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 | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 72 | 39 | 34 | 52 | 51 | 452 | 112 | 58 | 48 |
N.S. |
1 | 1.09 | 0.59 | 0.52 | 0.79 | 0.77 | 6.85 | 1.70 | 0.88 | 0.73 |
time (sec) |
N/A | 0.155 | 0.103 | 0.098 | 0.221 | 0.232 | 2.710 | 0.320 | 0.003 | 0.448 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 106 | 82 | 160 | 94 | 215 | 971 | 221 | 150 | 0 |
N.S. |
1 | 1.12 | 0.86 | 1.68 | 0.99 | 2.26 | 10.22 | 2.33 | 1.58 | 0.00 |
time (sec) |
N/A | 0.180 | 0.274 | 0.112 | 0.304 | 0.238 | 6.749 | 15.713 | 0.004 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 78 | 70 | 0 | 52 | 188 | 833 | 194 | 104 | 0 |
N.S. |
1 | 1.08 | 0.97 | 0.00 | 0.72 | 2.61 | 11.57 | 2.69 | 1.44 | 0.00 |
time (sec) |
N/A | 0.161 | 0.203 | 0.000 | 0.296 | 0.236 | 2.491 | 16.018 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 17 | 16 | 34 | 95 | 102 | 59 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.73 | 1.55 | 4.32 | 4.64 | 2.68 | 1.68 |
time (sec) |
N/A | 0.127 | 0.023 | 0.091 | 0.203 | 0.229 | 1.060 | 0.321 | 0.002 | 0.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 30 | 25 | 30 | 44 | 197 | 96 | 67 | 56 |
N.S. |
1 | 1.00 | 0.67 | 0.56 | 0.67 | 0.98 | 4.38 | 2.13 | 1.49 | 1.24 |
time (sec) |
N/A | 0.137 | 0.081 | 0.095 | 0.194 | 0.234 | 1.198 | 0.290 | 0.002 | 0.424 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 71 | 41 | 36 | 50 | 59 | 314 | 189 | 80 | 73 |
N.S. |
1 | 1.06 | 0.61 | 0.54 | 0.75 | 0.88 | 4.69 | 2.82 | 1.19 | 1.09 |
time (sec) |
N/A | 0.153 | 0.143 | 0.107 | 0.205 | 0.221 | 2.175 | 0.305 | 0.002 | 0.544 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 100 | 50 | 45 | 68 | 70 | 688 | 207 | 98 | 92 |
N.S. |
1 | 1.14 | 0.57 | 0.51 | 0.77 | 0.80 | 7.82 | 2.35 | 1.11 | 1.05 |
time (sec) |
N/A | 0.169 | 0.152 | 0.110 | 0.200 | 0.231 | 5.768 | 0.300 | 0.003 | 0.648 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 101 | 74 | 63 | 134 | 124 | 95 | 90 | 69 | 0 |
N.S. |
1 | 1.15 | 0.84 | 0.72 | 1.52 | 1.41 | 1.08 | 1.02 | 0.78 | 0.00 |
time (sec) |
N/A | 0.175 | 0.210 | 0.097 | 0.286 | 0.234 | 10.960 | 6.169 | 0.001 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 72 | 65 | 55 | 102 | 105 | 75 | 67 | 52 | 0 |
N.S. |
1 | 1.07 | 0.97 | 0.82 | 1.52 | 1.57 | 1.12 | 1.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.156 | 0.156 | 0.090 | 0.290 | 0.239 | 3.301 | 5.848 | 0.002 | 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 | 43 | 43 | 57 | 49 | 70 | 87 | 54 | 61 | 37 | 43 |
N.S. |
1 | 1.00 | 1.33 | 1.14 | 1.63 | 2.02 | 1.26 | 1.42 | 0.86 | 1.00 |
time (sec) |
N/A | 0.145 | 0.106 | 0.087 | 0.281 | 0.229 | 1.323 | 6.168 | 0.000 | 0.616 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 30 | 18 | 41 | 55 | 24 | 37 | 25 | 30 |
N.S. |
1 | 1.00 | 1.25 | 0.75 | 1.71 | 2.29 | 1.00 | 1.54 | 1.04 | 1.25 |
time (sec) |
N/A | 0.129 | 0.032 | 0.085 | 0.309 | 0.229 | 0.685 | 6.163 | 0.001 | 0.035 |
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 | 16 | 16 | 13 | 12 | 12 | 15 | 29 | 20 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 0.75 | 0.94 | 1.81 | 1.25 | 0.75 |
time (sec) |
N/A | 0.121 | 0.015 | 0.086 | 0.210 | 0.218 | 0.465 | 0.296 | 0.002 | 0.312 |
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 | 38 | 38 | 23 | 18 | 26 | 17 | 34 | 42 | 35 | 17 |
N.S. |
1 | 1.00 | 0.61 | 0.47 | 0.68 | 0.45 | 0.89 | 1.11 | 0.92 | 0.45 |
time (sec) |
N/A | 0.134 | 0.049 | 0.093 | 0.219 | 0.226 | 1.002 | 0.313 | 0.001 | 0.300 |
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 | 59 | 62 | 32 | 27 | 41 | 26 | 224 | 55 | 54 | 26 |
N.S. |
1 | 1.05 | 0.54 | 0.46 | 0.69 | 0.44 | 3.80 | 0.93 | 0.92 | 0.44 |
time (sec) |
N/A | 0.143 | 0.056 | 0.088 | 0.214 | 0.226 | 3.869 | 0.301 | 0.003 | 0.401 |
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 | 80 | 86 | 40 | 35 | 56 | 34 | 374 | 68 | 70 | 33 |
N.S. |
1 | 1.08 | 0.50 | 0.44 | 0.70 | 0.42 | 4.68 | 0.85 | 0.88 | 0.41 |
time (sec) |
N/A | 0.160 | 0.062 | 0.090 | 0.213 | 0.221 | 10.024 | 0.303 | 0.003 | 0.366 |
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 | 86 | 97 | 73 | 63 | 119 | 152 | 80 | 119 | 74 | 0 |
N.S. |
1 | 1.13 | 0.85 | 0.73 | 1.38 | 1.77 | 0.93 | 1.38 | 0.86 | 0.00 |
time (sec) |
N/A | 0.177 | 0.217 | 0.104 | 0.280 | 0.236 | 7.175 | 1.563 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 68 | 62 | 55 | 90 | 134 | 58 | 106 | 65 | 0 |
N.S. |
1 | 1.08 | 0.98 | 0.87 | 1.43 | 2.13 | 0.92 | 1.68 | 1.03 | 0.00 |
time (sec) |
N/A | 0.167 | 0.161 | 0.102 | 0.283 | 0.234 | 2.046 | 1.607 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 50 | 48 | 57 | 117 | 41 | 82 | 56 | 0 |
N.S. |
1 | 1.00 | 1.14 | 1.09 | 1.30 | 2.66 | 0.93 | 1.86 | 1.27 | 0.00 |
time (sec) |
N/A | 0.149 | 0.061 | 0.105 | 0.285 | 0.237 | 0.939 | 1.670 | 0.001 | 0.000 |
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 | 15 | 15 | 15 | 12 | 11 | 11 | 15 | 44 | 26 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 0.73 | 1.00 | 2.93 | 1.73 | 0.73 |
time (sec) |
N/A | 0.123 | 0.016 | 0.086 | 0.206 | 0.222 | 0.737 | 0.316 | 0.001 | 0.309 |
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 | 32 | 21 | 18 | 26 | 28 | 34 | 74 | 34 | 17 |
N.S. |
1 | 1.00 | 0.66 | 0.56 | 0.81 | 0.88 | 1.06 | 2.31 | 1.06 | 0.53 |
time (sec) |
N/A | 0.133 | 0.052 | 0.097 | 0.229 | 0.232 | 0.852 | 0.315 | 0.002 | 0.346 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 56 | 32 | 27 | 41 | 39 | 170 | 86 | 48 | 37 |
N.S. |
1 | 1.06 | 0.60 | 0.51 | 0.77 | 0.74 | 3.21 | 1.62 | 0.91 | 0.70 |
time (sec) |
N/A | 0.144 | 0.069 | 0.097 | 0.213 | 0.224 | 2.237 | 0.316 | 0.003 | 0.380 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 80 | 39 | 35 | 56 | 47 | 269 | 107 | 59 | 46 |
N.S. |
1 | 1.08 | 0.53 | 0.47 | 0.76 | 0.64 | 3.64 | 1.45 | 0.80 | 0.62 |
time (sec) |
N/A | 0.158 | 0.076 | 0.098 | 0.216 | 0.226 | 7.714 | 0.312 | 0.002 | 0.389 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 97 | 74 | 63 | 105 | 186 | 308 | 177 | 124 | 0 |
N.S. |
1 | 1.13 | 0.86 | 0.73 | 1.22 | 2.16 | 3.58 | 2.06 | 1.44 | 0.00 |
time (sec) |
N/A | 0.176 | 0.214 | 0.111 | 0.316 | 0.232 | 5.449 | 1.608 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 70 | 58 | 55 | 69 | 171 | 257 | 154 | 92 | 0 |
N.S. |
1 | 1.08 | 0.89 | 0.85 | 1.06 | 2.63 | 3.95 | 2.37 | 1.42 | 0.00 |
time (sec) |
N/A | 0.162 | 0.107 | 0.091 | 0.301 | 0.240 | 2.165 | 1.631 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 13 | 12 | 27 | 27 | 82 | 49 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.72 | 0.67 | 1.50 | 1.50 | 4.56 | 2.72 | 0.67 |
time (sec) |
N/A | 0.124 | 0.018 | 0.089 | 0.213 | 0.222 | 1.192 | 0.307 | 0.002 | 0.423 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 23 | 18 | 24 | 32 | 75 | 79 | 55 | 42 |
N.S. |
1 | 1.00 | 0.62 | 0.49 | 0.65 | 0.86 | 2.03 | 2.14 | 1.49 | 1.14 |
time (sec) |
N/A | 0.131 | 0.053 | 0.090 | 0.203 | 0.225 | 1.006 | 0.284 | 0.001 | 0.379 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 32 | 27 | 40 | 45 | 117 | 145 | 66 | 57 |
N.S. |
1 | 1.00 | 0.58 | 0.49 | 0.73 | 0.82 | 2.13 | 2.64 | 1.20 | 1.04 |
time (sec) |
N/A | 0.142 | 0.069 | 0.099 | 0.189 | 0.228 | 1.936 | 0.323 | 0.002 | 0.378 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 74 | 40 | 35 | 55 | 55 | 257 | 158 | 81 | 71 |
N.S. |
1 | 1.04 | 0.56 | 0.49 | 0.77 | 0.77 | 3.62 | 2.23 | 1.14 | 1.00 |
time (sec) |
N/A | 0.150 | 0.074 | 0.101 | 0.197 | 0.229 | 3.423 | 0.307 | 0.003 | 0.420 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 105 | 76 | 81 | 117 | 125 | 204 | 99 | 75 | 0 |
N.S. |
1 | 1.15 | 0.84 | 0.89 | 1.29 | 1.37 | 2.24 | 1.09 | 0.82 | 0.00 |
time (sec) |
N/A | 0.178 | 0.213 | 0.099 | 0.278 | 0.232 | 10.826 | 5.865 | 0.001 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 75 | 67 | 73 | 85 | 107 | 162 | 74 | 58 | 0 |
N.S. |
1 | 1.09 | 0.97 | 1.06 | 1.23 | 1.55 | 2.35 | 1.07 | 0.84 | 0.00 |
time (sec) |
N/A | 0.157 | 0.160 | 0.089 | 0.273 | 0.233 | 3.641 | 5.916 | 0.001 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 60 | 66 | 52 | 90 | 119 | 69 | 42 | 46 |
N.S. |
1 | 1.00 | 1.33 | 1.47 | 1.16 | 2.00 | 2.64 | 1.53 | 0.93 | 1.02 |
time (sec) |
N/A | 0.143 | 0.102 | 0.092 | 0.291 | 0.230 | 1.670 | 6.103 | 0.001 | 0.577 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 39 | 18 | 21 | 56 | 56 | 43 | 28 | 27 |
N.S. |
1 | 1.00 | 1.62 | 0.75 | 0.88 | 2.33 | 2.33 | 1.79 | 1.17 | 1.12 |
time (sec) |
N/A | 0.133 | 0.052 | 0.085 | 0.285 | 0.232 | 1.009 | 6.145 | 0.000 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 14 | 13 | 13 | 41 | 30 | 22 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 2.41 | 1.76 | 1.29 | 0.76 |
time (sec) |
N/A | 0.122 | 0.016 | 0.089 | 0.201 | 0.221 | 0.591 | 0.313 | 0.002 | 0.353 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 25 | 19 | 28 | 18 | 139 | 43 | 38 | 19 |
N.S. |
1 | 1.00 | 0.62 | 0.48 | 0.70 | 0.45 | 3.48 | 1.08 | 0.95 | 0.48 |
time (sec) |
N/A | 0.135 | 0.056 | 0.099 | 0.208 | 0.224 | 1.033 | 0.287 | 0.002 | 0.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 101 | 75 | 81 | 101 | 155 | 172 | 136 | 82 | 0 |
N.S. |
1 | 1.13 | 0.84 | 0.91 | 1.13 | 1.74 | 1.93 | 1.53 | 0.92 | 0.00 |
time (sec) |
N/A | 0.175 | 0.246 | 0.111 | 0.294 | 0.239 | 5.981 | 1.560 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 71 | 65 | 73 | 71 | 138 | 126 | 119 | 72 | 0 |
N.S. |
1 | 1.09 | 1.00 | 1.12 | 1.09 | 2.12 | 1.94 | 1.83 | 1.11 | 0.00 |
time (sec) |
N/A | 0.162 | 0.193 | 0.105 | 0.291 | 0.237 | 2.112 | 1.614 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 60 | 67 | 38 | 122 | 90 | 92 | 62 | 0 |
N.S. |
1 | 1.00 | 1.33 | 1.49 | 0.84 | 2.71 | 2.00 | 2.04 | 1.38 | 0.00 |
time (sec) |
N/A | 0.146 | 0.130 | 0.094 | 0.288 | 0.233 | 1.674 | 1.530 | 0.001 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 12 | 20 | 41 | 50 | 30 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 0.75 | 1.25 | 2.56 | 3.12 | 1.88 | 0.75 |
time (sec) |
N/A | 0.124 | 0.019 | 0.093 | 0.204 | 0.219 | 0.568 | 0.285 | 0.001 | 0.298 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 21 | 18 | 28 | 29 | 90 | 83 | 36 | 27 |
N.S. |
1 | 1.00 | 0.62 | 0.53 | 0.82 | 0.85 | 2.65 | 2.44 | 1.06 | 0.79 |
time (sec) |
N/A | 0.133 | 0.088 | 0.102 | 0.199 | 0.225 | 1.605 | 0.284 | 0.002 | 0.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 59 | 33 | 28 | 44 | 40 | 355 | 96 | 51 | 38 |
N.S. |
1 | 1.05 | 0.59 | 0.50 | 0.79 | 0.71 | 6.34 | 1.71 | 0.91 | 0.68 |
time (sec) |
N/A | 0.143 | 0.101 | 0.103 | 0.202 | 0.220 | 2.872 | 0.289 | 0.002 | 0.372 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 101 | 76 | 81 | 86 | 187 | 751 | 200 | 137 | 0 |
N.S. |
1 | 1.13 | 0.85 | 0.91 | 0.97 | 2.10 | 8.44 | 2.25 | 1.54 | 0.00 |
time (sec) |
N/A | 0.169 | 0.241 | 0.120 | 0.302 | 0.245 | 5.999 | 1.523 | 0.003 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 73 | 68 | 73 | 50 | 173 | 648 | 178 | 101 | 0 |
N.S. |
1 | 1.09 | 1.01 | 1.09 | 0.75 | 2.58 | 9.67 | 2.66 | 1.51 | 0.00 |
time (sec) |
N/A | 0.155 | 0.191 | 0.098 | 0.303 | 0.239 | 2.949 | 1.530 | 0.002 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 14 | 13 | 28 | 63 | 95 | 55 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.68 | 1.47 | 3.32 | 5.00 | 2.89 | 0.68 |
time (sec) |
N/A | 0.122 | 0.109 | 0.247 | 0.203 | 0.227 | 1.020 | 0.297 | 0.002 | 0.272 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 24 | 19 | 25 | 33 | 165 | 90 | 59 | 45 |
N.S. |
1 | 1.00 | 0.62 | 0.49 | 0.64 | 0.85 | 4.23 | 2.31 | 1.51 | 1.15 |
time (sec) |
N/A | 0.129 | 0.115 | 0.085 | 0.207 | 0.236 | 1.696 | 0.290 | 0.001 | 0.539 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 33 | 28 | 42 | 46 | 245 | 170 | 71 | 59 |
N.S. |
1 | 1.00 | 0.57 | 0.48 | 0.72 | 0.79 | 4.22 | 2.93 | 1.22 | 1.02 |
time (sec) |
N/A | 0.141 | 0.136 | 0.109 | 0.212 | 0.225 | 2.193 | 0.297 | 0.003 | 0.392 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 78 | 41 | 36 | 58 | 56 | 530 | 183 | 84 | 73 |
N.S. |
1 | 1.04 | 0.55 | 0.48 | 0.77 | 0.75 | 7.07 | 2.44 | 1.12 | 0.97 |
time (sec) |
N/A | 0.149 | 0.147 | 0.110 | 0.221 | 0.234 | 5.561 | 0.447 | 0.002 | 0.453 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 35 | 34 | 37 | 27 | 54 | 17 | 26 | 31 |
N.S. |
1 | 1.00 | 1.30 | 1.26 | 1.37 | 1.00 | 2.00 | 0.63 | 0.96 | 1.15 |
time (sec) |
N/A | 0.139 | 0.056 | 0.119 | 0.291 | 0.230 | 1.020 | 0.371 | 0.002 | 0.593 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | B | B | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 40 | 7 | 14 | 14 | 20 | 6 | 15 | 16 |
N.S. |
1 | 1.00 | 5.00 | 0.88 | 1.75 | 1.75 | 2.50 | 0.75 | 1.88 | 2.00 |
time (sec) |
N/A | 0.132 | 0.007 | 0.095 | 0.284 | 0.232 | 0.652 | 0.275 | 0.000 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 33 | 14 | 21 | 57 | 42 | 41 | 23 | 23 |
N.S. |
1 | 1.00 | 1.74 | 0.74 | 1.11 | 3.00 | 2.21 | 2.16 | 1.21 | 1.21 |
time (sec) |
N/A | 0.127 | 0.050 | 0.106 | 0.292 | 0.220 | 0.677 | 5.684 | 0.001 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 17 | 14 | 13 | 18 | 19 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 0.81 | 0.67 | 0.62 | 0.86 | 0.90 | 0.62 | 0.62 | 0.62 |
time (sec) |
N/A | 0.134 | 0.010 | 0.082 | 0.200 | 0.216 | 0.433 | 0.279 | 0.000 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 17 | 14 | 13 | 18 | 19 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 0.81 | 0.67 | 0.62 | 0.86 | 0.90 | 0.62 | 0.62 | 0.62 |
time (sec) |
N/A | 0.136 | 0.010 | 0.076 | 0.202 | 0.224 | 0.301 | 0.278 | 0.000 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 17 | 14 | 13 | 16 | 19 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 0.81 | 0.67 | 0.62 | 0.76 | 0.90 | 0.62 | 0.62 | 0.62 |
time (sec) |
N/A | 0.136 | 0.010 | 0.075 | 0.201 | 0.213 | 0.109 | 0.293 | 0.000 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 17 | 14 | 13 | 16 | 19 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 0.81 | 0.67 | 0.62 | 0.76 | 0.90 | 0.62 | 0.62 | 0.62 |
time (sec) |
N/A | 0.138 | 0.010 | 0.076 | 0.198 | 0.219 | 0.588 | 0.283 | 0.001 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 17 | 13 | 13 | 13 | 19 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 0.81 | 0.62 | 0.62 | 0.62 | 0.90 | 0.62 | 0.62 | 0.62 |
time (sec) |
N/A | 0.134 | 0.010 | 0.025 | 0.198 | 0.216 | 0.676 | 0.287 | 0.000 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 16 | 13 | 13 | 12 | 17 | 13 | 12 | 12 |
N.S. |
1 | 1.00 | 0.84 | 0.68 | 0.68 | 0.63 | 0.89 | 0.68 | 0.63 | 0.63 |
time (sec) |
N/A | 0.137 | 0.010 | 0.025 | 0.211 | 0.219 | 0.505 | 0.290 | 0.000 | 0.027 |
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 | 19 | 17 | 14 | 13 | 12 | 17 | 13 | 12 | 13 |
N.S. |
1 | 1.00 | 0.89 | 0.74 | 0.68 | 0.63 | 0.89 | 0.68 | 0.63 | 0.68 |
time (sec) |
N/A | 0.139 | 0.012 | 0.033 | 0.208 | 0.219 | 0.160 | 0.311 | 0.000 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 15 | 12 | 13 | 13 | 17 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 0.79 | 0.63 | 0.68 | 0.68 | 0.89 | 0.68 | 0.68 | 0.68 |
time (sec) |
N/A | 0.138 | 0.012 | 0.033 | 0.201 | 0.215 | 0.186 | 0.303 | 0.000 | 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 | 36 | 36 | 28 | 25 | 24 | 29 | 34 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 0.78 | 0.69 | 0.67 | 0.81 | 0.94 | 0.67 | 0.67 | 0.67 |
time (sec) |
N/A | 0.151 | 0.014 | 0.088 | 0.201 | 0.211 | 0.602 | 0.302 | 0.001 | 0.049 |
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 | 36 | 36 | 28 | 25 | 24 | 29 | 34 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 0.78 | 0.69 | 0.67 | 0.81 | 0.94 | 0.67 | 0.67 | 0.67 |
time (sec) |
N/A | 0.153 | 0.013 | 0.088 | 0.200 | 0.219 | 0.395 | 0.273 | 0.000 | 0.173 |
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 | 36 | 36 | 28 | 25 | 24 | 27 | 34 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 0.78 | 0.69 | 0.67 | 0.75 | 0.94 | 0.67 | 0.67 | 0.67 |
time (sec) |
N/A | 0.155 | 0.013 | 0.083 | 0.215 | 0.223 | 0.474 | 0.276 | 0.000 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 28 | 25 | 24 | 27 | 2633 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 0.78 | 0.69 | 0.67 | 0.75 | 73.14 | 0.67 | 0.67 | 0.67 |
time (sec) |
N/A | 0.156 | 0.013 | 0.088 | 0.196 | 0.228 | 1.567 | 0.283 | 0.000 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 28 | 24 | 24 | 24 | 1765 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 0.78 | 0.67 | 0.67 | 0.67 | 49.03 | 0.67 | 0.67 | 0.67 |
time (sec) |
N/A | 0.154 | 0.013 | 0.083 | 0.198 | 0.220 | 1.710 | 0.286 | 0.000 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 28 | 24 | 24 | 24 | 1741 | 24 | 24 | 24 |
N.S. |
1 | 1.00 | 0.82 | 0.71 | 0.71 | 0.71 | 51.21 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.150 | 0.013 | 0.082 | 0.200 | 0.220 | 1.466 | 0.286 | 0.001 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 28 | 25 | 24 | 23 | 1826 | 24 | 23 | 24 |
N.S. |
1 | 1.00 | 0.88 | 0.78 | 0.75 | 0.72 | 57.06 | 0.75 | 0.72 | 0.75 |
time (sec) |
N/A | 0.153 | 0.016 | 0.086 | 0.218 | 0.215 | 1.251 | 0.315 | 0.000 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 28 | 25 | 24 | 23 | 1957 | 24 | 23 | 24 |
N.S. |
1 | 1.00 | 0.82 | 0.74 | 0.71 | 0.68 | 57.56 | 0.71 | 0.68 | 0.71 |
time (sec) |
N/A | 0.154 | 0.020 | 0.085 | 0.212 | 0.214 | 1.388 | 0.301 | 0.000 | 0.037 |
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 | 51 | 51 | 39 | 36 | 35 | 40 | 49 | 35 | 35 | 35 |
N.S. |
1 | 1.00 | 0.76 | 0.71 | 0.69 | 0.78 | 0.96 | 0.69 | 0.69 | 0.69 |
time (sec) |
N/A | 0.161 | 0.016 | 0.103 | 0.206 | 0.227 | 0.702 | 0.284 | 0.001 | 0.046 |
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 | 51 | 51 | 39 | 36 | 35 | 40 | 49 | 35 | 35 | 35 |
N.S. |
1 | 1.00 | 0.76 | 0.71 | 0.69 | 0.78 | 0.96 | 0.69 | 0.69 | 0.69 |
time (sec) |
N/A | 0.158 | 0.016 | 0.088 | 0.205 | 0.213 | 0.452 | 0.315 | 0.000 | 0.044 |
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 | 51 | 51 | 39 | 36 | 35 | 38 | 49 | 35 | 35 | 35 |
N.S. |
1 | 1.00 | 0.76 | 0.71 | 0.69 | 0.75 | 0.96 | 0.69 | 0.69 | 0.69 |
time (sec) |
N/A | 0.161 | 0.015 | 0.084 | 0.222 | 0.226 | 0.533 | 0.278 | 0.000 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 39 | 36 | 35 | 38 | 5012 | 35 | 35 | 35 |
N.S. |
1 | 1.00 | 0.76 | 0.71 | 0.69 | 0.75 | 98.27 | 0.69 | 0.69 | 0.69 |
time (sec) |
N/A | 0.161 | 0.016 | 0.083 | 0.203 | 0.226 | 2.314 | 0.280 | 0.000 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 39 | 35 | 35 | 35 | 6246 | 35 | 35 | 35 |
N.S. |
1 | 1.00 | 0.76 | 0.69 | 0.69 | 0.69 | 122.47 | 0.69 | 0.69 | 0.69 |
time (sec) |
N/A | 0.165 | 0.016 | 0.087 | 0.207 | 0.216 | 2.302 | 0.276 | 0.001 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 39 | 35 | 35 | 35 | 6667 | 35 | 35 | 35 |
N.S. |
1 | 1.00 | 0.80 | 0.71 | 0.71 | 0.71 | 136.06 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.162 | 0.015 | 0.085 | 0.210 | 0.217 | 2.111 | 0.297 | 0.000 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 39 | 36 | 35 | 35 | 4004 | 35 | 35 | 35 |
N.S. |
1 | 1.00 | 0.80 | 0.73 | 0.71 | 0.71 | 81.71 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.163 | 0.017 | 0.086 | 0.204 | 0.228 | 2.218 | 0.320 | 0.000 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 39 | 36 | 35 | 35 | 3964 | 35 | 35 | 35 |
N.S. |
1 | 1.00 | 0.80 | 0.73 | 0.71 | 0.71 | 80.90 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.166 | 0.019 | 0.085 | 0.204 | 0.224 | 2.571 | 0.289 | 0.001 | 0.048 |
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 | 125 | 134 | 140 | 121 | 130 | 147 | 180 | 138 | 104 | 151 |
N.S. |
1 | 1.07 | 1.12 | 0.97 | 1.04 | 1.18 | 1.44 | 1.10 | 0.83 | 1.21 |
time (sec) |
N/A | 0.224 | 0.089 | 0.110 | 0.294 | 0.224 | 58.035 | 0.298 | 0.002 | 0.255 |
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 | 123 | 132 | 140 | 123 | 128 | 116 | 173 | 136 | 96 | 126 |
N.S. |
1 | 1.07 | 1.14 | 1.00 | 1.04 | 0.94 | 1.41 | 1.11 | 0.78 | 1.02 |
time (sec) |
N/A | 0.225 | 0.073 | 0.157 | 0.286 | 0.229 | 26.344 | 0.306 | 0.002 | 0.071 |
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 | 111 | 115 | 127 | 107 | 114 | 128 | 162 | 118 | 87 | 130 |
N.S. |
1 | 1.04 | 1.14 | 0.96 | 1.03 | 1.15 | 1.46 | 1.06 | 0.78 | 1.17 |
time (sec) |
N/A | 0.205 | 0.066 | 0.101 | 0.279 | 0.227 | 5.637 | 0.301 | 0.002 | 0.162 |
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 | 109 | 113 | 126 | 112 | 115 | 114 | 148 | 119 | 86 | 126 |
N.S. |
1 | 1.04 | 1.16 | 1.03 | 1.06 | 1.05 | 1.36 | 1.09 | 0.79 | 1.16 |
time (sec) |
N/A | 0.208 | 0.065 | 0.142 | 0.308 | 0.227 | 2.626 | 0.299 | 0.002 | 0.077 |
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 | 100 | 96 | 103 | 96 | 103 | 313 | 141 | 118 | 71 | 120 |
N.S. |
1 | 0.96 | 1.03 | 0.96 | 1.03 | 3.13 | 1.41 | 1.18 | 0.71 | 1.20 |
time (sec) |
N/A | 0.191 | 0.052 | 0.096 | 0.293 | 0.231 | 3.066 | 0.315 | 0.002 | 0.144 |
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 | 100 | 96 | 103 | 95 | 102 | 307 | 141 | 117 | 73 | 110 |
N.S. |
1 | 0.96 | 1.03 | 0.95 | 1.02 | 3.07 | 1.41 | 1.17 | 0.73 | 1.10 |
time (sec) |
N/A | 0.193 | 0.057 | 0.097 | 0.307 | 0.235 | 8.879 | 0.291 | 0.001 | 0.301 |
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 | 109 | 113 | 127 | 104 | 111 | 113 | 151 | 125 | 96 | 124 |
N.S. |
1 | 1.04 | 1.17 | 0.95 | 1.02 | 1.04 | 1.39 | 1.15 | 0.88 | 1.14 |
time (sec) |
N/A | 0.200 | 0.082 | 0.107 | 0.298 | 0.225 | 31.338 | 0.291 | 0.003 | 0.160 |
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 | 111 | 115 | 126 | 112 | 112 | 147 | 155 | 120 | 102 | 138 |
N.S. |
1 | 1.04 | 1.14 | 1.01 | 1.01 | 1.32 | 1.40 | 1.08 | 0.92 | 1.24 |
time (sec) |
N/A | 0.204 | 0.085 | 0.148 | 0.307 | 0.226 | 52.375 | 0.286 | 0.003 | 0.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 140 | 142 | 124 | 133 | 162 | 0 | 135 | 184 | 150 |
N.S. |
1 | 1.09 | 1.10 | 0.96 | 1.03 | 1.26 | 0.00 | 1.05 | 1.43 | 1.16 |
time (sec) |
N/A | 0.218 | 0.185 | 0.119 | 0.290 | 0.232 | 0.000 | 0.293 | 0.003 | 0.255 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 138 | 142 | 124 | 133 | 147 | 0 | 135 | 182 | 142 |
N.S. |
1 | 1.10 | 1.14 | 0.99 | 1.06 | 1.18 | 0.00 | 1.08 | 1.46 | 1.14 |
time (sec) |
N/A | 0.220 | 0.179 | 0.204 | 0.296 | 0.230 | 0.000 | 0.326 | 0.005 | 0.167 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 121 | 133 | 118 | 120 | 394 | 527 | 136 | 162 | 142 |
N.S. |
1 | 1.05 | 1.16 | 1.03 | 1.04 | 3.43 | 4.58 | 1.18 | 1.41 | 1.23 |
time (sec) |
N/A | 0.201 | 0.153 | 0.273 | 0.300 | 0.244 | 135.939 | 0.300 | 0.003 | 0.254 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 121 | 134 | 117 | 120 | 389 | 450 | 136 | 177 | 120 |
N.S. |
1 | 1.03 | 1.15 | 1.00 | 1.03 | 3.32 | 3.85 | 1.16 | 1.51 | 1.03 |
time (sec) |
N/A | 0.201 | 0.151 | 0.092 | 0.293 | 0.243 | 80.886 | 0.287 | 0.004 | 0.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 120 | 133 | 116 | 127 | 396 | 544 | 132 | 162 | 144 |
N.S. |
1 | 1.03 | 1.15 | 1.00 | 1.09 | 3.41 | 4.69 | 1.14 | 1.40 | 1.24 |
time (sec) |
N/A | 0.203 | 0.149 | 0.101 | 0.294 | 0.231 | 83.732 | 0.297 | 0.003 | 0.358 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 120 | 134 | 117 | 127 | 387 | 434 | 132 | 177 | 134 |
N.S. |
1 | 1.06 | 1.19 | 1.04 | 1.12 | 3.42 | 3.84 | 1.17 | 1.57 | 1.19 |
time (sec) |
N/A | 0.206 | 0.143 | 0.101 | 0.292 | 0.235 | 151.969 | 0.291 | 0.005 | 0.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 137 | 142 | 121 | 132 | 156 | 0 | 145 | 197 | 151 |
N.S. |
1 | 1.10 | 1.15 | 0.98 | 1.06 | 1.26 | 0.00 | 1.17 | 1.59 | 1.22 |
time (sec) |
N/A | 0.218 | 0.191 | 0.121 | 0.291 | 0.244 | 0.000 | 0.280 | 0.004 | 0.173 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 139 | 142 | 124 | 132 | 189 | 0 | 137 | 210 | 166 |
N.S. |
1 | 1.09 | 1.11 | 0.97 | 1.03 | 1.48 | 0.00 | 1.07 | 1.64 | 1.30 |
time (sec) |
N/A | 0.221 | 0.202 | 0.200 | 0.330 | 0.233 | 0.000 | 0.297 | 0.006 | 0.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 148 | 142 | 130 | 143 | 506 | 0 | 146 | 277 | 165 |
N.S. |
1 | 1.06 | 1.01 | 0.93 | 1.02 | 3.61 | 0.00 | 1.04 | 1.98 | 1.18 |
time (sec) |
N/A | 0.217 | 0.215 | 0.098 | 0.290 | 0.240 | 0.000 | 0.297 | 0.005 | 0.197 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 148 | 142 | 130 | 143 | 503 | 0 | 146 | 290 | 139 |
N.S. |
1 | 1.06 | 1.01 | 0.93 | 1.02 | 3.59 | 0.00 | 1.04 | 2.07 | 0.99 |
time (sec) |
N/A | 0.218 | 0.217 | 0.099 | 0.301 | 0.241 | 0.000 | 0.285 | 0.006 | 0.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 147 | 133 | 132 | 153 | 508 | 0 | 149 | 275 | 172 |
N.S. |
1 | 1.03 | 0.93 | 0.92 | 1.07 | 3.55 | 0.00 | 1.04 | 1.92 | 1.20 |
time (sec) |
N/A | 0.216 | 0.206 | 0.103 | 0.284 | 0.246 | 0.000 | 0.287 | 0.006 | 0.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 143 | 147 | 136 | 132 | 152 | 501 | 0 | 148 | 290 | 146 |
N.S. |
1 | 1.03 | 0.95 | 0.92 | 1.06 | 3.50 | 0.00 | 1.03 | 2.03 | 1.02 |
time (sec) |
N/A | 0.231 | 0.192 | 0.108 | 0.285 | 0.243 | 0.000 | 0.293 | 0.006 | 0.258 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 147 | 142 | 139 | 151 | 510 | 0 | 143 | 277 | 167 |
N.S. |
1 | 1.05 | 1.01 | 0.99 | 1.08 | 3.64 | 0.00 | 1.02 | 1.98 | 1.19 |
time (sec) |
N/A | 0.220 | 0.155 | 0.104 | 0.294 | 0.251 | 0.000 | 0.294 | 0.006 | 0.198 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 147 | 142 | 139 | 151 | 499 | 0 | 143 | 290 | 157 |
N.S. |
1 | 1.05 | 1.01 | 0.99 | 1.08 | 3.56 | 0.00 | 1.02 | 2.07 | 1.12 |
time (sec) |
N/A | 0.217 | 0.143 | 0.106 | 0.289 | 0.236 | 0.000 | 0.286 | 0.006 | 0.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 164 | 153 | 133 | 154 | 211 | 0 | 155 | 310 | 174 |
N.S. |
1 | 1.08 | 1.01 | 0.88 | 1.01 | 1.39 | 0.00 | 1.02 | 2.04 | 1.14 |
time (sec) |
N/A | 0.230 | 0.247 | 0.131 | 0.298 | 0.229 | 0.000 | 0.289 | 0.006 | 0.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 166 | 153 | 133 | 154 | 244 | 0 | 150 | 323 | 182 |
N.S. |
1 | 1.09 | 1.01 | 0.88 | 1.01 | 1.61 | 0.00 | 0.99 | 2.12 | 1.20 |
time (sec) |
N/A | 0.233 | 0.259 | 0.149 | 0.287 | 0.244 | 0.000 | 0.289 | 0.007 | 0.182 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | C | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 65 | 58 | 60 | 61 | 83 | 243 | 64 | 63 | 46 |
N.S. |
1 | 1.12 | 1.00 | 1.03 | 1.05 | 1.43 | 4.19 | 1.10 | 1.09 | 0.79 |
time (sec) |
N/A | 0.166 | 0.061 | 1.338 | 0.282 | 0.226 | 2.905 | 0.313 | 0.000 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 187 | 187 | 166 | 1534 | 187 | 1277 | 9996 | 1925 | 1533 | 1274 |
N.S. |
1 | 1.00 | 0.89 | 8.20 | 1.00 | 6.83 | 53.45 | 10.29 | 8.20 | 6.81 |
time (sec) |
N/A | 0.312 | 0.192 | 0.212 | 0.208 | 0.237 | 1.929 | 0.305 | 0.001 | 1.500 |
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 | 133 | 133 | 118 | 156 | 133 | 665 | 4257 | 992 | 780 | 683 |
N.S. |
1 | 1.00 | 0.89 | 1.17 | 1.00 | 5.00 | 32.01 | 7.46 | 5.86 | 5.14 |
time (sec) |
N/A | 0.257 | 0.082 | 0.147 | 0.240 | 0.230 | 1.060 | 0.292 | 0.001 | 1.002 |