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 | B | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 35 | 32 | 21 | 28 | 65 | 19 | 0 | 23 | 20 |
N.S. |
1 | 1.25 | 1.14 | 0.75 | 1.00 | 2.32 | 0.68 | 0.00 | 0.82 | 0.71 |
time (sec) |
N/A | 0.777 | 0.088 | 1.331 | 0.140 | 0.092 | 0.155 | 0.000 | 0.157 | 3.285 |
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 | 29 | 0 | 28 | 28 | 34 | 49 | 31 | 38 | 124 | 45 |
N.S. |
1 | 0.00 | 0.97 | 0.97 | 1.17 | 1.69 | 1.07 | 1.31 | 4.28 | 1.55 |
time (sec) |
N/A | 0.000 | 2.670 | 0.527 | 0.161 | 0.100 | 0.090 | 0.130 | 200.021 | 3.328 |
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 | 27 | 19 | 19 | 39 | 20 | 33 | 34 | 0 | 38 | 34 |
N.S. |
1 | 0.70 | 0.70 | 1.44 | 0.74 | 1.22 | 1.26 | 0.00 | 1.41 | 1.26 |
time (sec) |
N/A | 0.581 | 0.070 | 1.437 | 0.141 | 0.100 | 0.234 | 0.000 | 0.155 | 16.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | A | A | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 404 | 63 | 43 | 683 | 42 | 49 | 60 | 82 | 0 |
N.S. |
1 | 15.54 | 2.42 | 1.65 | 26.27 | 1.62 | 1.88 | 2.31 | 3.15 | 0.00 |
time (sec) |
N/A | 1.299 | 0.099 | 1.351 | 0.170 | 0.097 | 0.412 | 0.124 | 0.158 | 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 | 37 | 25 | 28 | 32 | 41 | 27 | 32 | 48 | 32 |
N.S. |
1 | 1.42 | 0.96 | 1.08 | 1.23 | 1.58 | 1.04 | 1.23 | 1.85 | 1.23 |
time (sec) |
N/A | 0.474 | 0.018 | 0.184 | 0.025 | 0.079 | 0.120 | 0.114 | 0.173 | 0.067 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 22 | 45 | 87 | 50 | 63 | 53 | 52 | 19 |
N.S. |
1 | 0.00 | 0.88 | 1.80 | 3.48 | 2.00 | 2.52 | 2.12 | 2.08 | 0.76 |
time (sec) |
N/A | 0.000 | 0.115 | 0.372 | 0.111 | 0.099 | 0.229 | 0.132 | 0.167 | 3.294 |
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 | 26 | 61 | 64 | 41 | 48 | 48 | 71 | 61 | 48 | 52 |
N.S. |
1 | 2.35 | 2.46 | 1.58 | 1.85 | 1.85 | 2.73 | 2.35 | 1.85 | 2.00 |
time (sec) |
N/A | 13.241 | 0.084 | 13.188 | 0.283 | 0.094 | 0.206 | 0.139 | 0.170 | 3.621 |
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 | 21 | 46 | 19 | 17 | 21 | 21 | 22 | 21 | 24 | 16 |
N.S. |
1 | 2.19 | 0.90 | 0.81 | 1.00 | 1.00 | 1.05 | 1.00 | 1.14 | 0.76 |
time (sec) |
N/A | 0.398 | 0.091 | 0.108 | 0.067 | 0.091 | 0.068 | 0.115 | 0.154 | 0.076 |
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 | 32 | 24 | 31 | 40 | 32 | 30 | 43 | 38 |
N.S. |
1 | 0.00 | 1.23 | 0.92 | 1.19 | 1.54 | 1.23 | 1.15 | 1.65 | 1.46 |
time (sec) |
N/A | 0.000 | 0.109 | 0.940 | 0.225 | 0.082 | 0.105 | 0.279 | 0.158 | 1.647 |
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 | 34 | 31 | 43 | 30 | 37 | 30 | 27 | 29 |
N.S. |
1 | 0.00 | 1.13 | 1.03 | 1.43 | 1.00 | 1.23 | 1.00 | 0.90 | 0.97 |
time (sec) |
N/A | 0.000 | 2.112 | 0.358 | 0.160 | 0.086 | 0.710 | 0.116 | 0.157 | 0.097 |
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 | 11 | 9 | 7 | 6 | 6 | 7 | 6 | 11 | 7 |
N.S. |
1 | 0.85 | 0.69 | 0.54 | 0.46 | 0.46 | 0.54 | 0.46 | 0.85 | 0.54 |
time (sec) |
N/A | 0.151 | 0.015 | 0.048 | 0.034 | 0.074 | 0.031 | 0.110 | 0.157 | 3.257 |
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 | 27 | 27 | 37 | 37 | 19 | 37 | 46 | 28 |
N.S. |
1 | 0.00 | 0.84 | 0.84 | 1.16 | 1.16 | 0.59 | 1.16 | 1.44 | 0.88 |
time (sec) |
N/A | 0.000 | 4.975 | 0.300 | 0.075 | 0.085 | 0.050 | 0.118 | 0.149 | 3.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | B | B | B | B | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 0 | 21 | 88 | 56 | 61 | 216 | 68 | 134 |
N.S. |
1 | 0.00 | 0.00 | 0.84 | 3.52 | 2.24 | 2.44 | 8.64 | 2.72 | 5.36 |
time (sec) |
N/A | 0.000 | 0.000 | 29.303 | 0.622 | 0.110 | 0.415 | 0.323 | 0.173 | 3.338 |
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 | 14 | 14 | 13 | 17 | 12 | 12 | 12 | 15 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 1.21 | 0.86 | 0.86 | 0.86 | 1.07 | 0.86 |
time (sec) |
N/A | 0.268 | 0.017 | 0.165 | 0.182 | 0.095 | 0.079 | 0.121 | 0.167 | 3.036 |
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 | 11 | 11 | 11 | 10 | 10 | 5 | 10 | 16 | 10 |
N.S. |
1 | 0.92 | 0.92 | 0.92 | 0.83 | 0.83 | 0.42 | 0.83 | 1.33 | 0.83 |
time (sec) |
N/A | 0.145 | 0.004 | 0.060 | 0.027 | 0.089 | 0.032 | 0.107 | 0.168 | 0.039 |
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 | 22 | 21 | 21 | 33 | 23 | 27 | 33 | 22 | 38 |
N.S. |
1 | 1.05 | 1.00 | 1.00 | 1.57 | 1.10 | 1.29 | 1.57 | 1.05 | 1.81 |
time (sec) |
N/A | 0.192 | 0.395 | 0.317 | 0.171 | 0.085 | 8.313 | 0.121 | 0.167 | 3.007 |
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 | 31 | 35 | 57 | 54 | 42 | 40 | 58 | 0 |
N.S. |
1 | 0.00 | 1.29 | 1.46 | 2.38 | 2.25 | 1.75 | 1.67 | 2.42 | 0.00 |
time (sec) |
N/A | 0.000 | 0.066 | 1.796 | 0.167 | 0.092 | 0.155 | 0.163 | 0.167 | 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 | 31 | 0 | 29 | 52 | 28 | 28 | 14 | 17 | 47 | 42 |
N.S. |
1 | 0.00 | 0.94 | 1.68 | 0.90 | 0.90 | 0.45 | 0.55 | 1.52 | 1.35 |
time (sec) |
N/A | 0.000 | 0.140 | 11.043 | 0.088 | 0.082 | 0.065 | 0.138 | 0.168 | 3.212 |
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 | 17 | 19 | 19 | 21 | 22 | 20 | 22 | 22 | 20 | 0 |
N.S. |
1 | 1.12 | 1.12 | 1.24 | 1.29 | 1.18 | 1.29 | 1.29 | 1.18 | 0.00 |
time (sec) |
N/A | 0.401 | 0.026 | 5.034 | 0.195 | 0.091 | 2.297 | 0.132 | 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 | 13 | 19 | 13 | 11 | 10 | 10 | 8 | 10 | 11 | 10 |
N.S. |
1 | 1.46 | 1.00 | 0.85 | 0.77 | 0.77 | 0.62 | 0.77 | 0.85 | 0.77 |
time (sec) |
N/A | 0.162 | 0.013 | 0.079 | 0.035 | 0.092 | 0.039 | 0.111 | 0.172 | 2.998 |
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 | 16 | 13 | 13 | 12 | 17 | 13 | 13 | 12 |
N.S. |
1 | 1.00 | 0.89 | 0.72 | 0.72 | 0.67 | 0.94 | 0.72 | 0.72 | 0.67 |
time (sec) |
N/A | 0.155 | 0.002 | 0.063 | 0.034 | 0.078 | 0.039 | 0.111 | 0.164 | 2.997 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | F(-1) | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 22 | 50 | 55 | 55 | 60 | 0 | 63 | 0 |
N.S. |
1 | 0.00 | 0.96 | 2.17 | 2.39 | 2.39 | 2.61 | 0.00 | 2.74 | 0.00 |
time (sec) |
N/A | 0.000 | 0.831 | 1.597 | 0.234 | 0.099 | 0.226 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 19 | 19 | 15 | 18 | 17 | 15 | 17 | 18 | 14 |
N.S. |
1 | 0.76 | 0.76 | 0.60 | 0.72 | 0.68 | 0.60 | 0.68 | 0.72 | 0.56 |
time (sec) |
N/A | 0.213 | 0.044 | 0.210 | 0.054 | 0.084 | 0.044 | 0.110 | 0.153 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 30 | 29 | 59 | 58 | 34 | 62 | 68 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.97 | 1.97 | 1.93 | 1.13 | 2.07 | 2.27 | 0.00 |
time (sec) |
N/A | 0.000 | 4.690 | 1.049 | 0.094 | 0.109 | 0.120 | 0.131 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 35 | 23 | 19 | 30 | 30 | 31 | 30 | 29 | 30 |
N.S. |
1 | 1.67 | 1.10 | 0.90 | 1.43 | 1.43 | 1.48 | 1.43 | 1.38 | 1.43 |
time (sec) |
N/A | 0.182 | 0.005 | 0.117 | 0.044 | 0.075 | 0.023 | 0.107 | 0.153 | 0.031 |
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 | 28 | 0 | 34 | 38 | 199 | 53 | 122 | 154 | 76 | 0 |
N.S. |
1 | 0.00 | 1.21 | 1.36 | 7.11 | 1.89 | 4.36 | 5.50 | 2.71 | 0.00 |
time (sec) |
N/A | 0.000 | 6.900 | 2.267 | 0.229 | 0.106 | 0.254 | 0.236 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 55 | 47 | 47 | 51 | 48 | 46 | 48 | 60 | 51 |
N.S. |
1 | 1.90 | 1.62 | 1.62 | 1.76 | 1.66 | 1.59 | 1.66 | 2.07 | 1.76 |
time (sec) |
N/A | 0.438 | 0.082 | 0.786 | 0.035 | 0.103 | 0.088 | 0.118 | 0.152 | 0.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 13 | 13 | 14 | 0 | 111 | 58 | 542 | 99 | 337 |
N.S. |
1 | 0.81 | 0.81 | 0.88 | 0.00 | 6.94 | 3.62 | 33.88 | 6.19 | 21.06 |
time (sec) |
N/A | 0.849 | 0.111 | 4.916 | 0.000 | 0.082 | 0.099 | 0.142 | 0.151 | 3.150 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 25 | 26 | 53 | 35 | 24 | 25 | 25 | 25 |
N.S. |
1 | 0.00 | 1.39 | 1.44 | 2.94 | 1.94 | 1.33 | 1.39 | 1.39 | 1.39 |
time (sec) |
N/A | 0.000 | 0.094 | 0.471 | 0.148 | 0.105 | 0.194 | 0.114 | 0.152 | 3.118 |
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 | 32 | 40 | 0 | 43 | 43 | 42 | 41 | 0 | 164 | 46 |
N.S. |
1 | 1.25 | 0.00 | 1.34 | 1.34 | 1.31 | 1.28 | 0.00 | 5.12 | 1.44 |
time (sec) |
N/A | 4.135 | 0.000 | 35.319 | 0.207 | 0.122 | 0.212 | 0.000 | 200.014 | 3.334 |
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 | 56 | 18 | 30 | 28 | 19 | 22 | 29 | 20 | 19 |
N.S. |
1 | 2.00 | 0.64 | 1.07 | 1.00 | 0.68 | 0.79 | 1.04 | 0.71 | 0.68 |
time (sec) |
N/A | 1.058 | 0.231 | 12.830 | 0.176 | 0.094 | 0.173 | 0.129 | 0.161 | 3.127 |
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 | 20 | 20 | 21 | 20 | 28 | 15 | 21 | 29 | 20 |
N.S. |
1 | 0.80 | 0.80 | 0.84 | 0.80 | 1.12 | 0.60 | 0.84 | 1.16 | 0.80 |
time (sec) |
N/A | 0.260 | 0.007 | 0.055 | 0.024 | 0.074 | 0.038 | 0.120 | 0.156 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | F(-2) | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 1104 | 57 | 34 | 0 | 42 | 100 | 1602 | 160 | 32 |
N.S. |
1 | 30.67 | 1.58 | 0.94 | 0.00 | 1.17 | 2.78 | 44.50 | 4.44 | 0.89 |
time (sec) |
N/A | 9.616 | 10.089 | 3.749 | 0.000 | 0.097 | 2.951 | 0.191 | 0.162 | 3.350 |
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 | 29 | 0 | 29 | 46 | 160 | 62 | 201 | 92 | 53 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.59 | 5.52 | 2.14 | 6.93 | 3.17 | 1.83 | 0.00 |
time (sec) |
N/A | 0.000 | 5.063 | 0.084 | 0.180 | 0.105 | 0.341 | 0.151 | 0.161 | 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 | 14 | 14 | 14 | 12 | 11 | 11 | 14 | 11 | 12 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.79 | 0.79 | 1.00 | 0.79 | 0.86 | 0.79 |
time (sec) |
N/A | 0.140 | 0.000 | 0.060 | 0.024 | 0.076 | 0.018 | 0.113 | 0.157 | 3.032 |
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 | 22 | 25 | 17 | 17 | 21 | 24 | 24 | 21 | 46 | 25 |
N.S. |
1 | 1.14 | 0.77 | 0.77 | 0.95 | 1.09 | 1.09 | 0.95 | 2.09 | 1.14 |
time (sec) |
N/A | 0.419 | 0.049 | 0.092 | 0.142 | 0.076 | 0.068 | 0.114 | 30.134 | 3.099 |
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 | 23 | 37 | 43 | 41 | 30 | 36 | 37 | 30 | 29 | 48 |
N.S. |
1 | 1.61 | 1.87 | 1.78 | 1.30 | 1.57 | 1.61 | 1.30 | 1.26 | 2.09 |
time (sec) |
N/A | 0.175 | 0.006 | 0.399 | 0.031 | 0.082 | 0.025 | 0.108 | 0.174 | 3.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 18 | 16 | 12 | 14 | 14 | 15 | 14 | 13 | 11 |
N.S. |
1 | 1.12 | 1.00 | 0.75 | 0.88 | 0.88 | 0.94 | 0.88 | 0.81 | 0.69 |
time (sec) |
N/A | 0.194 | 0.001 | 0.109 | 0.030 | 0.066 | 0.024 | 0.113 | 0.170 | 0.015 |
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 | 44 | 24 | 27 | 44 | 31 | 31 | 42 | 29 | 26 |
N.S. |
1 | 1.69 | 0.92 | 1.04 | 1.69 | 1.19 | 1.19 | 1.62 | 1.12 | 1.00 |
time (sec) |
N/A | 0.578 | 0.081 | 0.278 | 0.057 | 0.101 | 0.129 | 0.112 | 0.172 | 3.111 |
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 | 28 | 0 | 35 | 36 | 34 | 35 | 31 | 35 | 35 | 34 |
N.S. |
1 | 0.00 | 1.25 | 1.29 | 1.21 | 1.25 | 1.11 | 1.25 | 1.25 | 1.21 |
time (sec) |
N/A | 0.000 | 0.057 | 36.662 | 0.105 | 0.107 | 0.451 | 0.436 | 0.186 | 3.373 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F(-1) | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 51 | 0 | 58 | 58 | 42 | 4300 | 56 | 0 |
N.S. |
1 | 0.00 | 1.89 | 0.00 | 2.15 | 2.15 | 1.56 | 159.26 | 2.07 | 0.00 |
time (sec) |
N/A | 0.000 | 0.111 | 180.000 | 0.278 | 0.096 | 0.356 | 6.468 | 0.190 | 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 | 15 | 15 | 14 | 13 | 13 | 14 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 0.93 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.253 | 0.005 | 0.152 | 0.028 | 0.087 | 0.050 | 0.120 | 0.161 | 3.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 265 | 90 | 1473 | 420 | 405 | 2810 | 124 | 0 |
N.S. |
1 | 0.00 | 8.55 | 2.90 | 47.52 | 13.55 | 13.06 | 90.65 | 4.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.203 | 8.463 | 0.257 | 0.109 | 92.575 | 0.272 | 0.167 | 0.000 |
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 | 29 | 24 | 38 | 22 | 36 | 36 | 20 | 36 | 42 | 0 |
N.S. |
1 | 0.83 | 1.31 | 0.76 | 1.24 | 1.24 | 0.69 | 1.24 | 1.45 | 0.00 |
time (sec) |
N/A | 1.314 | 0.298 | 0.348 | 0.156 | 0.082 | 0.056 | 0.122 | 0.160 | 0.000 |
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 | 21 | 0 | 32 | 21 | 50 | 20 | 17 | 20 | 20 | 16 |
N.S. |
1 | 0.00 | 1.52 | 1.00 | 2.38 | 0.95 | 0.81 | 0.95 | 0.95 | 0.76 |
time (sec) |
N/A | 0.000 | 0.088 | 0.107 | 0.066 | 0.086 | 0.037 | 0.107 | 0.160 | 3.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 29 | 29 | 27 | 49 | 34 | 22 | 28 | 38 | 24 |
N.S. |
1 | 1.16 | 1.16 | 1.08 | 1.96 | 1.36 | 0.88 | 1.12 | 1.52 | 0.96 |
time (sec) |
N/A | 0.651 | 0.041 | 0.256 | 0.054 | 0.085 | 0.053 | 0.115 | 0.157 | 3.072 |
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 | 27 | 0 | 46 | 76 | 110 | 123 | 105 | 127 | 138 | 42 |
N.S. |
1 | 0.00 | 1.70 | 2.81 | 4.07 | 4.56 | 3.89 | 4.70 | 5.11 | 1.56 |
time (sec) |
N/A | 0.000 | 10.065 | 2.381 | 0.105 | 0.127 | 0.126 | 0.179 | 0.171 | 3.217 |
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 | 32 | 192 | 26 | 27 | 162 | 27 | 24 | 27 | 27 | 20 |
N.S. |
1 | 6.00 | 0.81 | 0.84 | 5.06 | 0.84 | 0.75 | 0.84 | 0.84 | 0.62 |
time (sec) |
N/A | 1.757 | 0.141 | 0.806 | 0.091 | 0.097 | 0.128 | 0.113 | 0.162 | 3.130 |
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 | 28 | 0 | 25 | 25 | 24 | 30 | 22 | 24 | 38 | 24 |
N.S. |
1 | 0.00 | 0.89 | 0.89 | 0.86 | 1.07 | 0.79 | 0.86 | 1.36 | 0.86 |
time (sec) |
N/A | 0.000 | 0.052 | 0.487 | 0.086 | 0.103 | 0.127 | 0.137 | 0.161 | 3.087 |
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 | 16 | 16 | 13 | 13 | 13 | 14 | 13 | 15 | 13 |
N.S. |
1 | 0.80 | 0.80 | 0.65 | 0.65 | 0.65 | 0.70 | 0.65 | 0.75 | 0.65 |
time (sec) |
N/A | 0.184 | 0.132 | 0.050 | 0.025 | 0.075 | 0.045 | 0.114 | 0.156 | 0.054 |
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 | 28 | 25 | 26 | 25 | 26 | 26 | 124 | 46 |
N.S. |
1 | 0.00 | 1.17 | 1.04 | 1.08 | 1.04 | 1.08 | 1.08 | 5.17 | 1.92 |
time (sec) |
N/A | 0.000 | 0.207 | 68.411 | 0.161 | 0.080 | 0.250 | 0.147 | 0.218 | 3.173 |
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 | 25 | 38 | 22 | 35 | 31 | 26 | 30 | 33 |
N.S. |
1 | 0.00 | 0.76 | 1.15 | 0.67 | 1.06 | 0.94 | 0.79 | 0.91 | 1.00 |
time (sec) |
N/A | 0.000 | 1.125 | 0.324 | 0.245 | 0.084 | 0.094 | 0.175 | 0.160 | 3.154 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 11 | 11 | 10 | 9 | 9 | 10 | 10 | 13 | 9 |
N.S. |
1 | 0.50 | 0.50 | 0.45 | 0.41 | 0.41 | 0.45 | 0.45 | 0.59 | 0.41 |
time (sec) |
N/A | 0.183 | 0.001 | 0.042 | 0.025 | 0.083 | 0.046 | 0.106 | 0.160 | 3.029 |
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 | 32 | 46 | 32 | 38 | 30 | 48 | 32 | 58 | 45 | 37 |
N.S. |
1 | 1.44 | 1.00 | 1.19 | 0.94 | 1.50 | 1.00 | 1.81 | 1.41 | 1.16 |
time (sec) |
N/A | 0.393 | 2.379 | 0.857 | 0.098 | 0.082 | 0.152 | 0.128 | 1.459 | 3.120 |
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 | 20 | 27 | 18 | 17 | 19 | 17 | 17 | 18 | 19 |
N.S. |
1 | 0.91 | 1.23 | 0.82 | 0.77 | 0.86 | 0.77 | 0.77 | 0.82 | 0.86 |
time (sec) |
N/A | 0.143 | 0.000 | 0.051 | 0.026 | 0.074 | 0.014 | 0.115 | 0.170 | 0.001 |
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 | 30 | 0 | 72 | 59 | 161 | 82 | 70 | 95 | 113 | 63 |
N.S. |
1 | 0.00 | 2.40 | 1.97 | 5.37 | 2.73 | 2.33 | 3.17 | 3.77 | 2.10 |
time (sec) |
N/A | 0.000 | 0.067 | 1.470 | 0.092 | 0.111 | 0.211 | 0.137 | 0.163 | 3.346 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 25 | 25 | 17 | 21 | 21 | 14 | 24 | 23 | 19 |
N.S. |
1 | 1.09 | 1.09 | 0.74 | 0.91 | 0.91 | 0.61 | 1.04 | 1.00 | 0.83 |
time (sec) |
N/A | 0.660 | 0.149 | 0.214 | 0.058 | 0.109 | 0.050 | 0.110 | 0.160 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 72 | 25 | 22 | 26 | 22 | 24 | 26 | 0 |
N.S. |
1 | 0.00 | 2.48 | 0.86 | 0.76 | 0.90 | 0.76 | 0.83 | 0.90 | 0.00 |
time (sec) |
N/A | 0.000 | 0.853 | 1.170 | 0.173 | 0.087 | 0.145 | 0.144 | 0.165 | 0.000 |
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 | 25 | 72 | 74 | 58 | 78 | 54 | 61 | 57 | 64 | 64 |
N.S. |
1 | 2.88 | 2.96 | 2.32 | 3.12 | 2.16 | 2.44 | 2.28 | 2.56 | 2.56 |
time (sec) |
N/A | 0.343 | 0.008 | 1.800 | 0.037 | 0.098 | 0.101 | 0.120 | 0.161 | 3.097 |
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 | 30 | 0 | 31 | 32 | 34 | 33 | 27 | 171 | 47 | 0 |
N.S. |
1 | 0.00 | 1.03 | 1.07 | 1.13 | 1.10 | 0.90 | 5.70 | 1.57 | 0.00 |
time (sec) |
N/A | 0.000 | 0.032 | 1.884 | 0.163 | 0.079 | 0.096 | 0.376 | 0.161 | 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 | 28 | 31 | 29 | 28 | 80 | 41 | 34 | 47 | 43 | 25 |
N.S. |
1 | 1.11 | 1.04 | 1.00 | 2.86 | 1.46 | 1.21 | 1.68 | 1.54 | 0.89 |
time (sec) |
N/A | 0.532 | 0.043 | 0.512 | 0.086 | 0.083 | 0.189 | 0.111 | 0.158 | 0.071 |
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 | 22 | 0 | 18 | 21 | 17 | 20 | 19 | 20 | 21 | 0 |
N.S. |
1 | 0.00 | 0.82 | 0.95 | 0.77 | 0.91 | 0.86 | 0.91 | 0.95 | 0.00 |
time (sec) |
N/A | 0.000 | 0.122 | 0.465 | 0.060 | 0.079 | 0.086 | 0.128 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 58 | 58 | 45 | 58 | 44 | 44 | 45 | 44 | 26 |
N.S. |
1 | 2.64 | 2.64 | 2.05 | 2.64 | 2.00 | 2.00 | 2.05 | 2.00 | 1.18 |
time (sec) |
N/A | 0.584 | 0.018 | 3.274 | 0.028 | 0.084 | 0.083 | 0.117 | 0.161 | 3.105 |
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 | 23 | 20 | 20 | 25 | 42 | 40 | 17 | 24 | 40 | 29 |
N.S. |
1 | 0.87 | 0.87 | 1.09 | 1.83 | 1.74 | 0.74 | 1.04 | 1.74 | 1.26 |
time (sec) |
N/A | 0.959 | 0.017 | 0.301 | 0.072 | 0.081 | 0.054 | 0.281 | 0.159 | 3.177 |
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 | 17 | 20 | 10 | 13 | 13 | 14 | 13 | 10 | 9 |
N.S. |
1 | 1.21 | 1.43 | 0.71 | 0.93 | 0.93 | 1.00 | 0.93 | 0.71 | 0.64 |
time (sec) |
N/A | 0.252 | 0.002 | 0.032 | 0.033 | 0.067 | 0.017 | 0.115 | 0.157 | 3.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | A | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 31 | 87 | 56 | 33 | 51 | 75 | 56 | 0 |
N.S. |
1 | 0.00 | 1.07 | 3.00 | 1.93 | 1.14 | 1.76 | 2.59 | 1.93 | 0.00 |
time (sec) |
N/A | 0.000 | 5.057 | 395.421 | 0.102 | 0.087 | 0.231 | 0.142 | 0.163 | 0.000 |
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 | 23 | 0 | 22 | 21 | 20 | 61 | 17 | 38 | 22 | 20 |
N.S. |
1 | 0.00 | 0.96 | 0.91 | 0.87 | 2.65 | 0.74 | 1.65 | 0.96 | 0.87 |
time (sec) |
N/A | 0.000 | 0.187 | 0.306 | 0.037 | 0.090 | 0.094 | 0.151 | 0.158 | 3.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-2) | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 28 | 39 | 49 | 27 | 0 | 41 | 87 | 0 |
N.S. |
1 | 0.00 | 1.27 | 1.77 | 2.23 | 1.23 | 0.00 | 1.86 | 3.95 | 0.00 |
time (sec) |
N/A | 0.000 | 0.029 | 55.575 | 0.156 | 0.089 | 0.000 | 0.136 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | F | A | F(-1) | F | F | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 0 | 28 | 0 | 49 | 0 | 0 | 89 | 26 |
N.S. |
1 | 0.00 | 0.00 | 0.88 | 0.00 | 1.53 | 0.00 | 0.00 | 2.78 | 0.81 |
time (sec) |
N/A | 0.000 | 0.000 | 0.203 | 0.000 | 0.093 | 0.000 | 0.000 | 79.157 | 3.214 |
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 | 16 | 29 | 21 | 21 | 34 | 19 | 17 | 22 | 21 | 21 |
N.S. |
1 | 1.81 | 1.31 | 1.31 | 2.12 | 1.19 | 1.06 | 1.38 | 1.31 | 1.31 |
time (sec) |
N/A | 0.592 | 0.031 | 0.148 | 0.065 | 0.084 | 0.065 | 0.114 | 0.155 | 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 | 20 | 63 | 41 | 47 | 48 | 48 | 51 | 48 | 56 | 49 |
N.S. |
1 | 3.15 | 2.05 | 2.35 | 2.40 | 2.40 | 2.55 | 2.40 | 2.80 | 2.45 |
time (sec) |
N/A | 0.201 | 0.018 | 0.099 | 0.027 | 0.096 | 0.023 | 0.111 | 0.170 | 0.061 |
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 | 25 | 17 | 16 | 23 | 16 | 19 | 34 | 18 | 16 |
N.S. |
1 | 1.32 | 0.89 | 0.84 | 1.21 | 0.84 | 1.00 | 1.79 | 0.95 | 0.84 |
time (sec) |
N/A | 0.275 | 0.091 | 0.046 | 0.068 | 0.068 | 0.054 | 0.112 | 0.154 | 3.149 |
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 | 27 | 0 | 34 | 37 | 52 | 52 | 31 | 67 | 66 | 0 |
N.S. |
1 | 0.00 | 1.26 | 1.37 | 1.93 | 1.93 | 1.15 | 2.48 | 2.44 | 0.00 |
time (sec) |
N/A | 0.000 | 0.059 | 0.134 | 0.100 | 0.090 | 0.126 | 0.331 | 0.158 | 0.000 |
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 | 20 | 22 | 22 | 29 | 29 | 22 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.87 | 0.96 | 0.96 | 1.26 | 1.26 | 0.96 | 0.00 |
time (sec) |
N/A | 0.000 | 1.384 | 4.059 | 0.098 | 0.089 | 0.194 | 0.119 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | F | F | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 0 | 34 | 36 | 36 | 34 | 0 | 1005 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.36 | 1.44 | 1.44 | 1.36 | 0.00 | 40.20 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.511 | 0.162 | 0.089 | 0.154 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | B | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 34 | 28 | 51 | 0 | 66 | 54 | 0 | 133 | 63 |
N.S. |
1 | 1.13 | 0.93 | 1.70 | 0.00 | 2.20 | 1.80 | 0.00 | 4.43 | 2.10 |
time (sec) |
N/A | 7.286 | 0.115 | 0.917 | 0.000 | 0.098 | 3.003 | 0.000 | 200.018 | 3.256 |
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 | 23 | 20 | 18 | 17 | 17 | 15 | 17 | 18 | 18 |
N.S. |
1 | 1.15 | 1.00 | 0.90 | 0.85 | 0.85 | 0.75 | 0.85 | 0.90 | 0.90 |
time (sec) |
N/A | 0.419 | 0.016 | 0.187 | 0.064 | 0.102 | 0.047 | 0.120 | 0.151 | 3.135 |
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 | 22 | 0 | 20 | 38 | 37 | 36 | 36 | 37 | 44 | 42 |
N.S. |
1 | 0.00 | 0.91 | 1.73 | 1.68 | 1.64 | 1.64 | 1.68 | 2.00 | 1.91 |
time (sec) |
N/A | 0.000 | 0.540 | 0.411 | 0.122 | 0.082 | 0.140 | 0.380 | 0.169 | 3.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 34 | 0 | 35 | 29 | 36 | 26 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.48 | 0.00 | 1.52 | 1.26 | 1.57 | 1.13 | 0.00 |
time (sec) |
N/A | 0.000 | 5.051 | 1.697 | 0.000 | 0.097 | 4.374 | 0.251 | 0.152 | 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 | 19 | 13 | 13 | 14 | 13 | 13 | 10 | 13 | 13 | 13 |
N.S. |
1 | 0.68 | 0.68 | 0.74 | 0.68 | 0.68 | 0.53 | 0.68 | 0.68 | 0.68 |
time (sec) |
N/A | 0.372 | 0.004 | 0.039 | 0.030 | 0.079 | 0.034 | 0.114 | 0.155 | 0.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 27 | 30 | 59 | 28 | 24 | 0 | 164 | 29 |
N.S. |
1 | 0.00 | 1.00 | 1.11 | 2.19 | 1.04 | 0.89 | 0.00 | 6.07 | 1.07 |
time (sec) |
N/A | 0.000 | 0.584 | 12.528 | 0.147 | 0.091 | 0.687 | 0.000 | 200.014 | 3.329 |
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 | 18 | 15 | 13 | 13 | 89 | 14 | 14 | 14 | 18 | 16 |
N.S. |
1 | 0.83 | 0.72 | 0.72 | 4.94 | 0.78 | 0.78 | 0.78 | 1.00 | 0.89 |
time (sec) |
N/A | 0.325 | 0.044 | 0.079 | 0.154 | 0.080 | 0.045 | 0.113 | 0.200 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | B | F(-1) | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 76 | 56 | 61 | 64 | 83 | 0 | 75 | 0 |
N.S. |
1 | 0.00 | 2.30 | 1.70 | 1.85 | 1.94 | 2.52 | 0.00 | 2.27 | 0.00 |
time (sec) |
N/A | 0.000 | 0.101 | 3.332 | 0.152 | 0.105 | 0.897 | 0.000 | 0.192 | 0.000 |
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 | 23 | 183 | 27 | 29 | 46 | 44 | 44 | 30 | 47 | 43 |
N.S. |
1 | 7.96 | 1.17 | 1.26 | 2.00 | 1.91 | 1.91 | 1.30 | 2.04 | 1.87 |
time (sec) |
N/A | 0.505 | 0.011 | 0.132 | 0.027 | 0.088 | 0.411 | 0.123 | 0.167 | 0.092 |
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 | 16 | 15 | 15 | 17 | 18 | 18 | 12 | 43 | 17 | 16 |
N.S. |
1 | 0.94 | 0.94 | 1.06 | 1.12 | 1.12 | 0.75 | 2.69 | 1.06 | 1.00 |
time (sec) |
N/A | 0.467 | 0.041 | 0.404 | 0.076 | 0.090 | 0.079 | 0.115 | 0.195 | 3.302 |
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 | 32 | 28 | 31 | 27 | 24 | 27 | 34 | 29 |
N.S. |
1 | 0.00 | 1.07 | 0.93 | 1.03 | 0.90 | 0.80 | 0.90 | 1.13 | 0.97 |
time (sec) |
N/A | 0.000 | 0.063 | 0.237 | 0.079 | 0.087 | 0.099 | 0.186 | 1.502 | 3.393 |
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 | 24 | 0 | 0 | 21 | 26 | 26 | 0 | 0 | 26 | 25 |
N.S. |
1 | 0.00 | 0.00 | 0.88 | 1.08 | 1.08 | 0.00 | 0.00 | 1.08 | 1.04 |
time (sec) |
N/A | 0.000 | 0.000 | 1.107 | 0.206 | 0.096 | 0.000 | 0.000 | 0.174 | 3.722 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 146 | 39 | 41 | 71 | 39 | 0 | 0 | 45 | 37 |
N.S. |
1 | 5.41 | 1.44 | 1.52 | 2.63 | 1.44 | 0.00 | 0.00 | 1.67 | 1.37 |
time (sec) |
N/A | 3.165 | 0.119 | 0.812 | 0.266 | 0.086 | 0.000 | 0.000 | 0.177 | 3.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 36 | 68 | 70 | 64 | 42 | 78 | 132 | 30 |
N.S. |
1 | 0.00 | 1.20 | 2.27 | 2.33 | 2.13 | 1.40 | 2.60 | 4.40 | 1.00 |
time (sec) |
N/A | 0.000 | 0.046 | 1.309 | 0.161 | 0.098 | 0.102 | 0.291 | 0.173 | 3.382 |
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 | 15 | 43 | 15 | 13 | 12 | 12 | 12 | 12 | 15 | 14 |
N.S. |
1 | 2.87 | 1.00 | 0.87 | 0.80 | 0.80 | 0.80 | 0.80 | 1.00 | 0.93 |
time (sec) |
N/A | 0.566 | 0.063 | 0.063 | 0.073 | 0.081 | 0.052 | 0.114 | 0.159 | 3.182 |
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 | 32 | 72 | 49 | 46 | 51 | 42 | 51 | 67 | 62 | 31 |
N.S. |
1 | 2.25 | 1.53 | 1.44 | 1.59 | 1.31 | 1.59 | 2.09 | 1.94 | 0.97 |
time (sec) |
N/A | 0.354 | 0.468 | 0.391 | 0.109 | 0.087 | 0.183 | 0.114 | 0.163 | 0.102 |
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 | 18 | 38 | 17 | 15 | 15 | 18 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 1.73 | 0.77 | 0.68 | 0.68 | 0.82 | 0.68 |
time (sec) |
N/A | 0.217 | 0.007 | 0.088 | 0.034 | 0.087 | 0.091 | 0.118 | 0.161 | 3.264 |
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 | 30 | 22 | 29 | 27 | 27 | 29 | 30 | 22 |
N.S. |
1 | 0.00 | 1.20 | 0.88 | 1.16 | 1.08 | 1.08 | 1.16 | 1.20 | 0.88 |
time (sec) |
N/A | 0.000 | 1.623 | 0.382 | 0.099 | 0.090 | 0.106 | 0.129 | 0.173 | 3.233 |
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 | 27 | 0 | 27 | 29 | 34 | 28 | 27 | 1134 | 32 | 28 |
N.S. |
1 | 0.00 | 1.00 | 1.07 | 1.26 | 1.04 | 1.00 | 42.00 | 1.19 | 1.04 |
time (sec) |
N/A | 0.000 | 0.089 | 8.739 | 0.211 | 0.085 | 4.709 | 1.126 | 0.250 | 5.631 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 29 | 31 | 28 | 24 | 29 | 31 | 28 |
N.S. |
1 | 0.00 | 0.00 | 0.97 | 1.03 | 0.93 | 0.80 | 0.97 | 1.03 | 0.93 |
time (sec) |
N/A | 0.000 | 0.000 | 8.367 | 0.195 | 0.102 | 0.468 | 0.186 | 0.177 | 3.345 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | A | A | A | A | B | F(-1) |
verified | N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 26 | 0 | 23 | 24 | 24 | 19 | 25 | 24 | 0 |
N.S. |
1 | 0.96 | 0.00 | 0.85 | 0.89 | 0.89 | 0.70 | 0.93 | 0.89 | 0.00 |
time (sec) |
N/A | 1.444 | 0.000 | 0.250 | 0.142 | 0.095 | 0.128 | 0.119 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 23 | 17 | 17 | 0 | 16 | 26 | 24 | 17 | 0 |
N.S. |
1 | 1.15 | 0.85 | 0.85 | 0.00 | 0.80 | 1.30 | 1.20 | 0.85 | 0.00 |
time (sec) |
N/A | 0.975 | 0.120 | 2.605 | 0.000 | 0.108 | 0.216 | 0.122 | 0.174 | 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 | 31 | 0 | 28 | 25 | 24 | 28 | 22 | 24 | 39 | 24 |
N.S. |
1 | 0.00 | 0.90 | 0.81 | 0.77 | 0.90 | 0.71 | 0.77 | 1.26 | 0.77 |
time (sec) |
N/A | 0.000 | 0.086 | 0.191 | 0.059 | 0.114 | 0.168 | 0.129 | 0.176 | 3.472 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 22 | 25 | 52 | 47 | 20 | 24 | 53 | 23 |
N.S. |
1 | 0.00 | 1.16 | 1.32 | 2.74 | 2.47 | 1.05 | 1.26 | 2.79 | 1.21 |
time (sec) |
N/A | 0.000 | 0.032 | 0.243 | 0.078 | 0.111 | 0.088 | 0.376 | 0.175 | 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 | 18 | 36 | 33 | 18 | 23 | 23 | 26 | 23 | 33 | 33 |
N.S. |
1 | 2.00 | 1.83 | 1.00 | 1.28 | 1.28 | 1.44 | 1.28 | 1.83 | 1.83 |
time (sec) |
N/A | 0.745 | 0.835 | 0.155 | 0.027 | 0.084 | 0.084 | 0.127 | 0.318 | 0.073 |