1.06 | 1.33 | 0.89 | 0.83 |
time (sec) |
N/A | 0.000 | 0.017 | 0.863 | 0.213 | 0.092 | 11.589 | 0.710 | 0.241 | 2.763 |
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 | 11 | 11 | 11 | 7 | 6 | 6 | 8 | 6 | 7 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.64 | 0.55 | 0.55 | 0.73 | 0.55 | 0.64 | 0.55 |
time (sec) |
N/A | 0.145 | 0.006 | 0.080 | 0.025 | 0.152 | 0.034 | 0.112 | 0.222 | 0.013 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 21 | 22 | 71 | 24 | 24 | 0 | 28 | 28 |
N.S. |
1 | 0.00 | 0.88 | 0.92 | 2.96 | 1.00 | 1.00 | 0.00 | 1.17 | 1.17 |
time (sec) |
N/A | 0.000 | 0.209 | 1.303 | 0.223 | 0.171 | 0.577 | 0.000 | 0.219 | 3.048 |
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 | 25 | 0 | 23 | 22 | 0 | 27 | 24 | 0 | 32 | 21 |
N.S. |
1 | 0.00 | 0.92 | 0.88 | 0.00 | 1.08 | 0.96 | 0.00 | 1.28 | 0.84 |
time (sec) |
N/A | 0.000 | 0.539 | 1.134 | 0.000 | 0.116 | 0.133 | 0.000 | 0.223 | 2.748 |
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 | 41 | 25 | 34 | 38 | 28 | 24 | 27 | 50 | 27 |
N.S. |
1 | 1.78 | 1.09 | 1.48 | 1.65 | 1.22 | 1.04 | 1.17 | 2.17 | 1.17 |
time (sec) |
N/A | 0.567 | 0.036 | 0.538 | 0.079 | 0.132 | 0.103 | 0.114 | 0.206 | 2.721 |
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 | 25 | 24 | 34 | 34 | 29 | 25 | 25 | 78 |
N.S. |
1 | 0.00 | 1.19 | 1.14 | 1.62 | 1.62 | 1.38 | 1.19 | 1.19 | 3.71 |
time (sec) |
N/A | 0.000 | 0.131 | 0.774 | 0.160 | 0.149 | 0.297 | 0.186 | 0.224 | 2.922 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 34 | 28 | 31 | 26 | 34 | 0 | 34 | 826 | 27 |
N.S. |
1 | 1.21 | 1.00 | 1.11 | 0.93 | 1.21 | 0.00 | 1.21 | 29.50 | 0.96 |
time (sec) |
N/A | 1.689 | 0.129 | 2405.155 | 0.291 | 0.153 | 0.000 | 0.151 | 0.454 | 3.356 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 38 | 46 | 1589 | 41 | 58 | 50 | 91 | 0 |
N.S. |
1 | 0.00 | 1.36 | 1.64 | 56.75 | 1.46 | 2.07 | 1.79 | 3.25 | 0.00 |
time (sec) |
N/A | 0.000 | 0.042 | 6.458 | 0.177 | 0.129 | 1.160 | 0.124 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 154 | 1045 | 807 | 274 | 279 | 0 | 921 | 399 |
N.S. |
1 | 0.00 | 5.50 | 37.32 | 28.82 | 9.79 | 9.96 | 0.00 | 32.89 | 14.25 |
time (sec) |
N/A | 0.000 | 11.058 | 0.072 | 1.195 | 0.129 | 3.053 | 0.000 | 200.046 | 4.305 |
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 | 25 | 51 | 27 | 26 | 25 | 25 | 22 | 25 | 40 | 28 |
N.S. |
1 | 2.04 | 1.08 | 1.04 | 1.00 | 1.00 | 0.88 | 1.00 | 1.60 | 1.12 |
time (sec) |
N/A | 0.258 | 0.047 | 0.129 | 0.033 | 0.149 | 0.089 | 0.117 | 0.244 | 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 | 12 | 12 | 15 | 13 | 14 | 14 | 14 | 14 | 13 | 12 |
N.S. |
1 | 1.00 | 1.25 | 1.08 | 1.17 | 1.17 | 1.17 | 1.17 | 1.08 | 1.00 |
time (sec) |
N/A | 0.137 | 0.000 | 0.028 | 0.024 | 0.081 | 0.019 | 0.111 | 0.246 | 2.679 |
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 | 21 | 21 | 18 | 17 | 17 | 24 | 22 | 22 | 17 |
N.S. |
1 | 1.24 | 1.24 | 1.06 | 1.00 | 1.00 | 1.41 | 1.29 | 1.29 | 1.00 |
time (sec) |
N/A | 0.485 | 0.060 | 0.189 | 0.059 | 0.097 | 0.130 | 0.127 | 0.239 | 2.779 |
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 | 53 | 47 | 44 | 40 | 34 | 49 | 54 | 213 |
N.S. |
1 | 0.00 | 1.61 | 1.42 | 1.33 | 1.21 | 1.03 | 1.48 | 1.64 | 6.45 |
time (sec) |
N/A | 0.000 | 0.416 | 4.407 | 0.074 | 0.101 | 0.084 | 0.123 | 0.242 | 2.899 |
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 | 38 | 29 | 21 | 27 | 27 | 22 | 27 | 34 | 20 |
N.S. |
1 | 1.46 | 1.12 | 0.81 | 1.04 | 1.04 | 0.85 | 1.04 | 1.31 | 0.77 |
time (sec) |
N/A | 0.187 | 0.019 | 0.116 | 0.032 | 0.154 | 0.067 | 0.115 | 0.239 | 0.045 |
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 | 16 | 25 | 15 | 24 | 24 | 46 | 21 | 24 |
N.S. |
1 | 0.00 | 1.00 | 1.56 | 0.94 | 1.50 | 1.50 | 2.88 | 1.31 | 1.50 |
time (sec) |
N/A | 0.000 | 0.134 | 0.127 | 0.140 | 0.090 | 0.137 | 0.116 | 0.235 | 2.802 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 19 | 14 | 13 | 60 | 14 | 13 | 17 | 14 |
N.S. |
1 | 0.00 | 1.00 | 0.74 | 0.68 | 3.16 | 0.74 | 0.68 | 0.89 | 0.74 |
time (sec) |
N/A | 0.000 | 0.087 | 0.164 | 0.142 | 0.151 | 0.204 | 0.337 | 0.219 | 0.119 |
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 | 11 | 12 | 11 | 11 | 10 | 11 | 7 | 7 |
N.S. |
1 | 0.69 | 0.69 | 0.75 | 0.69 | 0.69 | 0.62 | 0.69 | 0.44 | 0.44 |
time (sec) |
N/A | 0.193 | 0.001 | 0.034 | 0.023 | 0.152 | 0.049 | 0.117 | 0.215 | 2.693 |
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 | 16 | 12 | 13 | 19 | 16 | 14 | 19 | 16 | 12 |
N.S. |
1 | 1.23 | 0.92 | 1.00 | 1.46 | 1.23 | 1.08 | 1.46 | 1.23 | 0.92 |
time (sec) |
N/A | 0.276 | 0.001 | 0.042 | 0.026 | 0.122 | 0.041 | 0.115 | 0.209 | 0.017 |
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 | 27 | 115 | 37 | 93 | 99 | 130 | 102 | 132 | 117 | 86 |
N.S. |
1 | 4.26 | 1.37 | 3.44 | 3.67 | 4.81 | 3.78 | 4.89 | 4.33 | 3.19 |
time (sec) |
N/A | 3.293 | 0.210 | 0.119 | 0.156 | 0.167 | 0.249 | 0.195 | 0.227 | 3.399 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | A | B | B | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 20 | 397 | 37 | 30 | 29 | 54 | 28 | 27 |
N.S. |
1 | 0.00 | 0.95 | 18.90 | 1.76 | 1.43 | 1.38 | 2.57 | 1.33 | 1.29 |
time (sec) |
N/A | 0.000 | 0.358 | 0.238 | 0.181 | 0.118 | 1.089 | 1.096 | 0.243 | 3.956 |
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 | 24 | 24 | 26 | 45 | 25 | 24 | 25 | 26 | 25 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.88 | 1.04 | 1.00 | 1.04 | 1.08 | 1.04 |
time (sec) |
N/A | 0.173 | 0.009 | 0.221 | 0.028 | 0.087 | 0.096 | 0.108 | 0.222 | 2.912 |
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 | 24 | 20 | 20 | 29 | 54 | 28 | 27 | 28 | 77 | 30 |
N.S. |
1 | 0.83 | 0.83 | 1.21 | 2.25 | 1.17 | 1.12 | 1.17 | 3.21 | 1.25 |
time (sec) |
N/A | 0.313 | 0.024 | 0.321 | 0.169 | 0.095 | 0.113 | 0.157 | 0.217 | 3.089 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 34 | 52 | 118 | 43 | 41 | 151 | 0 | 64 |
N.S. |
1 | 0.00 | 1.06 | 1.62 | 3.69 | 1.34 | 1.28 | 4.72 | 0.00 | 2.00 |
time (sec) |
N/A | 0.000 | 0.124 | 35.740 | 81.226 | 0.105 | 0.871 | 0.285 | 1.704 | 3.310 |
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 | 30 | 28 | 23 | 27 | 28 | 24 | 27 | 26 | 22 |
N.S. |
1 | 1.30 | 1.22 | 1.00 | 1.17 | 1.22 | 1.04 | 1.17 | 1.13 | 0.96 |
time (sec) |
N/A | 0.252 | 0.010 | 0.141 | 0.032 | 0.083 | 0.086 | 0.105 | 0.235 | 2.952 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | A | B | F | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 37 | 222 | 37 | 39 | 31 | 78 | 1411 | 37 |
N.S. |
1 | 0.00 | 1.12 | 6.73 | 1.12 | 1.18 | 0.94 | 2.36 | 42.76 | 1.12 |
time (sec) |
N/A | 0.000 | 0.193 | 0.046 | 0.102 | 0.139 | 13.875 | 0.575 | 1.200 | 3.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 22 | 25 | 20 | 78 | 24 | 0 | 97 | 21 |
N.S. |
1 | 0.00 | 1.22 | 1.39 | 1.11 | 4.33 | 1.33 | 0.00 | 5.39 | 1.17 |
time (sec) |
N/A | 0.000 | 5.048 | 1.180 | 0.158 | 0.227 | 0.857 | 0.000 | 215.006 | 3.033 |
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 | 24 | 0 | 23 | 24 | 23 | 41 | 20 | 63 | 59 | 34 |
N.S. |
1 | 0.00 | 0.96 | 1.00 | 0.96 | 1.71 | 0.83 | 2.62 | 2.46 | 1.42 |
time (sec) |
N/A | 0.000 | 0.911 | 0.356 | 0.077 | 0.107 | 0.094 | 0.119 | 0.213 | 3.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 28 | 21 | 22 | 21 | 21 | 22 | 0 | 33 | 25 |
N.S. |
1 | 1.08 | 0.81 | 0.85 | 0.81 | 0.81 | 0.85 | 0.00 | 1.27 | 0.96 |
time (sec) |
N/A | 0.441 | 1.112 | 0.128 | 0.163 | 0.114 | 0.203 | 0.000 | 0.239 | 0.164 |
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 | 22 | 63 | 20 | 22 | 21 | 20 | 15 | 20 | 25 | 20 |
N.S. |
1 | 2.86 | 0.91 | 1.00 | 0.95 | 0.91 | 0.68 | 0.91 | 1.14 | 0.91 |
time (sec) |
N/A | 0.229 | 0.229 | 0.081 | 0.098 | 0.083 | 0.103 | 0.118 | 1.603 | 3.050 |
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 | 26 | 0 | 52 | 45 | 37 | 37 | 41 | 44 | 44 | 44 |
N.S. |
1 | 0.00 | 2.00 | 1.73 | 1.42 | 1.42 | 1.58 | 1.69 | 1.69 | 1.69 |
time (sec) |
N/A | 0.000 | 0.149 | 0.229 | 0.064 | 0.156 | 0.202 | 0.126 | 0.213 | 3.126 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 52 | 52 | 52 | 83 | 83 | 65 | 51 | 51 | 0 |
N.S. |
1 | 2.36 | 2.36 | 2.36 | 3.77 | 3.77 | 2.95 | 2.32 | 2.32 | 0.00 |
time (sec) |
N/A | 0.796 | 0.630 | 1.215 | 0.140 | 0.091 | 0.535 | 0.133 | 0.202 | 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 | 26 | 14 | 15 | 13 | 13 | 13 | 8 | 14 | 14 | 13 |
N.S. |
1 | 0.54 | 0.58 | 0.50 | 0.50 | 0.50 | 0.31 | 0.54 | 0.54 | 0.50 |
time (sec) |
N/A | 0.154 | 0.002 | 0.032 | 0.025 | 0.094 | 0.032 | 0.118 | 0.203 | 0.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 22 | 55 | 21 | 19 | 21 | 22 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 2.50 | 0.95 | 0.86 | 0.95 | 1.00 | 1.00 |
time (sec) |
N/A | 0.706 | 0.112 | 0.283 | 0.112 | 0.086 | 0.200 | 0.118 | 0.206 | 3.200 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 46 | 34 | 34 | 33 | 33 | 29 | 33 | 48 | 30 |
N.S. |
1 | 1.53 | 1.13 | 1.13 | 1.10 | 1.10 | 0.97 | 1.10 | 1.60 | 1.00 |
time (sec) |
N/A | 0.192 | 0.028 | 0.191 | 0.029 | 0.108 | 0.051 | 0.106 | 0.214 | 0.033 |
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 | 16 | 12 | 12 | 14 | 15 | 12 | 14 | 18 | 11 |
N.S. |
1 | 1.14 | 0.86 | 0.86 | 1.00 | 1.07 | 0.86 | 1.00 | 1.29 | 0.79 |
time (sec) |
N/A | 0.160 | 0.001 | 0.023 | 0.029 | 0.067 | 0.041 | 0.128 | 0.206 | 2.934 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 37 | 36 | 132 | 134 | 107 | 49 | 51 | 70 | 95 |
N.S. |
1 | 1.42 | 1.38 | 5.08 | 5.15 | 4.12 | 1.88 | 1.96 | 2.69 | 3.65 |
time (sec) |
N/A | 1.012 | 0.234 | 0.116 | 0.155 | 0.083 | 0.144 | 0.142 | 0.205 | 3.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | C | B | A | A | F | B | B |
verified | N/A | N/A | N/A | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 82 | 39 | 15 | 20 | 0 | 24 | 20 |
N.S. |
1 | 0.00 | 0.00 | 3.42 | 1.62 | 0.62 | 0.83 | 0.00 | 1.00 | 0.83 |
time (sec) |
N/A | 0.000 | 0.000 | 1.784 | 0.160 | 0.077 | 0.231 | 0.000 | 0.209 | 3.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 13 | 8 | 8 | 12 | 8 | 9 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.53 | 0.53 | 0.80 | 0.53 | 0.60 | 0.53 |
time (sec) |
N/A | 0.173 | 0.008 | 0.049 | 0.108 | 0.074 | 0.059 | 0.108 | 0.208 | 0.040 |
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 | 21 | 112 | 112 | 113 | 147 | 91 | 87 | 112 | 105 | 112 |
N.S. |
1 | 5.33 | 5.33 | 5.38 | 7.00 | 4.33 | 4.14 | 5.33 | 5.00 | 5.33 |
time (sec) |
N/A | 0.386 | 0.025 | 1.682 | 0.034 | 0.094 | 0.091 | 0.119 | 0.218 | 3.082 |
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 | 20 | 90 | 23 | 32 | 76 | 30 | 65 | 37 | 40 | 32 |
N.S. |
1 | 4.50 | 1.15 | 1.60 | 3.80 | 1.50 | 3.25 | 1.85 | 2.00 | 1.60 |
time (sec) |
N/A | 0.955 | 0.149 | 1.076 | 0.059 | 0.100 | 0.887 | 0.131 | 0.214 | 3.255 |
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 | 23 | 18 | 25 | 18 | 66 | 27 | 14 | 27 | 25 | 22 |
N.S. |
1 | 0.78 | 1.09 | 0.78 | 2.87 | 1.17 | 0.61 | 1.17 | 1.09 | 0.96 |
time (sec) |
N/A | 0.916 | 0.104 | 1.453 | 0.125 | 0.085 | 0.097 | 0.117 | 0.213 | 3.121 |
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 | 22 | 13 | 12 | 18 | 11 | 10 | 11 | 13 | 11 |
N.S. |
1 | 1.69 | 1.00 | 0.92 | 1.38 | 0.85 | 0.77 | 0.85 | 1.00 | 0.85 |
time (sec) |
N/A | 0.479 | 0.044 | 0.053 | 0.061 | 0.073 | 0.043 | 0.119 | 0.207 | 0.054 |
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 | 24 | 22 | 20 | 19 | 21 | 15 | 43 | 36 | 19 |
N.S. |
1 | 1.09 | 1.00 | 0.91 | 0.86 | 0.95 | 0.68 | 1.95 | 1.64 | 0.86 |
time (sec) |
N/A | 0.190 | 0.019 | 0.110 | 0.031 | 0.094 | 0.059 | 0.117 | 0.217 | 2.965 |
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 | 16 | 0 | 14 | 15 | 14 | 14 | 12 | 14 | 14 | 82 |
N.S. |
1 | 0.00 | 0.88 | 0.94 | 0.88 | 0.88 | 0.75 | 0.88 | 0.88 | 5.12 |
time (sec) |
N/A | 0.000 | 0.152 | 0.141 | 0.075 | 0.109 | 0.093 | 0.122 | 0.218 | 3.152 |
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 | 28 | 19 | 16 | 21 | 15 | 15 | 15 | 17 | 15 |
N.S. |
1 | 1.33 | 0.90 | 0.76 | 1.00 | 0.71 | 0.71 | 0.71 | 0.81 | 0.71 |
time (sec) |
N/A | 0.203 | 0.008 | 0.112 | 0.027 | 0.115 | 0.083 | 0.120 | 0.208 | 0.033 |
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 | 26 | 26 | 16 | 18 | 18 | 20 | 22 | 15 | 15 |
N.S. |
1 | 1.53 | 1.53 | 0.94 | 1.06 | 1.06 | 1.18 | 1.29 | 0.88 | 0.88 |
time (sec) |
N/A | 0.200 | 0.008 | 0.139 | 0.032 | 0.100 | 0.057 | 0.112 | 0.207 | 2.997 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 20 | 24 | 19 | 20 | 68 | 21 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 1.04 | 0.83 | 0.87 | 2.96 | 0.91 | 0.00 |
time (sec) |
N/A | 3.336 | 0.486 | 0.976 | 0.167 | 0.089 | 0.229 | 0.147 | 0.215 | 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 | 12 | 16 | 14 | 11 | 11 | 15 | 13 | 9 | 8 |
N.S. |
1 | 0.57 | 0.76 | 0.67 | 0.52 | 0.52 | 0.71 | 0.62 | 0.43 | 0.38 |
time (sec) |
N/A | 0.139 | 0.000 | 0.068 | 0.028 | 0.089 | 0.039 | 0.108 | 0.214 | 3.007 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 29 | 29 | 49 | 25 | 43 | 49 | 46 | 99 | 47 |
N.S. |
1 | 1.07 | 1.07 | 1.81 | 0.93 | 1.59 | 1.81 | 1.70 | 3.67 | 1.74 |
time (sec) |
N/A | 1.705 | 0.068 | 0.359 | 0.067 | 0.115 | 0.421 | 0.279 | 200.024 | 3.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 14 | 16 | 16 | 12 | 16 | 13 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.23 | 1.23 | 0.92 | 1.23 | 1.00 | 1.08 |
time (sec) |
N/A | 0.156 | 0.001 | 0.026 | 0.024 | 0.099 | 0.019 | 0.119 | 0.171 | 2.923 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | B | F(-1) | F | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 25 | 26 | 48 | 0 | 0 | 30 | 26 |
N.S. |
1 | 0.00 | 0.00 | 0.83 | 0.87 | 1.60 | 0.00 | 0.00 | 1.00 | 0.87 |
time (sec) |
N/A | 0.000 | 0.000 | 0.229 | 0.297 | 0.092 | 0.000 | 0.000 | 0.231 | 3.322 |
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 | 31 | 0 | 41 | 41 | 57 | 36 | 37 | 63 | 41 | 57 |
N.S. |
1 | 0.00 | 1.32 | 1.32 | 1.84 | 1.16 | 1.19 | 2.03 | 1.32 | 1.84 |
time (sec) |
N/A | 0.000 | 0.090 | 3.459 | 0.241 | 0.102 | 0.155 | 0.306 | 0.167 | 3.190 |
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 | 23 | 160 | 76 | 87 | 128 | 72 | 100 | 97 | 114 | 94 |
N.S. |
1 | 6.96 | 3.30 | 3.78 | 5.57 | 3.13 | 4.35 | 4.22 | 4.96 | 4.09 |
time (sec) |
N/A | 0.527 | 0.082 | 1.503 | 0.033 | 0.103 | 0.143 | 0.115 | 0.157 | 3.014 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | F(-1) | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 1192 | 1517 | 1403 | 2015 | 1856 | 0 | 1904 | 3054 | 13908 |
N.S. |
1 | 42.57 | 54.18 | 50.11 | 71.96 | 66.29 | 0.00 | 68.00 | 109.07 | 496.71 |
time (sec) |
N/A | 19.220 | 1.691 | 3.196 | 0.120 | 0.140 | 0.000 | 0.173 | 66.087 | 17.723 |
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 | 33 | 0 | 36 | 47 | 45 | 45 | 41 | 49 | 55 | 0 |
N.S. |
1 | 0.00 | 1.09 | 1.42 | 1.36 | 1.36 | 1.24 | 1.48 | 1.67 | 0.00 |
time (sec) |
N/A | 0.000 | 3.361 | 0.232 | 0.132 | 0.101 | 0.203 | 0.132 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | F(-1) | B | B | F(-1) |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 22245 | 42 | 35 | 0 | 2231 | 36 | 0 |
N.S. |
1 | 0.00 | 1.00 | 767.07 | 1.45 | 1.21 | 0.00 | 76.93 | 1.24 | 0.00 |
time (sec) |
N/A | 0.000 | 0.314 | 0.215 | 0.233 | 0.118 | 0.000 | 6.362 | 0.227 | 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 | 15 | 13 | 13 | 13 | 12 | 12 | 8 | 12 | 13 | 12 |
N.S. |
1 | 0.87 | 0.87 | 0.87 | 0.80 | 0.80 | 0.53 | 0.80 | 0.87 | 0.80 |
time (sec) |
N/A | 0.233 | 0.005 | 0.117 | 0.026 | 0.080 | 0.065 | 0.115 | 0.171 | 0.068 |
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 | 20 | 0 | 20 | 21 | 20 | 20 | 0 | 20 | 20 | 20 |
N.S. |
1 | 0.00 | 1.00 | 1.05 | 1.00 | 1.00 | 0.00 | 1.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.056 | 16.402 | 0.071 | 0.087 | 0.000 | 0.203 | 8.947 | 3.241 |
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 | 24 | 23 | 7 | 22 | 24 | 27 | 28 | 23 | 23 |
N.S. |
1 | 0.96 | 0.92 | 0.28 | 0.88 | 0.96 | 1.08 | 1.12 | 0.92 | 0.92 |
time (sec) |
N/A | 0.578 | 0.024 | 0.247 | 0.032 | 0.089 | 0.118 | 0.114 | 0.186 | 3.114 |
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 | 24 | 0 | 24 | 28 | 34 | 36 | 34 | 38 | 27 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.17 | 1.42 | 1.50 | 1.42 | 1.58 | 1.12 | 0.00 |
time (sec) |
N/A | 0.000 | 5.034 | 1.129 | 0.189 | 0.085 | 0.172 | 0.128 | 0.181 | 0.000 |
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 | 31 | 70 | 27 | 36 | 156 | 35 | 36 | 40 | 38 | 23 |
N.S. |
1 | 2.26 | 0.87 | 1.16 | 5.03 | 1.13 | 1.16 | 1.29 | 1.23 | 0.74 |
time (sec) |
N/A | 0.444 | 0.294 | 0.121 | 0.037 | 0.103 | 0.084 | 0.112 | 0.181 | 2.947 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 18 | 18 | 15 | 14 | 14 | 10 | 0 | 15 | 13 |
N.S. |
1 | 0.82 | 0.82 | 0.68 | 0.64 | 0.64 | 0.45 | 0.00 | 0.68 | 0.59 |
time (sec) |
N/A | 0.257 | 0.015 | 0.091 | 0.073 | 0.080 | 0.091 | 0.000 | 0.187 | 3.183 |
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 | 22 | 0 | 41 | 45 | 51 | 25 | 37 | 41 | 94 | 38 |
N.S. |
1 | 0.00 | 1.86 | 2.05 | 2.32 | 1.14 | 1.68 | 1.86 | 4.27 | 1.73 |
time (sec) |
N/A | 0.000 | 0.493 | 0.445 | 0.146 | 0.084 | 0.202 | 0.148 | 0.196 | 3.170 |
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 | 16 | 16 | 16 | 27 | 15 | 15 | 15 | 16 | 15 |
N.S. |
1 | 0.76 | 0.76 | 0.76 | 1.29 | 0.71 | 0.71 | 0.71 | 0.76 | 0.71 |
time (sec) |
N/A | 0.233 | 0.021 | 0.182 | 0.027 | 0.087 | 0.059 | 0.120 | 0.186 | 0.028 |
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 | 24 | 0 | 24 | 26 | 29 | 29 | 24 | 47 | 29 | 29 |
N.S. |
1 | 0.00 | 1.00 | 1.08 | 1.21 | 1.21 | 1.00 | 1.96 | 1.21 | 1.21 |
time (sec) |
N/A | 0.000 | 0.429 | 0.799 | 0.087 | 0.089 | 0.231 | 0.192 | 0.184 | 3.147 |
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 | 25 | 22 | 21 | 21 | 19 | 21 | 23 | 21 |
N.S. |
1 | 0.00 | 1.00 | 0.88 | 0.84 | 0.84 | 0.76 | 0.84 | 0.92 | 0.84 |
time (sec) |
N/A | 0.000 | 2.863 | 34.289 | 0.099 | 0.088 | 0.708 | 0.155 | 0.192 | 3.311 |
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 | 26 | 24 | 24 | 23 | 20 | 23 | 28 | 28 |
N.S. |
1 | 0.84 | 0.81 | 0.75 | 0.75 | 0.72 | 0.62 | 0.72 | 0.88 | 0.88 |
time (sec) |
N/A | 1.041 | 0.176 | 0.313 | 0.163 | 0.105 | 0.136 | 0.144 | 0.188 | 0.290 |
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 | 29 | 0 | 43 | 41 | 67 | 43 | 29 | 51 | 34 | 40 |
N.S. |
1 | 0.00 | 1.48 | 1.41 | 2.31 | 1.48 | 1.00 | 1.76 | 1.17 | 1.38 |
time (sec) |
N/A | 0.000 | 0.928 | 1.744 | 0.186 | 0.101 | 0.146 | 0.182 | 0.193 | 3.110 |
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 | 25 | 31 | 26 | 30 | 27 | 30 | 30 | 22 |
N.S. |
1 | 0.00 | 0.93 | 1.15 | 0.96 | 1.11 | 1.00 | 1.11 | 1.11 | 0.81 |
time (sec) |
N/A | 0.000 | 0.078 | 0.132 | 0.083 | 0.086 | 0.187 | 0.134 | 0.191 | 3.358 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 29 | 25 | 21 | 28 | 33 | 26 | 92 | 36 | 21 |
N.S. |
1 | 1.38 | 1.19 | 1.00 | 1.33 | 1.57 | 1.24 | 4.38 | 1.71 | 1.00 |
time (sec) |
N/A | 0.576 | 0.080 | 0.192 | 0.069 | 0.085 | 0.077 | 0.116 | 0.184 | 0.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 30 | 20 | 24 | 21 | 27 | 24 | 26 | 19 |
N.S. |
1 | 0.00 | 1.67 | 1.11 | 1.33 | 1.17 | 1.50 | 1.33 | 1.44 | 1.06 |
time (sec) |
N/A | 0.000 | 0.115 | 0.106 | 0.077 | 0.098 | 0.185 | 0.134 | 0.186 | 0.125 |
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 | 35 | 33 | 43 | 36 | 39 | 0 | 99 | 38 |
N.S. |
1 | 0.00 | 1.25 | 1.18 | 1.54 | 1.29 | 1.39 | 0.00 | 3.54 | 1.36 |
time (sec) |
N/A | 0.000 | 0.132 | 22.389 | 0.172 | 0.108 | 11.062 | 0.000 | 200.027 | 3.161 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | B | C | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 406 | 113 | 120 | 193 | 106 | 141 | 139 | 164 | 96 |
N.S. |
1 | 11.94 | 3.32 | 3.53 | 5.68 | 3.12 | 4.15 | 4.09 | 4.82 | 2.82 |
time (sec) |
N/A | 1.404 | 6.386 | 2.576 | 0.114 | 0.089 | 1.594 | 0.118 | 0.175 | 0.105 |
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 | 21 | 21 | 17 | 21 | 24 | 22 | 23 | 27 | 19 |
N.S. |
1 | 0.75 | 0.75 | 0.61 | 0.75 | 0.86 | 0.79 | 0.82 | 0.96 | 0.68 |
time (sec) |
N/A | 0.495 | 0.003 | 0.140 | 0.035 | 0.076 | 0.051 | 0.105 | 0.171 | 2.927 |
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 | 22 | 28 | 30 | 34 | 42 | 29 | 21 | 50 | 32 |
N.S. |
1 | 1.00 | 1.27 | 1.36 | 1.55 | 1.91 | 1.32 | 0.95 | 2.27 | 1.45 |
time (sec) |
N/A | 0.478 | 0.017 | 0.173 | 0.034 | 0.071 | 0.305 | 0.114 | 0.174 | 2.977 |
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 | 24 | 39 | 25 | 24 | 36 | 36 | 34 | 36 | 50 | 23 |
N.S. |
1 | 1.62 | 1.04 | 1.00 | 1.50 | 1.50 | 1.42 | 1.50 | 2.08 | 0.96 |
time (sec) |
N/A | 1.548 | 0.458 | 0.095 | 0.061 | 0.079 | 0.075 | 0.120 | 0.179 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 46 | 72 | 87 | 72 | 88 | 85 | 143 | 66 |
N.S. |
1 | 0.00 | 2.42 | 3.79 | 4.58 | 3.79 | 4.63 | 4.47 | 7.53 | 3.47 |
time (sec) |
N/A | 0.000 | 0.050 | 0.339 | 0.036 | 0.108 | 4.918 | 0.127 | 0.195 | 3.310 |
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 | 25 | 24 | 34 | 32 | 26 | 0 | 35 | 26 |
N.S. |
1 | 0.00 | 1.04 | 1.00 | 1.42 | 1.33 | 1.08 | 0.00 | 1.46 | 1.08 |
time (sec) |
N/A | 0.000 | 1.052 | 3.481 | 0.180 | 0.107 | 0.222 | 0.000 | 0.178 | 3.083 |
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 | 22 | 0 | 38 | 24 | 64 | 23 | 22 | 44 | 25 | 44 |
N.S. |
1 | 0.00 | 1.73 | 1.09 | 2.91 | 1.05 | 1.00 | 2.00 | 1.14 | 2.00 |
time (sec) |
N/A | 0.000 | 5.077 | 1.200 | 0.256 | 0.083 | 0.383 | 0.133 | 0.181 | 3.278 |
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 | 27 | 0 | 22 | 22 | 21 | 21 | 22 | 21 | 35 | 0 |
N.S. |
1 | 0.00 | 0.81 | 0.81 | 0.78 | 0.78 | 0.81 | 0.78 | 1.30 | 0.00 |
time (sec) |
N/A | 0.000 | 0.411 | 0.960 | 0.099 | 0.099 | 0.138 | 0.159 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 33 | 32 | 27 | 25 | 25 | 24 | 25 | 33 | 31 |
N.S. |
1 | 1.94 | 1.88 | 1.59 | 1.47 | 1.47 | 1.41 | 1.47 | 1.94 | 1.82 |
time (sec) |
N/A | 0.219 | 0.050 | 0.144 | 0.027 | 0.077 | 0.057 | 0.111 | 0.179 | 2.970 |
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 | 30 | 41 | 22 | 20 | 39 | 23 | 15 | 24 | 23 | 18 |
N.S. |
1 | 1.37 | 0.73 | 0.67 | 1.30 | 0.77 | 0.50 | 0.80 | 0.77 | 0.60 |
time (sec) |
N/A | 0.365 | 0.046 | 0.391 | 0.058 | 0.085 | 0.084 | 0.106 | 0.176 | 3.026 |
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 | 21 | 21 | 19 | 18 | 18 | 17 | 18 | 28 | 20 |
N.S. |
1 | 0.78 | 0.78 | 0.70 | 0.67 | 0.67 | 0.63 | 0.67 | 1.04 | 0.74 |
time (sec) |
N/A | 0.288 | 0.278 | 0.112 | 0.161 | 0.102 | 0.099 | 0.123 | 0.197 | 0.048 |
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 | 32 | 0 | 49 | 30 | 43 | 54 | 26 | 198 | 86 | 45 |
N.S. |
1 | 0.00 | 1.53 | 0.94 | 1.34 | 1.69 | 0.81 | 6.19 | 2.69 | 1.41 |
time (sec) |
N/A | 0.000 | 10.073 | 18.870 | 0.077 | 0.090 | 0.087 | 2.367 | 0.187 | 0.154 |
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 | 18 | 70 | 18 | 24 | 23 | 23 | 22 | 0 | 25 | 16 |
N.S. |
1 | 3.89 | 1.00 | 1.33 | 1.28 | 1.28 | 1.22 | 0.00 | 1.39 | 0.89 |
time (sec) |
N/A | 0.399 | 0.092 | 1.567 | 0.077 | 0.107 | 0.147 | 0.000 | 0.180 | 2.871 |
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 | 26 | 79 | 39 | 58 | 60 | 66 | 63 | 67 | 73 | 49 |
N.S. |
1 | 3.04 | 1.50 | 2.23 | 2.31 | 2.54 | 2.42 | 2.58 | 2.81 | 1.88 |
time (sec) |
N/A | 0.436 | 0.023 | 0.168 | 0.039 | 0.103 | 1.079 | 0.113 | 0.196 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 51 | 59 | 44 | 39 | 39 | 58 | 45 | 0 | 0 |
N.S. |
1 | 2.32 | 2.68 | 2.00 | 1.77 | 1.77 | 2.64 | 2.05 | 0.00 | 0.00 |
time (sec) |
N/A | 0.256 | 0.038 | 0.892 | 0.103 | 0.345 | 0.226 | 0.138 | 0.656 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 38 | 42 | 19 | 44 | 18 | 17 | 32 | 17 | 33 |
N.S. |
1 | 2.11 | 2.33 | 1.06 | 2.44 | 1.00 | 0.94 | 1.78 | 0.94 | 1.83 |
time (sec) |
N/A | 0.261 | 0.096 | 0.240 | 0.144 | 0.086 | 0.115 | 0.115 | 0.179 | 0.401 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 21 | 35 | 37 | 36 | 32 | 36 | 172 | 36 |
N.S. |
1 | 0.00 | 0.88 | 1.46 | 1.54 | 1.50 | 1.33 | 1.50 | 7.17 | 1.50 |
time (sec) |
N/A | 0.000 | 0.390 | 0.103 | 0.080 | 0.121 | 0.219 | 0.153 | 0.279 | 2.852 |
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 | 24 | 36 | 40 | 24 | 27 | 36 | 26 | 27 | 20 | 26 |
N.S. |
1 | 1.50 | 1.67 | 1.00 | 1.12 | 1.50 | 1.08 | 1.12 | 0.83 | 1.08 |
time (sec) |
N/A | 0.286 | 0.012 | 0.165 | 0.028 | 0.090 | 0.166 | 0.112 | 0.176 | 0.073 |
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 | 19 | 16 | 18 | 17 | 22 | 26 | 24 | 30 | 1027 |
N.S. |
1 | 0.86 | 0.73 | 0.82 | 0.77 | 1.00 | 1.18 | 1.09 | 1.36 | 46.68 |
time (sec) |
N/A | 0.167 | 0.011 | 0.211 | 0.031 | 0.089 | 0.181 | 0.121 | 0.184 | 3.790 |
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 | 23 | 20 | 24 | 17 | 15 | 19 | 20 | 19 |
N.S. |
1 | 0.79 | 0.82 | 0.71 | 0.86 | 0.61 | 0.54 | 0.68 | 0.71 | 0.68 |
time (sec) |
N/A | 0.624 | 0.117 | 0.213 | 0.065 | 0.084 | 0.136 | 0.114 | 0.176 | 2.851 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | F | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 138 | 138 | 99 | 111 | 111 | 112 | 135 | 0 | 0 |
N.S. |
1 | 8.62 | 8.62 | 6.19 | 6.94 | 6.94 | 7.00 | 8.44 | 0.00 | 0.00 |
time (sec) |
N/A | 4.109 | 0.147 | 11.201 | 0.096 | 0.134 | 0.837 | 0.801 | 0.275 | 0.000 |