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 | 21 | 24 | 24 | 24 | 23 | 23 | 20 | 23 | 24 | 23 |
N.S. |
1 | 1.14 | 1.14 | 1.14 | 1.10 | 1.10 | 0.95 | 1.10 | 1.14 | 1.10 |
time (sec) |
N/A | 0.154 | 0.003 | 0.145 | 0.031 | 0.082 | 0.038 | 0.106 | 0.158 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | B | B | B | F | B | B |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 31 | 0 | 105 | 70 | 63 | 0 | 70 | 33 |
N.S. |
1 | 0.00 | 1.03 | 0.00 | 3.50 | 2.33 | 2.10 | 0.00 | 2.33 | 1.10 |
time (sec) |
N/A | 0.000 | 0.061 | 0.000 | 0.112 | 0.090 | 0.593 | 0.000 | 0.164 | 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 | 31 | 42 | 22 | 23 | 21 | 20 | 26 | 22 | 40 | 20 |
N.S. |
1 | 1.35 | 0.71 | 0.74 | 0.68 | 0.65 | 0.84 | 0.71 | 1.29 | 0.65 |
time (sec) |
N/A | 0.270 | 0.053 | 0.142 | 0.040 | 0.074 | 0.111 | 0.112 | 0.194 | 0.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 20 | 16 | 15 | 15 | 15 | 15 | 19 | 17 |
N.S. |
1 | 0.00 | 0.91 | 0.73 | 0.68 | 0.68 | 0.68 | 0.68 | 0.86 | 0.77 |
time (sec) |
N/A | 0.000 | 0.212 | 0.206 | 0.089 | 0.084 | 0.072 | 0.117 | 0.166 | 3.233 |
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 | 23 | 15 | 15 | 14 | 14 | 12 | 16 | 15 | 14 |
N.S. |
1 | 1.35 | 0.88 | 0.88 | 0.82 | 0.82 | 0.71 | 0.94 | 0.88 | 0.82 |
time (sec) |
N/A | 0.200 | 0.005 | 0.154 | 0.034 | 0.076 | 0.101 | 0.113 | 0.172 | 2.978 |
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 | 24 | 25 | 23 | 26 | 20 | 23 | 26 | 23 |
N.S. |
1 | 0.96 | 0.96 | 1.00 | 0.92 | 1.04 | 0.80 | 0.92 | 1.04 | 0.92 |
time (sec) |
N/A | 0.776 | 0.464 | 0.706 | 0.169 | 0.105 | 0.111 | 0.123 | 0.160 | 0.205 |
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 | 23 | 30 | 21 | 20 | 20 | 24 | 20 | 20 | 15 |
N.S. |
1 | 1.35 | 1.76 | 1.24 | 1.18 | 1.18 | 1.41 | 1.18 | 1.18 | 0.88 |
time (sec) |
N/A | 0.164 | 0.002 | 0.218 | 0.040 | 0.080 | 0.021 | 0.111 | 0.163 | 2.940 |
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 | 45 | 23 | 21 | 35 | 25 | 20 | 33 | 21 | 21 |
N.S. |
1 | 1.88 | 0.96 | 0.88 | 1.46 | 1.04 | 0.83 | 1.38 | 0.88 | 0.88 |
time (sec) |
N/A | 0.428 | 0.073 | 0.270 | 0.081 | 0.077 | 0.113 | 0.114 | 0.170 | 2.959 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 26 | 34 | 83 | 73 | 66 | 87 | 55 | 434 |
N.S. |
1 | 0.00 | 1.24 | 1.62 | 3.95 | 3.48 | 3.14 | 4.14 | 2.62 | 20.67 |
time (sec) |
N/A | 0.000 | 0.040 | 1.392 | 0.189 | 0.090 | 0.151 | 0.152 | 0.172 | 3.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 34 | 42 | 33 | 33 | 32 | 31 | 0 | 432 | 32 |
N.S. |
1 | 1.42 | 1.75 | 1.38 | 1.38 | 1.33 | 1.29 | 0.00 | 18.00 | 1.33 |
time (sec) |
N/A | 0.578 | 0.046 | 0.984 | 0.171 | 0.086 | 0.333 | 0.000 | 0.184 | 3.211 |
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 | 11 | 12 | 11 | 10 | 10 | 12 | 11 | 10 | 10 |
N.S. |
1 | 0.79 | 0.86 | 0.79 | 0.71 | 0.71 | 0.86 | 0.79 | 0.71 | 0.71 |
time (sec) |
N/A | 0.155 | 0.002 | 0.052 | 0.045 | 0.072 | 0.039 | 0.107 | 0.177 | 2.914 |
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 | 31 | 79 | 46 | 37 | 35 | 53 | 31 | 37 | 108 | 35 |
N.S. |
1 | 2.55 | 1.48 | 1.19 | 1.13 | 1.71 | 1.00 | 1.19 | 3.48 | 1.13 |
time (sec) |
N/A | 0.434 | 0.031 | 0.401 | 0.042 | 0.077 | 0.380 | 0.107 | 0.168 | 3.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 64 | 17 | 24 | 93 | 24 | 31 | 40 | 23 | 17 |
N.S. |
1 | 3.37 | 0.89 | 1.26 | 4.89 | 1.26 | 1.63 | 2.11 | 1.21 | 0.89 |
time (sec) |
N/A | 0.653 | 0.035 | 0.220 | 0.089 | 0.082 | 0.091 | 0.113 | 0.170 | 2.980 |
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 | 18 | 16 | 14 | 13 | 17 | 10 | 17 | 18 | 13 |
N.S. |
1 | 0.95 | 0.84 | 0.74 | 0.68 | 0.89 | 0.53 | 0.89 | 0.95 | 0.68 |
time (sec) |
N/A | 0.177 | 0.006 | 0.108 | 0.037 | 0.092 | 0.043 | 0.108 | 0.177 | 2.935 |
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 | 16 | 14 | 12 | 19 | 11 | 12 | 11 | 15 | 11 |
N.S. |
1 | 1.14 | 1.00 | 0.86 | 1.36 | 0.79 | 0.86 | 0.79 | 1.07 | 0.79 |
time (sec) |
N/A | 0.183 | 0.053 | 0.125 | 0.085 | 0.074 | 0.044 | 0.111 | 0.173 | 0.032 |
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 | 34 | 28 | 28 | 26 | 36 | 31 | 22 | 33 | 43 | 35 |
N.S. |
1 | 0.82 | 0.82 | 0.76 | 1.06 | 0.91 | 0.65 | 0.97 | 1.26 | 1.03 |
time (sec) |
N/A | 0.661 | 0.046 | 0.552 | 0.097 | 0.086 | 0.079 | 0.113 | 0.170 | 0.086 |
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 | 27 | 27 | 23 | 23 | 23 | 20 | 27 | 20 | 18 |
N.S. |
1 | 1.50 | 1.50 | 1.28 | 1.28 | 1.28 | 1.11 | 1.50 | 1.11 | 1.00 |
time (sec) |
N/A | 0.192 | 0.004 | 0.261 | 0.024 | 0.080 | 0.049 | 0.114 | 0.167 | 2.990 |
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 | 38 | 0 | 51 | 169 | 90 | 171 | 170 | 1565 | 172 | 1582 |
N.S. |
1 | 0.00 | 1.34 | 4.45 | 2.37 | 4.50 | 4.47 | 41.18 | 4.53 | 41.63 |
time (sec) |
N/A | 0.000 | 0.126 | 0.005 | 5.806 | 0.118 | 2.913 | 0.451 | 0.289 | 3.469 |
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 | 27 | 0 | 27 | 28 | 27 | 27 | 20 | 0 | 28 | 24 |
N.S. |
1 | 0.00 | 1.00 | 1.04 | 1.00 | 1.00 | 0.74 | 0.00 | 1.04 | 0.89 |
time (sec) |
N/A | 0.000 | 0.085 | 10.336 | 0.097 | 0.104 | 0.243 | 0.000 | 0.182 | 3.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 27 | 182 | 47 | 47 | 22 | 27 | 47 | 0 |
N.S. |
1 | 0.00 | 1.00 | 6.74 | 1.74 | 1.74 | 0.81 | 1.00 | 1.74 | 0.00 |
time (sec) |
N/A | 0.000 | 0.070 | 0.265 | 0.100 | 0.085 | 0.134 | 0.323 | 0.235 | 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 | 30 | 32 | 27 | 23 | 20 | 30 | 19 | 20 | 26 | 34 |
N.S. |
1 | 1.07 | 0.90 | 0.77 | 0.67 | 1.00 | 0.63 | 0.67 | 0.87 | 1.13 |
time (sec) |
N/A | 0.288 | 0.012 | 0.171 | 0.032 | 0.076 | 0.200 | 0.116 | 0.181 | 3.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 9 | 9 | 10 | 9 | 9 | 7 | 9 | 9 | 9 |
N.S. |
1 | 0.90 | 0.90 | 1.00 | 0.90 | 0.90 | 0.70 | 0.90 | 0.90 | 0.90 |
time (sec) |
N/A | 0.261 | 0.001 | 0.066 | 0.025 | 0.098 | 0.044 | 0.110 | 0.172 | 2.971 |
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 | 22 | 19 | 20 | 12 | 10 | 15 | 18 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.91 | 0.55 | 0.45 | 0.68 | 0.82 | 0.68 |
time (sec) |
N/A | 0.151 | 0.003 | 0.080 | 0.027 | 0.082 | 0.050 | 0.112 | 0.163 | 3.041 |
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 | 56 | 34 | 50 | 49 | 46 | 46 | 46 | 67 | 50 |
N.S. |
1 | 2.00 | 1.21 | 1.79 | 1.75 | 1.64 | 1.64 | 1.64 | 2.39 | 1.79 |
time (sec) |
N/A | 0.281 | 1.050 | 0.386 | 0.037 | 0.094 | 0.066 | 0.107 | 0.171 | 3.001 |
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 | 9 | 8 | 8 | 12 | 8 | 11 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.64 | 0.57 | 0.57 | 0.86 | 0.57 | 0.79 | 0.57 |
time (sec) |
N/A | 0.133 | 0.000 | 0.046 | 0.040 | 0.071 | 0.014 | 0.117 | 0.162 | 0.001 |
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 | 44 | 38 | 46 | 36 | 44 | 48 | 45 | 52 | 36 |
N.S. |
1 | 1.52 | 1.31 | 1.59 | 1.24 | 1.52 | 1.66 | 1.55 | 1.79 | 1.24 |
time (sec) |
N/A | 1.213 | 3.801 | 1.522 | 0.180 | 0.090 | 0.204 | 0.963 | 0.199 | 3.656 |
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 | 17 | 17 | 18 | 18 | 17 | 19 | 17 | 18 |
N.S. |
1 | 0.81 | 0.81 | 0.81 | 0.86 | 0.86 | 0.81 | 0.90 | 0.81 | 0.86 |
time (sec) |
N/A | 0.146 | 0.003 | 0.316 | 0.029 | 0.076 | 0.104 | 0.110 | 0.159 | 2.992 |
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 | 20 | 0 | 20 | 33 | 30 | 31 | 32 | 33 | 36 | 32 |
N.S. |
1 | 0.00 | 1.00 | 1.65 | 1.50 | 1.55 | 1.60 | 1.65 | 1.80 | 1.60 |
time (sec) |
N/A | 0.000 | 0.177 | 0.552 | 0.170 | 0.086 | 0.139 | 0.422 | 0.162 | 0.183 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 6 | 6 | 7 | 6 | 6 | 5 | 7 | 6 | 6 |
N.S. |
1 | 0.67 | 0.67 | 0.78 | 0.67 | 0.67 | 0.56 | 0.78 | 0.67 | 0.67 |
time (sec) |
N/A | 0.143 | 0.001 | 0.046 | 0.032 | 0.078 | 0.025 | 0.123 | 0.152 | 0.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 16 | 16 | 16 | 15 | 26 | 19 | 16 | 23 | 23 |
N.S. |
1 | 0.70 | 0.70 | 0.70 | 0.65 | 1.13 | 0.83 | 0.70 | 1.00 | 1.00 |
time (sec) |
N/A | 0.220 | 0.135 | 0.396 | 0.036 | 0.086 | 0.089 | 0.120 | 0.154 | 3.140 |
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 | 17 | 17 | 16 | 15 | 27 | 10 | 15 | 74 | 15 |
N.S. |
1 | 0.71 | 0.71 | 0.67 | 0.62 | 1.12 | 0.42 | 0.62 | 3.08 | 0.62 |
time (sec) |
N/A | 0.374 | 0.023 | 0.151 | 0.081 | 0.082 | 0.056 | 0.118 | 0.166 | 0.108 |
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 | 22 | 22 | 20 | 20 | 20 | 37 | 27 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.91 | 0.91 | 0.91 | 1.68 | 1.23 | 0.00 |
time (sec) |
N/A | 0.000 | 0.293 | 3.710 | 0.138 | 0.089 | 0.482 | 0.165 | 0.210 | 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 | 23 | 31 | 30 | 30 | 32 | 31 | 22 | 31 | 82 | 29 |
N.S. |
1 | 1.35 | 1.30 | 1.30 | 1.39 | 1.35 | 0.96 | 1.35 | 3.57 | 1.26 |
time (sec) |
N/A | 15.338 | 0.030 | 1.502 | 0.036 | 0.085 | 0.097 | 0.143 | 0.161 | 3.159 |
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 | 18 | 17 | 21 | 17 | 19 | 21 | 23 | 21 |
N.S. |
1 | 0.00 | 0.86 | 0.81 | 1.00 | 0.81 | 0.90 | 1.00 | 1.10 | 1.00 |
time (sec) |
N/A | 0.000 | 0.091 | 0.789 | 0.129 | 0.099 | 0.261 | 0.148 | 0.197 | 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 | 26 | 14 | 14 | 18 | 17 | 15 | 14 | 32 | 18 | 14 |
N.S. |
1 | 0.54 | 0.54 | 0.69 | 0.65 | 0.58 | 0.54 | 1.23 | 0.69 | 0.54 |
time (sec) |
N/A | 0.171 | 0.002 | 0.266 | 0.035 | 0.085 | 0.051 | 0.114 | 0.169 | 3.014 |
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 | 22 | 14 | 15 | 14 | 14 | 14 | 14 | 13 | 8 |
N.S. |
1 | 2.00 | 1.27 | 1.36 | 1.27 | 1.27 | 1.27 | 1.27 | 1.18 | 0.73 |
time (sec) |
N/A | 0.161 | 0.003 | 0.141 | 0.036 | 0.077 | 0.036 | 0.111 | 0.166 | 0.025 |
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 | 31 | 0 | 40 | 44 | 50 | 50 | 56 | 61 | 49 | 85 |
N.S. |
1 | 0.00 | 1.29 | 1.42 | 1.61 | 1.61 | 1.81 | 1.97 | 1.58 | 2.74 |
time (sec) |
N/A | 0.000 | 0.031 | 3.309 | 0.157 | 0.087 | 0.120 | 0.121 | 0.171 | 3.174 |
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 | 26 | 37 | 23 | 28 | 36 | 55 | 27 | 36 | 31 | 22 |
N.S. |
1 | 1.42 | 0.88 | 1.08 | 1.38 | 2.12 | 1.04 | 1.38 | 1.19 | 0.85 |
time (sec) |
N/A | 0.287 | 0.050 | 0.580 | 0.067 | 0.085 | 0.125 | 0.114 | 0.177 | 3.087 |
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 | 21 | 0 | 22 | 21 | 20 | 20 | 17 | 27 | 22 | 0 |
N.S. |
1 | 0.00 | 1.05 | 1.00 | 0.95 | 0.95 | 0.81 | 1.29 | 1.05 | 0.00 |
time (sec) |
N/A | 0.000 | 0.210 | 0.811 | 0.142 | 0.098 | 0.084 | 0.128 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 0 | 37 | 48 | 62 | 56 | 75 | 1267 | 45 | 0 |
N.S. |
1 | 0.00 | 0.92 | 1.20 | 1.55 | 1.40 | 1.88 | 31.68 | 1.12 | 0.00 |
time (sec) |
N/A | 0.000 | 0.110 | 87.253 | 0.194 | 0.102 | 0.279 | 147.045 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | F | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 68 | 64 | 81 | 63 | 0 | 0 | 82 | 0 |
N.S. |
1 | 0.00 | 1.94 | 1.83 | 2.31 | 1.80 | 0.00 | 0.00 | 2.34 | 0.00 |
time (sec) |
N/A | 0.000 | 0.146 | 0.088 | 0.217 | 0.104 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 1452 | 39 | 39 | 410 | 61 | 42 | 75 | 75 | 38 |
N.S. |
1 | 48.40 | 1.30 | 1.30 | 13.67 | 2.03 | 1.40 | 2.50 | 2.50 | 1.27 |
time (sec) |
N/A | 4.940 | 0.540 | 1.387 | 0.164 | 0.083 | 0.146 | 0.130 | 0.161 | 0.253 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | A | A | F(-1) | F | B | B |
verified | N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 26 | 0 | 0 | 35 | 30 | 0 | 0 | 40 | 36 |
N.S. |
1 | 0.93 | 0.00 | 0.00 | 1.25 | 1.07 | 0.00 | 0.00 | 1.43 | 1.29 |
time (sec) |
N/A | 1.954 | 0.000 | 0.000 | 0.284 | 0.096 | 0.000 | 0.000 | 0.226 | 3.723 |
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 | 34 | 0 | 45 | 48 | 50 | 37 | 46 | 0 | 54 | 64 |
N.S. |
1 | 0.00 | 1.32 | 1.41 | 1.47 | 1.09 | 1.35 | 0.00 | 1.59 | 1.88 |
time (sec) |
N/A | 0.000 | 5.094 | 1.306 | 0.106 | 0.093 | 0.150 | 0.000 | 5.139 | 3.287 |
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 | 25 | 15 | 19 | 28 | 15 | 14 | 26 | 17 |
N.S. |
1 | 0.92 | 1.00 | 0.60 | 0.76 | 1.12 | 0.60 | 0.56 | 1.04 | 0.68 |
time (sec) |
N/A | 0.241 | 0.116 | 0.165 | 0.029 | 0.098 | 0.050 | 0.113 | 0.173 | 0.077 |
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 | 19 | 15 | 16 | 18 | 15 | 14 | 15 | 14 |
N.S. |
1 | 0.00 | 1.12 | 0.88 | 0.94 | 1.06 | 0.88 | 0.82 | 0.88 | 0.82 |
time (sec) |
N/A | 0.000 | 0.062 | 2.628 | 0.156 | 0.105 | 0.068 | 0.112 | 0.170 | 3.388 |
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 | 32 | 41 | 45 | 40 | 37 | 45 | 507 | 40 |
N.S. |
1 | 0.00 | 1.10 | 1.41 | 1.55 | 1.38 | 1.28 | 1.55 | 17.48 | 1.38 |
time (sec) |
N/A | 0.000 | 0.047 | 8.967 | 0.069 | 0.101 | 0.229 | 0.164 | 0.187 | 3.264 |
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 | 32 | 22 | 22 | 39 | 20 | 20 | 20 | 32 | 28 |
N.S. |
1 | 1.10 | 0.76 | 0.76 | 1.34 | 0.69 | 0.69 | 0.69 | 1.10 | 0.97 |
time (sec) |
N/A | 0.283 | 0.113 | 0.345 | 0.029 | 0.085 | 0.063 | 0.110 | 0.176 | 3.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | C | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 21 | 26 | 124 | 24 | 22 | 525 | 27 | 843 |
N.S. |
1 | 0.00 | 0.88 | 1.08 | 5.17 | 1.00 | 0.92 | 21.88 | 1.12 | 35.12 |
time (sec) |
N/A | 0.000 | 0.221 | 44.228 | 0.291 | 0.080 | 0.148 | 0.224 | 0.187 | 3.640 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | F | B |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 22 | 21 | 23 | 20 | 27 | 41 | 27 |
N.S. |
1 | 0.00 | 0.00 | 0.92 | 0.88 | 0.96 | 0.83 | 1.12 | 1.71 | 1.12 |
time (sec) |
N/A | 0.000 | 0.000 | 0.347 | 0.173 | 0.087 | 0.106 | 0.168 | 200.045 | 3.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 184 | 344 | 407 | 256 | 286 | 407 | 634 | 453 |
N.S. |
1 | 0.00 | 6.13 | 11.47 | 13.57 | 8.53 | 9.53 | 13.57 | 21.13 | 15.10 |
time (sec) |
N/A | 0.000 | 0.971 | 0.204 | 1.722 | 0.112 | 1.810 | 5.010 | 200.028 | 3.497 |
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 | 29 | 29 | 27 | 34 | 29 | 31 | 31 | 34 | 30 |
N.S. |
1 | 1.04 | 1.04 | 0.96 | 1.21 | 1.04 | 1.11 | 1.11 | 1.21 | 1.07 |
time (sec) |
N/A | 1.223 | 2.035 | 0.375 | 0.085 | 0.098 | 0.106 | 0.115 | 0.166 | 0.117 |
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 | 15 | 22 | 15 | 28 | 17 | 15 |
N.S. |
1 | 0.71 | 0.71 | 0.67 | 0.62 | 0.92 | 0.62 | 1.17 | 0.71 | 0.62 |
time (sec) |
N/A | 0.297 | 0.012 | 0.168 | 0.036 | 0.088 | 0.044 | 0.117 | 0.155 | 0.051 |
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 | 30 | 0 | 29 | 30 | 37 | 29 | 24 | 137 | 29 | 51 |
N.S. |
1 | 0.00 | 0.97 | 1.00 | 1.23 | 0.97 | 0.80 | 4.57 | 0.97 | 1.70 |
time (sec) |
N/A | 0.000 | 0.041 | 8.802 | 0.097 | 0.073 | 0.091 | 0.197 | 0.165 | 3.347 |
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 | 23 | 0 | 29 | 30 | 27 | 33 | 27 | 27 | 207 | 29 |
N.S. |
1 | 0.00 | 1.26 | 1.30 | 1.17 | 1.43 | 1.17 | 1.17 | 9.00 | 1.26 |
time (sec) |
N/A | 0.000 | 0.425 | 0.829 | 0.141 | 0.097 | 0.098 | 0.209 | 0.196 | 3.288 |
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 | 7 | 7 | 7 | 6 | 6 | 5 | 6 | 9 | 7 |
N.S. |
1 | 0.33 | 0.33 | 0.33 | 0.29 | 0.29 | 0.24 | 0.29 | 0.43 | 0.33 |
time (sec) |
N/A | 0.153 | 0.012 | 0.051 | 0.037 | 0.069 | 0.028 | 0.109 | 0.164 | 0.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | F(-1) | B | B | B | F | B | B |
verified | N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 0 | 0 | 388 | 46 | 51 | 0 | 106 | 429 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 13.86 | 1.64 | 1.82 | 0.00 | 3.79 | 15.32 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 2.194 | 0.093 | 1.164 | 0.000 | 0.175 | 3.287 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | A | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 29 | 91 | 30 | 79 | 78 | 101 | 100 | 79 |
N.S. |
1 | 0.00 | 1.21 | 3.79 | 1.25 | 3.29 | 3.25 | 4.21 | 4.17 | 3.29 |
time (sec) |
N/A | 0.000 | 0.235 | 6.479 | 0.853 | 0.086 | 0.770 | 0.742 | 0.165 | 4.141 |
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 | 22 | 21 | 23 | 21 | 30 | 31 | 22 | 31 | 28 | 0 |
N.S. |
1 | 0.95 | 1.05 | 0.95 | 1.36 | 1.41 | 1.00 | 1.41 | 1.27 | 0.00 |
time (sec) |
N/A | 0.760 | 0.155 | 1.132 | 0.078 | 0.086 | 0.058 | 0.123 | 0.150 | 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 | 35 | 33 | 33 | 28 | 33 | 29 | 26 | 29 | 31 | 27 |
N.S. |
1 | 0.94 | 0.94 | 0.80 | 0.94 | 0.83 | 0.74 | 0.83 | 0.89 | 0.77 |
time (sec) |
N/A | 0.264 | 0.192 | 0.347 | 0.067 | 0.085 | 0.063 | 0.112 | 0.150 | 0.053 |
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 | 12 | 13 | 13 | 12 | 15 | 13 | 11 |
N.S. |
1 | 0.87 | 0.87 | 0.80 | 0.87 | 0.87 | 0.80 | 1.00 | 0.87 | 0.73 |
time (sec) |
N/A | 0.161 | 0.004 | 0.105 | 0.025 | 0.082 | 0.044 | 0.111 | 0.151 | 0.032 |
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 | 169 | 27 | 81 | 94 | 94 | 122 | 56 | 95 | 111 |
N.S. |
1 | 6.50 | 1.04 | 3.12 | 3.62 | 3.62 | 4.69 | 2.15 | 3.65 | 4.27 |
time (sec) |
N/A | 0.999 | 0.015 | 0.145 | 0.031 | 0.082 | 0.559 | 0.121 | 0.161 | 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 | 24 | 34 | 33 | 21 | 35 | 34 | 17 | 23 | 35 | 35 |
N.S. |
1 | 1.42 | 1.38 | 0.88 | 1.46 | 1.42 | 0.71 | 0.96 | 1.46 | 1.46 |
time (sec) |
N/A | 0.404 | 0.030 | 0.232 | 0.036 | 0.086 | 0.058 | 0.126 | 0.154 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 21 | 15 | 14 | 3 | 2 | 3 | 17 | 14 |
N.S. |
1 | 1.00 | 1.31 | 0.94 | 0.88 | 0.19 | 0.12 | 0.19 | 1.06 | 0.88 |
time (sec) |
N/A | 0.394 | 0.032 | 0.229 | 0.037 | 0.087 | 0.025 | 0.112 | 0.149 | 3.132 |
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 | 19 | 48 | 16 | 17 | 44 | 19 | 14 | 19 | 16 | 16 |
N.S. |
1 | 2.53 | 0.84 | 0.89 | 2.32 | 1.00 | 0.74 | 1.00 | 0.84 | 0.84 |
time (sec) |
N/A | 1.005 | 0.237 | 0.348 | 0.068 | 0.081 | 0.051 | 0.118 | 0.147 | 3.203 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 29 | 45 | 78 | 78 | 48 | 0 | 84 | 18 |
N.S. |
1 | 0.00 | 1.32 | 2.05 | 3.55 | 3.55 | 2.18 | 0.00 | 3.82 | 0.82 |
time (sec) |
N/A | 0.000 | 0.102 | 95.424 | 0.092 | 0.115 | 0.690 | 0.000 | 0.156 | 3.239 |
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 | 30 | 30 | 38 | 41 | 26 | 145 | 44 | 29 |
N.S. |
1 | 0.00 | 1.11 | 1.11 | 1.41 | 1.52 | 0.96 | 5.37 | 1.63 | 1.07 |
time (sec) |
N/A | 0.000 | 3.360 | 0.415 | 0.092 | 0.089 | 0.058 | 0.157 | 0.149 | 3.196 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-2) | F(-1) | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 43 | 41 | 43 | 43 | 0 | 0 | 43 | 40 |
N.S. |
1 | 0.00 | 1.30 | 1.24 | 1.30 | 1.30 | 0.00 | 0.00 | 1.30 | 1.21 |
time (sec) |
N/A | 0.000 | 0.152 | 0.070 | 0.298 | 0.098 | 0.000 | 0.000 | 0.269 | 3.621 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 69 | 58 | 76 | 67 | 66 | 60 | 0 | 77 | 63 |
N.S. |
1 | 2.76 | 2.32 | 3.04 | 2.68 | 2.64 | 2.40 | 0.00 | 3.08 | 2.52 |
time (sec) |
N/A | 0.324 | 0.049 | 0.487 | 0.028 | 0.095 | 0.168 | 0.000 | 0.159 | 3.221 |
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 | 38 | 42 | 41 | 38 | 50 | 36 | 40 | 41 | 37 |
N.S. |
1 | 1.41 | 1.56 | 1.52 | 1.41 | 1.85 | 1.33 | 1.48 | 1.52 | 1.37 |
time (sec) |
N/A | 0.282 | 0.020 | 0.263 | 0.027 | 0.091 | 0.068 | 0.116 | 0.162 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | C | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 123 | 80 | 106 | 224 | 86 | 107 | 111 | 124 | 101 |
N.S. |
1 | 3.62 | 2.35 | 3.12 | 6.59 | 2.53 | 3.15 | 3.26 | 3.65 | 2.97 |
time (sec) |
N/A | 0.769 | 0.463 | 7.502 | 0.089 | 0.089 | 0.133 | 0.117 | 0.165 | 0.085 |
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 | 10 | 11 | 11 | 10 | 11 | 11 | 9 |
N.S. |
1 | 0.92 | 0.92 | 0.83 | 0.92 | 0.92 | 0.83 | 0.92 | 0.92 | 0.75 |
time (sec) |
N/A | 0.151 | 0.002 | 0.954 | 0.039 | 0.080 | 0.033 | 0.114 | 0.157 | 0.024 |
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 | 42 | 41 | 38 | 38 | 36 | 56 | 62 | 56 |
N.S. |
1 | 0.00 | 1.24 | 1.21 | 1.12 | 1.12 | 1.06 | 1.65 | 1.82 | 1.65 |
time (sec) |
N/A | 0.000 | 0.719 | 0.148 | 0.040 | 0.108 | 0.100 | 0.111 | 0.150 | 3.168 |
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 | 23 | 22 | 26 | 33 | 19 | 0 | 34 | 25 |
N.S. |
1 | 0.00 | 0.96 | 0.92 | 1.08 | 1.38 | 0.79 | 0.00 | 1.42 | 1.04 |
time (sec) |
N/A | 0.000 | 1.053 | 8.116 | 0.259 | 0.091 | 0.224 | 0.000 | 0.152 | 3.392 |
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 | 25 | 19 | 18 | 21 | 22 | 21 | 24 | 18 |
N.S. |
1 | 0.00 | 0.96 | 0.73 | 0.69 | 0.81 | 0.85 | 0.81 | 0.92 | 0.69 |
time (sec) |
N/A | 0.000 | 0.199 | 0.451 | 0.065 | 0.098 | 0.078 | 0.123 | 0.152 | 3.280 |
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 | 34 | 0 | 31 | 29 | 0 | 30 | 29 | 26 | 31 | 0 |
N.S. |
1 | 0.00 | 0.91 | 0.85 | 0.00 | 0.88 | 0.85 | 0.76 | 0.91 | 0.00 |
time (sec) |
N/A | 0.000 | 0.084 | 0.921 | 0.000 | 0.093 | 0.094 | 0.239 | 0.159 | 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 | 16 | 15 | 15 | 13 | 12 | 24 | 14 | 24 | 25 | 12 |
N.S. |
1 | 0.94 | 0.94 | 0.81 | 0.75 | 1.50 | 0.88 | 1.50 | 1.56 | 0.75 |
time (sec) |
N/A | 0.188 | 0.004 | 0.137 | 0.032 | 0.105 | 0.045 | 0.112 | 0.150 | 3.148 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 25 | 26 | 26 | 25 | 24 | 26 | 25 | 141 |
N.S. |
1 | 0.00 | 1.14 | 1.18 | 1.18 | 1.14 | 1.09 | 1.18 | 1.14 | 6.41 |
time (sec) |
N/A | 0.000 | 0.339 | 183.748 | 0.193 | 0.091 | 1.586 | 0.393 | 0.164 | 5.782 |
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 | 40 | 40 | 27 | 32 | 32 | 39 | 32 | 36 | 37 |
N.S. |
1 | 1.25 | 1.25 | 0.84 | 1.00 | 1.00 | 1.22 | 1.00 | 1.12 | 1.16 |
time (sec) |
N/A | 0.174 | 0.005 | 0.092 | 0.032 | 0.078 | 0.021 | 0.115 | 0.157 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 18 | 17 | 0 | 16 | 12 | 30 | 20 | 16 |
N.S. |
1 | 0.00 | 1.00 | 0.94 | 0.00 | 0.89 | 0.67 | 1.67 | 1.11 | 0.89 |
time (sec) |
N/A | 0.000 | 0.546 | 0.365 | 0.000 | 0.090 | 0.652 | 0.116 | 0.156 | 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 | 20 | 0 | 16 | 17 | 16 | 23 | 17 | 16 | 23 | 16 |
N.S. |
1 | 0.00 | 0.80 | 0.85 | 0.80 | 1.15 | 0.85 | 0.80 | 1.15 | 0.80 |
time (sec) |
N/A | 0.000 | 0.194 | 0.429 | 0.092 | 0.090 | 0.046 | 0.121 | 0.152 | 3.272 |
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 | 20 | 19 | 18 | 18 | 19 | 18 | 24 | 20 |
N.S. |
1 | 2.19 | 0.95 | 0.90 | 0.86 | 0.86 | 0.90 | 0.86 | 1.14 | 0.95 |
time (sec) |
N/A | 0.220 | 0.032 | 0.125 | 0.104 | 0.101 | 0.098 | 0.118 | 0.149 | 3.213 |
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 | 19 | 19 | 20 | 21 | 21 | 19 | 21 | 23 | 35 |
N.S. |
1 | 0.90 | 0.90 | 0.95 | 1.00 | 1.00 | 0.90 | 1.00 | 1.10 | 1.67 |
time (sec) |
N/A | 0.447 | 0.026 | 0.270 | 0.161 | 0.092 | 0.082 | 0.120 | 0.149 | 3.415 |
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 | 23 | 22 | 21 | 31 | 15 | 21 | 22 | 21 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 0.91 | 1.35 | 0.65 | 0.91 | 0.96 | 0.91 |
time (sec) |
N/A | 0.000 | 0.132 | 0.121 | 0.073 | 0.103 | 0.119 | 0.119 | 0.148 | 3.341 |
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 | 22 | 33 | 33 | 32 | 29 | 33 | 32 | 32 |
N.S. |
1 | 0.00 | 0.92 | 1.38 | 1.38 | 1.33 | 1.21 | 1.38 | 1.33 | 1.33 |
time (sec) |
N/A | 0.000 | 0.037 | 0.874 | 0.057 | 0.098 | 0.173 | 0.150 | 0.153 | 3.302 |
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 | 21 | 32 | 23 | 24 | 44 | 32 | 27 | 31 | 29 | 19 |
N.S. |
1 | 1.52 | 1.10 | 1.14 | 2.10 | 1.52 | 1.29 | 1.48 | 1.38 | 0.90 |
time (sec) |
N/A | 0.360 | 0.050 | 0.151 | 0.060 | 0.096 | 0.045 | 0.120 | 0.149 | 3.256 |
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 | 15 | 0 | 17 | 15 | 15 | 14 | 10 | 26 | 16 | 12 |
N.S. |
1 | 0.00 | 1.13 | 1.00 | 1.00 | 0.93 | 0.67 | 1.73 | 1.07 | 0.80 |
time (sec) |
N/A | 0.000 | 0.018 | 0.065 | 0.075 | 0.097 | 0.055 | 0.128 | 0.152 | 0.047 |
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 | 24 | 18 | 20 | 25 | 17 | 22 | 18 | 23 | 12 |
N.S. |
1 | 1.20 | 0.90 | 1.00 | 1.25 | 0.85 | 1.10 | 0.90 | 1.15 | 0.60 |
time (sec) |
N/A | 0.282 | 0.176 | 0.229 | 0.091 | 0.118 | 0.137 | 0.117 | 0.159 | 3.516 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 33 | 31 | 32 | 68 | 38 | 29 | 59 | 675 | 28 |
N.S. |
1 | 1.10 | 1.03 | 1.07 | 2.27 | 1.27 | 0.97 | 1.97 | 22.50 | 0.93 |
time (sec) |
N/A | 8.754 | 0.198 | 10.306 | 0.326 | 0.098 | 0.159 | 45.157 | 0.210 | 3.584 |
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 | 32 | 31 | 31 | 40 | 36 | 42 | 29 | 49 | 40 | 0 |
N.S. |
1 | 0.97 | 0.97 | 1.25 | 1.12 | 1.31 | 0.91 | 1.53 | 1.25 | 0.00 |
time (sec) |
N/A | 1.307 | 0.265 | 1.162 | 0.163 | 0.106 | 0.119 | 0.161 | 0.163 | 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 | 13 | 13 | 12 | 11 | 17 | 10 | 11 | 23 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.85 | 1.31 | 0.77 | 0.85 | 1.77 | 0.85 |
time (sec) |
N/A | 0.238 | 0.020 | 0.168 | 0.033 | 0.094 | 0.049 | 0.111 | 0.162 | 0.063 |
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 | 25 | 0 | 31 | 52 | 93 | 93 | 83 | 90 | 119 | 0 |
N.S. |
1 | 0.00 | 1.24 | 2.08 | 3.72 | 3.72 | 3.32 | 3.60 | 4.76 | 0.00 |
time (sec) |
N/A | 0.000 | 0.033 | 3.835 | 0.073 | 0.098 | 0.122 | 0.134 | 0.170 | 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 | 23 | 19 | 19 | 17 | 16 | 16 | 15 | 16 | 19 | 16 |
N.S. |
1 | 0.83 | 0.83 | 0.74 | 0.70 | 0.70 | 0.65 | 0.70 | 0.83 | 0.70 |
time (sec) |
N/A | 0.166 | 0.009 | 0.078 | 0.034 | 0.085 | 0.067 | 0.115 | 0.161 | 3.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 56 | 30 | 40 | 81 | 53 | 60 | 90 | 35 | 43 |
N.S. |
1 | 2.00 | 1.07 | 1.43 | 2.89 | 1.89 | 2.14 | 3.21 | 1.25 | 1.54 |
time (sec) |
N/A | 0.258 | 0.033 | 0.381 | 0.106 | 0.085 | 0.104 | 0.115 | 0.165 | 3.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 27 | 28 | 77 | 78 | 82 | 27 | 87 | 27 |
N.S. |
1 | 0.00 | 1.08 | 1.12 | 3.08 | 3.12 | 3.28 | 1.08 | 3.48 | 1.08 |
time (sec) |
N/A | 0.000 | 0.019 | 0.355 | 0.042 | 0.095 | 4.641 | 0.137 | 0.166 | 0.165 |
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 | 18 | 0 | 18 | 19 | 34 | 29 | 20 | 257 | 18 | 31 |
N.S. |
1 | 0.00 | 1.00 | 1.06 | 1.89 | 1.61 | 1.11 | 14.28 | 1.00 | 1.72 |
time (sec) |
N/A | 0.000 | 0.148 | 8.483 | 0.179 | 0.090 | 0.081 | 0.466 | 0.166 | 3.366 |
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 | 30 | 147 | 114 | 55 | 329 | 117 | 99 | 237 | 61 | 130 |
N.S. |
1 | 4.90 | 3.80 | 1.83 | 10.97 | 3.90 | 3.30 | 7.90 | 2.03 | 4.33 |
time (sec) |
N/A | 1.303 | 2.200 | 1.611 | 0.093 | 0.088 | 0.307 | 0.130 | 0.166 | 3.611 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | A | F(-2) | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 321 | 28 | 59 | 54 | 29 | 0 | 82 | 33 |
N.S. |
1 | 0.00 | 12.35 | 1.08 | 2.27 | 2.08 | 1.12 | 0.00 | 3.15 | 1.27 |
time (sec) |
N/A | 0.000 | 27.703 | 0.375 | 0.083 | 0.092 | 0.077 | 0.000 | 0.172 | 3.427 |
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 | 28 | 0 | 29 | 26 | 26 | 27 | 20 | 0 | 43 | 28 |
N.S. |
1 | 0.00 | 1.04 | 0.93 | 0.93 | 0.96 | 0.71 | 0.00 | 1.54 | 1.00 |
time (sec) |
N/A | 0.000 | 0.945 | 0.336 | 0.182 | 0.095 | 0.133 | 0.000 | 0.175 | 3.183 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 29 | 26 | 23 | 29 | 24 | 0 | 0 | 796 | 24 |
N.S. |
1 | 1.04 | 0.93 | 0.82 | 1.04 | 0.86 | 0.00 | 0.00 | 28.43 | 0.86 |
time (sec) |
N/A | 4.466 | 0.143 | 0.034 | 0.184 | 0.104 | 0.000 | 0.000 | 0.320 | 3.552 |