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 | B | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 31 | 8 | 7 | 61 | 10 | 5 | 6 | 6 | 6 |
N.S. |
1 | 3.88 | 1.00 | 0.88 | 7.62 | 1.25 | 0.62 | 0.75 | 0.75 | 0.75 |
time (sec) |
N/A | 0.371 | 0.022 | 0.085 | 0.025 | 0.068 | 0.144 | 0.111 | 0.154 | 0.034 |
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 | 26 | 73 | 23 | 23 | 165 | 28 | 41 | 52 | 22 | 39 |
N.S. |
1 | 2.81 | 0.88 | 0.88 | 6.35 | 1.08 | 1.58 | 2.00 | 0.85 | 1.50 |
time (sec) |
N/A | 0.496 | 0.166 | 0.365 | 0.033 | 0.070 | 0.514 | 0.154 | 0.154 | 15.980 |
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 | 44 | 49 | 22 | 17 | 26 | 33 | 32 | 57 | 17 | 35 |
N.S. |
1 | 1.11 | 0.50 | 0.39 | 0.59 | 0.75 | 0.73 | 1.30 | 0.39 | 0.80 |
time (sec) |
N/A | 0.214 | 0.063 | 0.109 | 0.110 | 0.074 | 0.177 | 0.139 | 0.154 | 15.978 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 49 | 22 | 17 | 26 | 33 | 0 | 57 | 17 | 16 |
N.S. |
1 | 1.11 | 0.50 | 0.39 | 0.59 | 0.75 | 0.00 | 1.30 | 0.39 | 0.36 |
time (sec) |
N/A | 0.283 | 0.014 | 0.227 | 0.107 | 0.074 | 0.000 | 0.204 | 0.151 | 15.873 |
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 | 48 | 22 | 22 | 17 | 16 | 43 | 246 | 57 | 55 | 35 |
N.S. |
1 | 0.46 | 0.46 | 0.35 | 0.33 | 0.90 | 5.12 | 1.19 | 1.15 | 0.73 |
time (sec) |
N/A | 0.174 | 0.195 | 0.134 | 0.106 | 0.075 | 3.901 | 0.142 | 0.202 | 15.864 |
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 | 50 | 22 | 22 | 17 | 16 | 43 | 246 | 57 | 55 | 35 |
N.S. |
1 | 0.44 | 0.44 | 0.34 | 0.32 | 0.86 | 4.92 | 1.14 | 1.10 | 0.70 |
time (sec) |
N/A | 0.183 | 0.720 | 0.113 | 0.103 | 0.074 | 3.273 | 0.135 | 0.156 | 15.582 |
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 | 48 | 22 | 22 | 17 | 16 | 43 | 246 | 57 | 23 | 35 |
N.S. |
1 | 0.46 | 0.46 | 0.35 | 0.33 | 0.90 | 5.12 | 1.19 | 0.48 | 0.73 |
time (sec) |
N/A | 0.192 | 0.020 | 0.153 | 0.105 | 0.082 | 3.320 | 0.185 | 0.155 | 15.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 22 | 22 | 17 | 16 | 43 | 0 | 16 | 55 | 16 |
N.S. |
1 | 0.46 | 0.46 | 0.35 | 0.33 | 0.90 | 0.00 | 0.33 | 1.15 | 0.33 |
time (sec) |
N/A | 0.213 | 0.007 | 0.382 | 0.105 | 0.077 | 0.000 | 0.831 | 0.157 | 16.161 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 22 | 22 | 17 | 16 | 43 | 0 | 57 | 55 | 16 |
N.S. |
1 | 0.46 | 0.46 | 0.35 | 0.33 | 0.90 | 0.00 | 1.19 | 1.15 | 0.33 |
time (sec) |
N/A | 0.206 | 0.008 | 0.228 | 0.102 | 0.082 | 0.000 | 0.297 | 0.160 | 16.057 |
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 | 60 | 22 | 22 | 17 | 54 | 74 | 42 | 39 | 33 | 16 |
N.S. |
1 | 0.37 | 0.37 | 0.28 | 0.90 | 1.23 | 0.70 | 0.65 | 0.55 | 0.27 |
time (sec) |
N/A | 0.175 | 0.091 | 0.105 | 0.107 | 0.072 | 0.170 | 0.133 | 0.153 | 16.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 22 | 22 | 17 | 54 | 74 | 0 | 39 | 33 | 16 |
N.S. |
1 | 0.37 | 0.37 | 0.28 | 0.90 | 1.23 | 0.00 | 0.65 | 0.55 | 0.27 |
time (sec) |
N/A | 0.251 | 0.062 | 0.221 | 0.103 | 0.074 | 0.000 | 0.188 | 0.154 | 15.429 |
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 | 22 | 22 | 22 | 17 | 34 | 86 | 1644 | 39 | 54 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 1.55 | 3.91 | 74.73 | 1.77 | 2.45 | 0.73 |
time (sec) |
N/A | 0.178 | 0.380 | 0.125 | 0.103 | 0.073 | 8.492 | 0.136 | 0.155 | 15.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 17 | 34 | 86 | 1644 | 39 | 54 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 1.55 | 3.91 | 74.73 | 1.77 | 2.45 | 0.73 |
time (sec) |
N/A | 0.179 | 0.985 | 0.104 | 0.114 | 0.075 | 8.425 | 0.186 | 0.155 | 15.855 |
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 | 60 | 22 | 22 | 17 | 34 | 86 | 1644 | 39 | 54 | 16 |
N.S. |
1 | 0.37 | 0.37 | 0.28 | 0.57 | 1.43 | 27.40 | 0.65 | 0.90 | 0.27 |
time (sec) |
N/A | 0.201 | 0.017 | 0.153 | 0.103 | 0.078 | 8.501 | 0.174 | 0.156 | 15.912 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 22 | 22 | 17 | 34 | 86 | 0 | 39 | 54 | 16 |
N.S. |
1 | 0.37 | 0.37 | 0.28 | 0.57 | 1.43 | 0.00 | 0.65 | 0.90 | 0.27 |
time (sec) |
N/A | 0.206 | 0.008 | 0.375 | 0.109 | 0.078 | 0.000 | 1.057 | 0.190 | 15.919 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 22 | 22 | 17 | 34 | 86 | 0 | 39 | 54 | 16 |
N.S. |
1 | 0.37 | 0.37 | 0.28 | 0.57 | 1.43 | 0.00 | 0.65 | 0.90 | 0.27 |
time (sec) |
N/A | 0.211 | 0.015 | 0.230 | 0.105 | 0.082 | 0.000 | 0.286 | 0.150 | 15.559 |
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 | 42 | 47 | 22 | 18 | 27 | 31 | 34 | 57 | 16 | 36 |
N.S. |
1 | 1.12 | 0.52 | 0.43 | 0.64 | 0.74 | 0.81 | 1.36 | 0.38 | 0.86 |
time (sec) |
N/A | 0.202 | 0.055 | 0.086 | 0.106 | 0.074 | 0.135 | 0.107 | 0.150 | 16.758 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 47 | 22 | 18 | 27 | 31 | 0 | 57 | 16 | 17 |
N.S. |
1 | 1.12 | 0.52 | 0.43 | 0.64 | 0.74 | 0.00 | 1.36 | 0.38 | 0.40 |
time (sec) |
N/A | 0.243 | 0.011 | 0.211 | 0.113 | 0.083 | 0.000 | 0.157 | 0.149 | 16.577 |
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 | 50 | 22 | 22 | 18 | 17 | 43 | 76 | 57 | 41 | 36 |
N.S. |
1 | 0.44 | 0.44 | 0.36 | 0.34 | 0.86 | 1.52 | 1.14 | 0.82 | 0.72 |
time (sec) |
N/A | 0.174 | 0.008 | 0.117 | 0.108 | 0.076 | 0.292 | 0.129 | 0.152 | 16.263 |
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 | 48 | 22 | 22 | 18 | 17 | 43 | 76 | 57 | 41 | 36 |
N.S. |
1 | 0.46 | 0.46 | 0.38 | 0.35 | 0.90 | 1.58 | 1.19 | 0.85 | 0.75 |
time (sec) |
N/A | 0.177 | 0.193 | 0.100 | 0.103 | 0.079 | 0.288 | 0.155 | 0.152 | 16.316 |
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 | 48 | 22 | 22 | 18 | 17 | 43 | 76 | 57 | 23 | 36 |
N.S. |
1 | 0.46 | 0.46 | 0.38 | 0.35 | 0.90 | 1.58 | 1.19 | 0.48 | 0.75 |
time (sec) |
N/A | 0.192 | 0.009 | 0.154 | 0.104 | 0.079 | 0.334 | 0.127 | 0.151 | 17.248 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 22 | 22 | 18 | 17 | 43 | 0 | 17 | 41 | 17 |
N.S. |
1 | 0.46 | 0.46 | 0.38 | 0.35 | 0.90 | 0.00 | 0.35 | 0.85 | 0.35 |
time (sec) |
N/A | 0.203 | 0.007 | 0.356 | 0.112 | 0.089 | 0.000 | 0.650 | 0.156 | 16.147 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 22 | 22 | 18 | 17 | 43 | 0 | 57 | 41 | 17 |
N.S. |
1 | 0.46 | 0.46 | 0.38 | 0.35 | 0.90 | 0.00 | 1.19 | 0.85 | 0.35 |
time (sec) |
N/A | 0.209 | 0.007 | 0.230 | 0.104 | 0.085 | 0.000 | 0.275 | 0.154 | 15.716 |
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 | 61 | 22 | 22 | 18 | 53 | 74 | 39 | 39 | 29 | 17 |
N.S. |
1 | 0.36 | 0.36 | 0.30 | 0.87 | 1.21 | 0.64 | 0.64 | 0.48 | 0.28 |
time (sec) |
N/A | 0.176 | 0.061 | 0.092 | 0.105 | 0.075 | 0.155 | 0.141 | 0.155 | 15.794 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 22 | 22 | 18 | 53 | 74 | 0 | 39 | 29 | 17 |
N.S. |
1 | 0.36 | 0.36 | 0.30 | 0.87 | 1.21 | 0.00 | 0.64 | 0.48 | 0.28 |
time (sec) |
N/A | 0.247 | 0.014 | 0.212 | 0.113 | 0.081 | 0.000 | 0.219 | 0.155 | 16.224 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 18 | 32 | 85 | 1481 | 39 | 59 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 1.45 | 3.86 | 67.32 | 1.77 | 2.68 | 0.77 |
time (sec) |
N/A | 0.179 | 1.129 | 0.129 | 0.105 | 0.074 | 7.182 | 0.153 | 0.153 | 15.072 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 18 | 32 | 85 | 1481 | 39 | 59 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 1.45 | 3.86 | 67.32 | 1.77 | 2.68 | 0.77 |
time (sec) |
N/A | 0.180 | 0.514 | 0.108 | 0.104 | 0.076 | 6.876 | 0.137 | 0.154 | 15.166 |
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 | 61 | 22 | 22 | 18 | 32 | 85 | 1481 | 39 | 59 | 17 |
N.S. |
1 | 0.36 | 0.36 | 0.30 | 0.52 | 1.39 | 24.28 | 0.64 | 0.97 | 0.28 |
time (sec) |
N/A | 0.196 | 0.024 | 0.160 | 0.187 | 0.074 | 6.563 | 0.208 | 0.160 | 15.859 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 22 | 22 | 18 | 32 | 85 | 0 | 37 | 59 | 17 |
N.S. |
1 | 0.36 | 0.36 | 0.30 | 0.52 | 1.39 | 0.00 | 0.61 | 0.97 | 0.28 |
time (sec) |
N/A | 0.209 | 0.007 | 0.364 | 0.100 | 0.080 | 0.000 | 0.668 | 0.154 | 15.755 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 22 | 22 | 18 | 32 | 85 | 0 | 39 | 59 | 17 |
N.S. |
1 | 0.36 | 0.36 | 0.30 | 0.52 | 1.39 | 0.00 | 0.64 | 0.97 | 0.28 |
time (sec) |
N/A | 0.210 | 0.020 | 0.241 | 0.108 | 0.075 | 0.000 | 0.277 | 0.156 | 15.788 |
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 | 30 | 30 | 25 | 24 | 22 | 41 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.73 | 1.37 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.200 | 0.042 | 4.485 | 0.035 | 0.074 | 0.095 | 0.156 | 0.163 | 15.844 |
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 | 56 | 56 | 48 | 57 | 48 | 46 | 85 | 46 | 49 | 46 |
N.S. |
1 | 1.00 | 0.86 | 1.02 | 0.86 | 0.82 | 1.52 | 0.82 | 0.88 | 0.82 |
time (sec) |
N/A | 0.249 | 0.057 | 0.089 | 0.029 | 0.072 | 0.093 | 0.115 | 0.153 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 213 | 163 | 233 | 0 | 187 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 0.77 | 1.09 | 0.00 | 0.88 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.646 | 0.740 | 0.322 | 0.000 | 0.086 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 271 | 245 | 328 | 0 | 434 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.21 | 0.00 | 1.60 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.953 | 1.257 | 0.521 | 0.000 | 0.096 | 0.000 | 0.000 | 0.155 | 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 | 10 | 10 | 10 | 9 | 8 | 8 | 10 | 8 | 7 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.80 | 0.80 | 1.00 | 0.80 | 0.70 | 0.80 |
time (sec) |
N/A | 0.206 | 0.026 | 0.119 | 0.028 | 0.073 | 0.109 | 0.144 | 0.149 | 15.891 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 46 | 72 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 1.64 | 2.57 | 0.00 | 0.00 | 0.00 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.613 | 0.571 | 0.247 | 0.000 | 0.000 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 26 | 12 | 17 | 22 | 10 | 11 | 16 | 11 |
N.S. |
1 | 1.00 | 2.17 | 1.00 | 1.42 | 1.83 | 0.83 | 0.92 | 1.33 | 0.92 |
time (sec) |
N/A | 0.199 | 0.034 | 0.124 | 0.029 | 0.067 | 0.574 | 0.116 | 0.157 | 16.690 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 108 | 324 | 142 | 0 | 104 | 0 | 630 | 929 | 0 |
N.S. |
1 | 1.08 | 3.24 | 1.42 | 0.00 | 1.04 | 0.00 | 6.30 | 9.29 | 0.00 |
time (sec) |
N/A | 0.597 | 0.755 | 0.422 | 0.000 | 0.080 | 0.000 | 3.508 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 115 | 495 | 195 | 0 | 113 | 0 | 681 | 18 | 0 |
N.S. |
1 | 1.07 | 4.63 | 1.82 | 0.00 | 1.06 | 0.00 | 6.36 | 0.17 | 0.00 |
time (sec) |
N/A | 0.596 | 3.682 | 0.648 | 0.000 | 0.081 | 0.000 | 25.739 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 180 | 845 | 295 | 0 | 212 | 0 | 1239 | 18 | 0 |
N.S. |
1 | 0.93 | 4.36 | 1.52 | 0.00 | 1.09 | 0.00 | 6.39 | 0.09 | 0.00 |
time (sec) |
N/A | 0.512 | 7.750 | 1.257 | 0.000 | 0.095 | 0.000 | 68.948 | 5.991 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 57 | 53 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 0.98 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.342 | 0.327 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 57 | 57 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 0.98 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.311 | 0.223 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 0 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.256 | 0.117 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 36 | 30 | 33 | 32 | 29 | 32 | 33 | 35 |
N.S. |
1 | 1.00 | 1.06 | 0.88 | 0.97 | 0.94 | 0.85 | 0.94 | 0.97 | 1.03 |
time (sec) |
N/A | 0.267 | 3.241 | 0.085 | 0.167 | 0.077 | 3.788 | 0.224 | 0.213 | 15.635 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 38 | 32 | 696 | 34 | 31 | 34 | 35 | 35 |
N.S. |
1 | 1.00 | 1.06 | 0.89 | 19.33 | 0.94 | 0.86 | 0.94 | 0.97 | 0.97 |
time (sec) |
N/A | 0.300 | 19.247 | 0.097 | 0.229 | 0.089 | 3.606 | 0.215 | 2.064 | 15.486 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 26 | 25 | 24 | 23 | 41 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 0.87 | 0.83 | 0.80 | 0.77 | 1.37 | 0.80 | 0.80 | 0.80 |
time (sec) |
N/A | 0.203 | 0.050 | 4.248 | 0.028 | 0.076 | 0.072 | 0.121 | 0.161 | 15.860 |
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 | 56 | 56 | 51 | 57 | 46 | 44 | 85 | 46 | 47 | 48 |
N.S. |
1 | 1.00 | 0.91 | 1.02 | 0.82 | 0.79 | 1.52 | 0.82 | 0.84 | 0.86 |
time (sec) |
N/A | 0.247 | 0.080 | 0.090 | 0.028 | 0.072 | 0.091 | 0.121 | 0.168 | 0.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 213 | 213 | 164 | 231 | 0 | 189 | 0 | 0 | 61 | 0 |
N.S. |
1 | 1.00 | 0.77 | 1.08 | 0.00 | 0.89 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.536 | 0.524 | 0.299 | 0.000 | 0.086 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 271 | 271 | 243 | 326 | 0 | 436 | 0 | 0 | 136 | 0 |
N.S. |
1 | 1.00 | 0.90 | 1.20 | 0.00 | 1.61 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.833 | 0.664 | 0.462 | 0.000 | 0.096 | 0.000 | 0.000 | 0.176 | 0.000 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 27 | 10 | 9 | 8 | 8 | 8 | 8 | 25 | 8 |
N.S. |
1 | 2.70 | 1.00 | 0.90 | 0.80 | 0.80 | 0.80 | 0.80 | 2.50 | 0.80 |
time (sec) |
N/A | 0.340 | 0.030 | 0.103 | 0.028 | 0.065 | 0.152 | 0.119 | 0.167 | 15.938 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 38 | 22 | 18 | 17 | 37 | 20 | 17 | 37 | 15 |
N.S. |
1 | 1.73 | 1.00 | 0.82 | 0.77 | 1.68 | 0.91 | 0.77 | 1.68 | 0.68 |
time (sec) |
N/A | 0.391 | 0.043 | 0.120 | 0.100 | 0.069 | 0.211 | 0.106 | 0.168 | 15.694 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 36 | 20 | 16 | 16 | 15 | 15 | 19 | 70 | 16 |
N.S. |
1 | 1.50 | 0.83 | 0.67 | 0.67 | 0.62 | 0.62 | 0.79 | 2.92 | 0.67 |
time (sec) |
N/A | 0.660 | 0.693 | 0.508 | 0.023 | 0.072 | 2.110 | 0.105 | 0.164 | 15.752 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 108 | 319 | 142 | 0 | 105 | 0 | 633 | 984 | 0 |
N.S. |
1 | 1.07 | 3.16 | 1.41 | 0.00 | 1.04 | 0.00 | 6.27 | 9.74 | 0.00 |
time (sec) |
N/A | 0.583 | 0.754 | 0.367 | 0.000 | 0.080 | 0.000 | 5.226 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 114 | 497 | 195 | 0 | 109 | 0 | 683 | 18 | 0 |
N.S. |
1 | 1.07 | 4.64 | 1.82 | 0.00 | 1.02 | 0.00 | 6.38 | 0.17 | 0.00 |
time (sec) |
N/A | 0.604 | 3.591 | 0.619 | 0.000 | 0.086 | 0.000 | 27.162 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 57 | 53 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 0.98 | 0.91 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.334 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.379 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 57 | 51 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 0.98 | 0.88 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.315 | 0.028 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 0 | 0 | 0 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.264 | 0.007 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 36 | 30 | 33 | 32 | 29 | 32 | 33 | 35 |
N.S. |
1 | 1.00 | 1.06 | 0.88 | 0.97 | 0.94 | 0.85 | 0.94 | 0.97 | 1.03 |
time (sec) |
N/A | 0.274 | 3.011 | 0.078 | 0.247 | 0.075 | 5.296 | 0.254 | 0.210 | 15.645 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 38 | 32 | 420 | 34 | 31 | 34 | 35 | 35 |
N.S. |
1 | 1.00 | 1.06 | 0.89 | 11.67 | 0.94 | 0.86 | 0.94 | 0.97 | 0.97 |
time (sec) |
N/A | 0.304 | 12.434 | 0.096 | 0.229 | 0.080 | 5.505 | 0.202 | 0.226 | 17.341 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 8 | 7 | 13 | 10 | 8 | 8 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.78 | 1.44 | 1.11 | 0.89 | 0.89 | 2.11 |
time (sec) |
N/A | 0.191 | 0.011 | 0.040 | 0.025 | 0.075 | 0.085 | 0.127 | 0.165 | 18.145 |
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 | 18 | 15 | 12 | 12 | 14 | 12 | 10 | 20 |
N.S. |
1 | 1.00 | 1.12 | 0.94 | 0.75 | 0.75 | 0.88 | 0.75 | 0.62 | 1.25 |
time (sec) |
N/A | 0.201 | 0.027 | 0.074 | 0.110 | 0.077 | 0.079 | 0.130 | 0.204 | 17.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 90 | 70 | 0 | 80 | 0 | 0 | 0 | 8 | 0 |
N.S. |
1 | 1.29 | 1.00 | 0.00 | 1.14 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.432 | 0.016 | 0.000 | 0.125 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 18 | 18 | 83 | 23 | 0 | 18 | 21 | 21 |
N.S. |
1 | 1.00 | 0.95 | 0.95 | 4.37 | 1.21 | 0.00 | 0.95 | 1.11 | 1.11 |
time (sec) |
N/A | 0.164 | 0.691 | 0.172 | 0.079 | 0.074 | 0.000 | 3.750 | 0.169 | 0.359 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 18 | 26 | 16 | 14 | 28 | 15 | 22 | 10 | 20 |
N.S. |
1 | 1.12 | 1.62 | 1.00 | 0.88 | 1.75 | 0.94 | 1.38 | 0.62 | 1.25 |
time (sec) |
N/A | 0.209 | 0.035 | 0.082 | 0.109 | 0.077 | 0.086 | 0.132 | 0.169 | 16.895 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 85 | 120 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.30 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.405 | 5.623 | 4.071 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 33 | 35 | 43 | 6257 | 72 | 0 | 66 | 110 | 29 |
N.S. |
1 | 0.94 | 1.00 | 1.23 | 178.77 | 2.06 | 0.00 | 1.89 | 3.14 | 0.83 |
time (sec) |
N/A | 0.212 | 0.030 | 0.235 | 81.744 | 0.084 | 0.000 | 0.159 | 0.172 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 33 | 35 | 43 | 6257 | 72 | 0 | 66 | 110 | 29 |
N.S. |
1 | 0.94 | 1.00 | 1.23 | 178.77 | 2.06 | 0.00 | 1.89 | 3.14 | 0.83 |
time (sec) |
N/A | 0.216 | 0.002 | 0.172 | 81.523 | 0.088 | 0.000 | 0.123 | 0.172 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 50 | 57 | 22 | 0 | 0 | 9 | 20 |
N.S. |
1 | 1.00 | 1.00 | 3.85 | 4.38 | 1.69 | 0.00 | 0.00 | 0.69 | 1.54 |
time (sec) |
N/A | 0.238 | 0.095 | 0.890 | 0.126 | 0.076 | 0.000 | 0.000 | 0.207 | 15.710 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 55 | 23 | 150 | 57 | 26 | 0 | 0 | 13 | 0 |
N.S. |
1 | 1.77 | 0.74 | 4.84 | 1.84 | 0.84 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.319 | 0.061 | 1.067 | 0.122 | 0.074 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 76 | 29 | 165 | 82 | 38 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.52 | 0.58 | 3.30 | 1.64 | 0.76 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.401 | 0.108 | 1.657 | 0.121 | 0.078 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 188 | 19 | 0 | 12 | 9 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 14.46 | 1.46 | 0.00 | 0.92 | 0.69 | 1.38 |
time (sec) |
N/A | 0.244 | 0.080 | 0.441 | 0.170 | 0.072 | 0.000 | 0.129 | 0.166 | 16.609 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 55 | 21 | 17 | 314 | 23 | 0 | 19 | 13 | 0 |
N.S. |
1 | 1.77 | 0.68 | 0.55 | 10.13 | 0.74 | 0.00 | 0.61 | 0.42 | 0.00 |
time (sec) |
N/A | 0.346 | 0.061 | 0.527 | 0.181 | 0.076 | 0.000 | 0.126 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 76 | 29 | 29 | 427 | 35 | 0 | 27 | 17 | 0 |
N.S. |
1 | 1.52 | 0.58 | 0.58 | 8.54 | 0.70 | 0.00 | 0.54 | 0.34 | 0.00 |
time (sec) |
N/A | 0.414 | 0.110 | 3.421 | 0.193 | 0.083 | 0.000 | 0.119 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 64 | 56 | 159 | 0 | 236 | 0 | 0 | 114 | 0 |
N.S. |
1 | 1.10 | 0.97 | 2.74 | 0.00 | 4.07 | 0.00 | 0.00 | 1.97 | 0.00 |
time (sec) |
N/A | 0.275 | 0.109 | 0.209 | 0.000 | 0.092 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | B | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 95 | 84 | 257 | 0 | 459 | 0 | 0 | 321 | 0 |
N.S. |
1 | 1.12 | 0.99 | 3.02 | 0.00 | 5.40 | 0.00 | 0.00 | 3.78 | 0.00 |
time (sec) |
N/A | 0.385 | 0.202 | 0.345 | 0.000 | 0.095 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | A | F(-1) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 58 | 154 | 0 | 227 | 0 | 0 | 126 | 132 |
N.S. |
1 | 1.00 | 0.98 | 2.61 | 0.00 | 3.85 | 0.00 | 0.00 | 2.14 | 2.24 |
time (sec) |
N/A | 0.268 | 0.079 | 0.158 | 0.000 | 0.095 | 0.000 | 0.000 | 0.157 | 17.248 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | B | F(-1) | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 103 | 85 | 250 | 0 | 417 | 0 | 0 | 275 | 0 |
N.S. |
1 | 1.17 | 0.97 | 2.84 | 0.00 | 4.74 | 0.00 | 0.00 | 3.12 | 0.00 |
time (sec) |
N/A | 0.360 | 0.238 | 0.271 | 0.000 | 0.100 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 53 | 48 | 86 | 250 | 80 | 0 | 322 | 1206 | 0 |
N.S. |
1 | 1.06 | 0.96 | 1.72 | 5.00 | 1.60 | 0.00 | 6.44 | 24.12 | 0.00 |
time (sec) |
N/A | 0.364 | 0.149 | 1.097 | 0.046 | 0.090 | 0.000 | 0.269 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 54 | 48 | 87 | 250 | 81 | 0 | 322 | 118 | 0 |
N.S. |
1 | 1.08 | 0.96 | 1.74 | 5.00 | 1.62 | 0.00 | 6.44 | 2.36 | 0.00 |
time (sec) |
N/A | 0.364 | 0.139 | 0.435 | 0.046 | 0.082 | 0.000 | 0.213 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 32 | 24 | 23 | 205 | 0 | 23 | 68 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.75 | 0.72 | 6.41 | 0.00 | 0.72 | 2.12 | 0.75 |
time (sec) |
N/A | 0.224 | 0.413 | 0.729 | 0.108 | 0.090 | 0.000 | 0.153 | 0.171 | 16.660 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 211 | 241 | 512 | 1003 | 0 | 3284 | 0 | 0 | 93 | 0 |
N.S. |
1 | 1.14 | 2.43 | 4.75 | 0.00 | 15.56 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.923 | 1.893 | 0.827 | 0.000 | 3.277 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 337 | 349 | 294 | 1251 | 0 | 4568 | 0 | 0 | 97 | 0 |
N.S. |
1 | 1.04 | 0.87 | 3.71 | 0.00 | 13.55 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.407 | 0.897 | 0.841 | 0.000 | 1.995 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 40 | 34 | 43 | 300 | 0 | 53 | 35 | 45 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 1.08 | 7.50 | 0.00 | 1.32 | 0.88 | 1.12 |
time (sec) |
N/A | 0.650 | 0.804 | 0.765 | 0.111 | 0.116 | 0.000 | 0.224 | 0.217 | 15.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 267 | 289 | 751 | 1670 | 0 | 4100 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.08 | 2.81 | 6.25 | 0.00 | 15.36 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.122 | 3.907 | 0.929 | 0.000 | 3.974 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 407 | 417 | 314 | 2061 | 0 | 5696 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.02 | 0.77 | 5.06 | 0.00 | 14.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 1.590 | 1.643 | 0.897 | 0.000 | 3.003 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | F | B | F | F | F | F(-1) |
verified |
N/A | N/A | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 0 | 1037 | 928 | 0 | 393 | 0 | 0 | 16 | 0 |
N.S. |
1 | 0.00 | 5.26 | 4.71 | 0.00 | 1.99 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.000 | 0.763 | 0.262 | 0.000 | 0.146 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 97 | 61 | 0 | 0 | 0 | 0 | 156 | 31 | 111 |
N.S. |
1 | 0.63 | 0.39 | 0.00 | 0.00 | 0.00 | 0.00 | 1.01 | 0.20 | 0.72 |
time (sec) |
N/A | 0.648 | 2.807 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 0.168 | 16.532 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 78 | 54 | 0 | 0 | 0 | 0 | 119 | 31 | 86 |
N.S. |
1 | 0.66 | 0.46 | 0.00 | 0.00 | 0.00 | 0.00 | 1.01 | 0.26 | 0.73 |
time (sec) |
N/A | 0.509 | 1.324 | 0.000 | 0.000 | 0.000 | 0.000 | 0.149 | 0.165 | 15.822 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 58 | 44 | 0 | 0 | 0 | 0 | 82 | 29 | 61 |
N.S. |
1 | 0.78 | 0.59 | 0.00 | 0.00 | 0.00 | 0.00 | 1.11 | 0.39 | 0.82 |
time (sec) |
N/A | 0.383 | 0.681 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.165 | 17.484 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 52 | 52 | 0 | 0 | 0 | 0 | 274 | 31 | 0 |
N.S. |
1 | 0.60 | 0.60 | 0.00 | 0.00 | 0.00 | 0.00 | 3.19 | 0.36 | 0.00 |
time (sec) |
N/A | 0.502 | 0.680 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 66 | 65 | 0 | 0 | 0 | 0 | 886 | 85 | 0 |
N.S. |
1 | 0.54 | 0.53 | 0.00 | 0.00 | 0.00 | 0.00 | 7.20 | 0.69 | 0.00 |
time (sec) |
N/A | 0.583 | 0.848 | 0.000 | 0.000 | 0.000 | 0.000 | 0.275 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 85 | 87 | 0 | 0 | 0 | 0 | 1022 | 31 | 0 |
N.S. |
1 | 0.48 | 0.49 | 0.00 | 0.00 | 0.00 | 0.00 | 5.81 | 0.18 | 0.00 |
time (sec) |
N/A | 0.687 | 0.897 | 0.000 | 0.000 | 0.000 | 0.000 | 0.324 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F(-1) | B | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 393 | 206 | 113 | 0 | 0 | 0 | 0 | 1487 | 65 | 216 |
N.S. |
1 | 0.52 | 0.29 | 0.00 | 0.00 | 0.00 | 0.00 | 3.78 | 0.17 | 0.55 |
time (sec) |
N/A | 0.655 | 1.270 | 0.000 | 0.000 | 0.000 | 0.000 | 0.446 | 0.186 | 17.936 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | B | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 265 | 151 | 95 | 0 | 0 | 0 | 0 | 739 | 65 | 159 |
N.S. |
1 | 0.57 | 0.36 | 0.00 | 0.00 | 0.00 | 0.00 | 2.79 | 0.25 | 0.60 |
time (sec) |
N/A | 0.553 | 0.967 | 0.000 | 0.000 | 0.000 | 0.000 | 0.316 | 0.189 | 17.371 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | B | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 115 | 73 | 0 | 0 | 0 | 0 | 311 | 61 | 123 |
N.S. |
1 | 0.68 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 1.85 | 0.36 | 0.73 |
time (sec) |
N/A | 0.413 | 0.799 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 0.180 | 16.356 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-2) | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 186 | 79 | 150 | 0 | 0 | 0 | 0 | 160 | 65 | 0 |
N.S. |
1 | 0.42 | 0.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.86 | 0.35 | 0.00 |
time (sec) |
N/A | 0.838 | 2.397 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-2) | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 273 | 106 | 231 | 0 | 0 | 0 | 0 | 608 | 160 | 0 |
N.S. |
1 | 0.39 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 2.23 | 0.59 | 0.00 |
time (sec) |
N/A | 0.865 | 2.623 | 0.000 | 0.000 | 0.000 | 0.000 | 0.224 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-2) | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 385 | 152 | 317 | 0 | 0 | 0 | 0 | 1502 | 65 | 0 |
N.S. |
1 | 0.39 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 3.90 | 0.17 | 0.00 |
time (sec) |
N/A | 0.943 | 2.876 | 0.000 | 0.000 | 0.000 | 0.000 | 0.329 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 767 | 372 | 247 | 0 | 0 | 0 | 0 | 0 | 168 | 0 |
N.S. |
1 | 0.49 | 0.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.401 | 2.732 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 555 | 268 | 194 | 0 | 0 | 0 | 0 | 0 | 124 | 0 |
N.S. |
1 | 0.48 | 0.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 1.088 | 2.439 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |