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 | C | C | F | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 4 | 4 | 36 | 27 | 0 | 34 | 61 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 9.00 | 6.75 | 0.00 | 8.50 | 15.25 | 0.00 | 5.00 | 0.00 |
time (sec) |
N/A | 0.227 | 10.019 | 0.723 | 0.000 | 0.081 | 0.651 | 0.000 | 0.236 | 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 | 4 | 4 | 4 | 70 | 0 | 34 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 1.00 | 17.50 | 0.00 | 8.50 | 0.00 | 0.00 | 5.00 | 0.00 |
time (sec) |
N/A | 0.220 | 10.158 | 1.087 | 0.000 | 0.085 | 0.000 | 0.000 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 4 | 4 | 4 | 5 | 0 | 41 | 10 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.25 | 0.00 | 10.25 | 2.50 | 0.00 | 6.50 | 0.00 |
time (sec) |
N/A | 0.207 | 0.416 | 0.995 | 0.000 | 0.076 | 1.020 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 47 | 38 | 0 | 65 | 71 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 4.70 | 3.80 | 0.00 | 6.50 | 7.10 | 0.00 | 2.70 | 0.00 |
time (sec) |
N/A | 0.240 | 10.031 | 1.874 | 0.000 | 0.076 | 0.786 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 31 | 118 | 0 | 65 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 3.10 | 11.80 | 0.00 | 6.50 | 0.00 | 0.00 | 2.70 | 0.00 |
time (sec) |
N/A | 0.239 | 10.235 | 2.497 | 0.000 | 0.075 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 15 | 0 | 76 | 0 | 0 | 37 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 0.00 | 7.60 | 0.00 | 0.00 | 3.70 | 0.00 |
time (sec) |
N/A | 0.205 | 0.659 | 2.282 | 0.000 | 0.075 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 87 | 138 | 0 | 90 | 78 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 1.47 | 2.34 | 0.00 | 1.53 | 1.32 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.334 | 10.054 | 2.232 | 0.000 | 0.081 | 0.880 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 78 | 67 | 138 | 0 | 90 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.32 | 1.14 | 2.34 | 0.00 | 1.53 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.343 | 10.202 | 1.230 | 0.000 | 0.078 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 141 | 95 | 188 | 0 | 110 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.47 | 0.99 | 1.96 | 0.00 | 1.15 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.427 | 10.282 | 1.278 | 0.000 | 0.083 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 0 | 112 | 188 | 0 | 110 | 83 | 0 | 47 | 0 |
N.S. |
1 | 0.00 | 1.18 | 1.98 | 0.00 | 1.16 | 0.87 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.000 | 10.208 | 2.276 | 0.000 | 0.084 | 2.733 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 36 | 27 | 0 | 23 | 61 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 2.77 | 2.08 | 0.00 | 1.77 | 4.69 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 0.276 | 10.038 | 0.903 | 0.000 | 0.077 | 0.691 | 0.000 | 0.180 | 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 | 13 | 13 | 13 | 69 | 0 | 23 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 1.00 | 5.31 | 0.00 | 1.77 | 0.00 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 0.279 | 10.114 | 0.491 | 0.000 | 0.084 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 12 | 14 | 0 | 31 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.08 | 0.00 | 2.38 | 0.00 | 0.00 | 1.85 | 0.00 |
time (sec) |
N/A | 0.263 | 0.423 | 0.398 | 0.000 | 0.078 | 0.000 | 0.000 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 47 | 38 | 0 | 62 | 71 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 2.04 | 1.65 | 0.00 | 2.70 | 3.09 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.312 | 10.030 | 2.285 | 0.000 | 0.085 | 0.825 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 52 | 117 | 0 | 62 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 2.26 | 5.09 | 0.00 | 2.70 | 0.00 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.299 | 10.244 | 1.070 | 0.000 | 0.076 | 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 | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 24 | 28 | 0 | 73 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 1.04 | 1.22 | 0.00 | 3.17 | 0.00 | 0.00 | 1.52 | 0.00 |
time (sec) |
N/A | 0.276 | 0.712 | 0.770 | 0.000 | 0.078 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 90 | 88 | 137 | 0 | 91 | 78 | 0 | 25 | 0 |
N.S. |
1 | 0.74 | 0.73 | 1.13 | 0.00 | 0.75 | 0.64 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.420 | 10.046 | 2.181 | 0.000 | 0.080 | 0.854 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 175 | 89 | 137 | 0 | 91 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.45 | 0.74 | 1.13 | 0.00 | 0.75 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.506 | 10.263 | 1.213 | 0.000 | 0.075 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 214 | 135 | 191 | 0 | 113 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.37 | 0.87 | 1.22 | 0.00 | 0.72 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.574 | 10.256 | 1.277 | 0.000 | 0.086 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 0 | 112 | 191 | 0 | 113 | 83 | 0 | 47 | 0 |
N.S. |
1 | 0.00 | 0.73 | 1.25 | 0.00 | 0.74 | 0.54 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.000 | 10.067 | 2.225 | 0.000 | 0.080 | 2.254 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 51 | 42 | 0 | 116 | 75 | 54 | 71 | 42 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.00 | 2.27 | 1.47 | 1.06 | 1.39 | 0.82 |
time (sec) |
N/A | 0.323 | 0.026 | 0.161 | 0.000 | 0.080 | 0.090 | 0.106 | 0.171 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 38 | 31 | 0 | 90 | 58 | 42 | 56 | 28 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.00 | 2.37 | 1.53 | 1.11 | 1.47 | 0.74 |
time (sec) |
N/A | 0.306 | 0.020 | 0.149 | 0.000 | 0.081 | 0.084 | 0.103 | 0.169 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 22 | 0 | 73 | 34 | 23 | 43 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.76 | 0.00 | 2.52 | 1.17 | 0.79 | 1.48 | 0.72 |
time (sec) |
N/A | 0.274 | 0.011 | 0.145 | 0.000 | 0.082 | 0.071 | 0.102 | 0.174 | 17.485 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 16 | 0 | 68 | 46 | 18 | 38 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.00 | 2.83 | 1.92 | 0.75 | 1.58 | 0.67 |
time (sec) |
N/A | 0.253 | 0.006 | 0.136 | 0.000 | 0.075 | 0.063 | 0.102 | 0.166 | 17.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 75 | 65 | 54 | 0 | 189 | 226 | 56 | 142 | 74 |
N.S. |
1 | 1.04 | 0.90 | 0.75 | 0.00 | 2.62 | 3.14 | 0.78 | 1.97 | 1.03 |
time (sec) |
N/A | 0.351 | 0.041 | 0.282 | 0.000 | 0.089 | 0.206 | 0.109 | 0.162 | 17.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 101 | 76 | 64 | 0 | 278 | 257 | 66 | 244 | 96 |
N.S. |
1 | 1.13 | 0.85 | 0.72 | 0.00 | 3.12 | 2.89 | 0.74 | 2.74 | 1.08 |
time (sec) |
N/A | 0.408 | 0.064 | 0.303 | 0.000 | 0.088 | 0.288 | 0.105 | 0.177 | 0.176 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 70 | 50 | 0 | 199 | 0 | 109 | 153 | 0 |
N.S. |
1 | 1.00 | 1.13 | 0.81 | 0.00 | 3.21 | 0.00 | 1.76 | 2.47 | 0.00 |
time (sec) |
N/A | 0.363 | 0.124 | 1.025 | 0.000 | 0.092 | 0.000 | 0.141 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 50 | 33 | 0 | 138 | 0 | 82 | 127 | 0 |
N.S. |
1 | 1.00 | 1.32 | 0.87 | 0.00 | 3.63 | 0.00 | 2.16 | 3.34 | 0.00 |
time (sec) |
N/A | 0.278 | 0.083 | 0.837 | 0.000 | 0.087 | 0.000 | 0.120 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 69 | 47 | 0 | 209 | 0 | 101 | 327 | 0 |
N.S. |
1 | 1.00 | 1.13 | 0.77 | 0.00 | 3.43 | 0.00 | 1.66 | 5.36 | 0.00 |
time (sec) |
N/A | 0.312 | 0.132 | 0.848 | 0.000 | 0.087 | 0.000 | 0.143 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 88 | 80 | 69 | 0 | 279 | 0 | 113 | 542 | 0 |
N.S. |
1 | 1.10 | 1.00 | 0.86 | 0.00 | 3.49 | 0.00 | 1.41 | 6.78 | 0.00 |
time (sec) |
N/A | 0.375 | 0.178 | 0.611 | 0.000 | 0.094 | 0.000 | 0.130 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 234 | 71 | 124 | 0 | 92 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.58 | 0.48 | 0.84 | 0.00 | 0.62 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.718 | 10.045 | 4.000 | 0.000 | 0.077 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 234 | 134 | 124 | 0 | 92 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.55 | 0.89 | 0.82 | 0.00 | 0.61 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.711 | 10.360 | 1.711 | 0.000 | 0.082 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 234 | 134 | 124 | 0 | 92 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.55 | 0.89 | 0.82 | 0.00 | 0.61 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.739 | 10.180 | 2.754 | 0.000 | 0.086 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 306 | 143 | 194 | 0 | 148 | 184 | 0 | 159 | 0 |
N.S. |
1 | 1.49 | 0.70 | 0.95 | 0.00 | 0.72 | 0.90 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.801 | 8.424 | 7.879 | 0.000 | 0.079 | 1.759 | 0.000 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 277 | 122 | 183 | 0 | 137 | 133 | 0 | 135 | 0 |
N.S. |
1 | 1.56 | 0.69 | 1.03 | 0.00 | 0.77 | 0.75 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.752 | 7.570 | 5.599 | 0.000 | 0.085 | 1.379 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 0 | 87 | 172 | 0 | 126 | 85 | 0 | 111 | 0 |
N.S. |
1 | 0.00 | 0.56 | 1.10 | 0.00 | 0.81 | 0.54 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.000 | 6.817 | 3.735 | 0.000 | 0.082 | 1.032 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 86 | 82 | 0 | 54 | 39 | 0 | 52 | 46 |
N.S. |
1 | 1.00 | 1.02 | 0.98 | 0.00 | 0.64 | 0.46 | 0.00 | 0.62 | 0.55 |
time (sec) |
N/A | 0.315 | 5.135 | 0.940 | 0.000 | 0.079 | 0.463 | 0.000 | 0.186 | 17.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 175 | 89 | 137 | 0 | 91 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.45 | 0.74 | 1.13 | 0.00 | 0.75 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.501 | 0.042 | 1.290 | 0.000 | 0.079 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 233 | 100 | 121 | 0 | 85 | 0 | 0 | 36 | 0 |
N.S. |
1 | 3.28 | 1.41 | 1.70 | 0.00 | 1.20 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.700 | 10.528 | 1.793 | 0.000 | 0.085 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 253 | 172 | 222 | 0 | 166 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.32 | 0.90 | 1.16 | 0.00 | 0.87 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.685 | 10.679 | 2.408 | 0.000 | 0.085 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 287 | 187 | 256 | 0 | 225 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.28 | 0.83 | 1.14 | 0.00 | 1.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.767 | 10.823 | 3.160 | 0.000 | 0.083 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 257 | 331 | 152 | 290 | 0 | 280 | 0 | 0 | 69 | 0 |
N.S. |
1 | 1.29 | 0.59 | 1.13 | 0.00 | 1.09 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.859 | 11.087 | 4.122 | 0.000 | 0.095 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 374 | 135 | 216 | 0 | 169 | 279 | 0 | 207 | 0 |
N.S. |
1 | 1.56 | 0.56 | 0.90 | 0.00 | 0.71 | 1.17 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.987 | 10.160 | 7.943 | 0.000 | 0.081 | 2.591 | 0.000 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 341 | 126 | 205 | 0 | 158 | 180 | 0 | 183 | 0 |
N.S. |
1 | 1.61 | 0.59 | 0.97 | 0.00 | 0.75 | 0.85 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.901 | 9.714 | 5.613 | 0.000 | 0.084 | 1.814 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 0 | 90 | 194 | 0 | 147 | 180 | 0 | 159 | 0 |
N.S. |
1 | 0.00 | 0.47 | 1.02 | 0.00 | 0.77 | 0.95 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.000 | 8.744 | 3.760 | 0.000 | 0.088 | 1.757 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 113 | 58 | 96 | 0 | 70 | 41 | 0 | 76 | 46 |
N.S. |
1 | 1.05 | 0.54 | 0.89 | 0.00 | 0.65 | 0.38 | 0.00 | 0.70 | 0.43 |
time (sec) |
N/A | 0.365 | 6.081 | 0.950 | 0.000 | 0.078 | 0.501 | 0.000 | 0.199 | 17.417 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 243 | 88 | 172 | 0 | 126 | 85 | 0 | 111 | 0 |
N.S. |
1 | 1.56 | 0.56 | 1.10 | 0.00 | 0.81 | 0.54 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.665 | 6.577 | 3.354 | 0.000 | 0.079 | 1.808 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 209 | 142 | 160 | 0 | 112 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.45 | 0.99 | 1.11 | 0.00 | 0.78 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.584 | 10.480 | 3.780 | 0.000 | 0.093 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 201 | 131 | 181 | 0 | 145 | 0 | 0 | 140 | 0 |
N.S. |
1 | 1.35 | 0.88 | 1.21 | 0.00 | 0.97 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.590 | 10.598 | 2.385 | 0.000 | 0.085 | 0.000 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 138 | 91 | 93 | 0 | 83 | 0 | 0 | 383 | 0 |
N.S. |
1 | 1.48 | 0.98 | 1.00 | 0.00 | 0.89 | 0.00 | 0.00 | 4.12 | 0.00 |
time (sec) |
N/A | 0.435 | 10.824 | 3.178 | 0.000 | 0.083 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 286 | 187 | 253 | 0 | 225 | 0 | 0 | 1023 | 0 |
N.S. |
1 | 1.29 | 0.85 | 1.14 | 0.00 | 1.02 | 0.00 | 0.00 | 4.63 | 0.00 |
time (sec) |
N/A | 0.793 | 11.104 | 4.227 | 0.000 | 0.094 | 0.000 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 254 | 320 | 152 | 287 | 0 | 280 | 0 | 0 | 871 | 0 |
N.S. |
1 | 1.26 | 0.60 | 1.13 | 0.00 | 1.10 | 0.00 | 0.00 | 3.43 | 0.00 |
time (sec) |
N/A | 0.852 | 11.362 | 5.306 | 0.000 | 0.098 | 0.000 | 0.000 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 287 | 359 | 163 | 321 | 0 | 336 | 0 | 0 | 1311 | 0 |
N.S. |
1 | 1.25 | 0.57 | 1.12 | 0.00 | 1.17 | 0.00 | 0.00 | 4.57 | 0.00 |
time (sec) |
N/A | 0.935 | 11.739 | 6.905 | 0.000 | 0.106 | 0.000 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 243 | 141 | 171 | 0 | 124 | 172 | 0 | 111 | 0 |
N.S. |
1 | 1.44 | 0.83 | 1.01 | 0.00 | 0.73 | 1.02 | 0.00 | 0.66 | 0.00 |
time (sec) |
N/A | 0.677 | 10.102 | 7.809 | 0.000 | 0.087 | 1.838 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 209 | 121 | 160 | 0 | 111 | 122 | 0 | 60 | 0 |
N.S. |
1 | 1.45 | 0.84 | 1.11 | 0.00 | 0.77 | 0.85 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.594 | 10.079 | 5.464 | 0.000 | 0.084 | 1.424 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 87 | 138 | 0 | 90 | 78 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 1.47 | 2.34 | 0.00 | 1.53 | 1.32 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.334 | 0.015 | 2.252 | 0.000 | 0.081 | 0.927 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 66 | 60 | 0 | 23 | 37 | 0 | 30 | 46 |
N.S. |
1 | 1.00 | 1.12 | 1.02 | 0.00 | 0.39 | 0.63 | 0.00 | 0.51 | 0.78 |
time (sec) |
N/A | 0.284 | 10.041 | 0.741 | 0.000 | 0.078 | 0.420 | 0.000 | 0.171 | 17.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 141 | 95 | 188 | 0 | 110 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.47 | 0.99 | 1.96 | 0.00 | 1.15 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.428 | 0.081 | 1.285 | 0.000 | 0.083 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 248 | 172 | 222 | 0 | 170 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.30 | 0.90 | 1.16 | 0.00 | 0.89 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.678 | 10.791 | 1.730 | 0.000 | 0.086 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 292 | 187 | 256 | 0 | 225 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.30 | 0.83 | 1.14 | 0.00 | 1.00 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.777 | 10.782 | 2.342 | 0.000 | 0.082 | 0.000 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 201 | 112 | 184 | 0 | 144 | 0 | 0 | 141 | 0 |
N.S. |
1 | 1.37 | 0.76 | 1.25 | 0.00 | 0.98 | 0.00 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.572 | 10.096 | 6.327 | 0.000 | 0.083 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 234 | 71 | 124 | 0 | 92 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.58 | 0.48 | 0.84 | 0.00 | 0.62 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.716 | 0.016 | 4.045 | 0.000 | 0.086 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 0 | 112 | 191 | 0 | 113 | 83 | 0 | 47 | 0 |
N.S. |
1 | 0.00 | 0.73 | 1.25 | 0.00 | 0.74 | 0.54 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.000 | 0.021 | 2.300 | 0.000 | 0.082 | 2.329 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 64 | 90 | 0 | 73 | 39 | 0 | 40 | 46 |
N.S. |
1 | 1.00 | 0.74 | 1.03 | 0.00 | 0.84 | 0.45 | 0.00 | 0.46 | 0.53 |
time (sec) |
N/A | 0.327 | 7.860 | 0.762 | 0.000 | 0.077 | 0.483 | 0.000 | 0.164 | 17.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 292 | 172 | 270 | 0 | 224 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.52 | 0.90 | 1.41 | 0.00 | 1.17 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.779 | 10.479 | 1.341 | 0.000 | 0.079 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 225 | 326 | 187 | 304 | 0 | 238 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.45 | 0.83 | 1.35 | 0.00 | 1.06 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.873 | 10.703 | 1.780 | 0.000 | 0.081 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 258 | 364 | 153 | 338 | 0 | 338 | 0 | 0 | 89 | 0 |
N.S. |
1 | 1.41 | 0.59 | 1.31 | 0.00 | 1.31 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.926 | 10.847 | 2.426 | 0.000 | 0.080 | 0.000 | 0.000 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 253 | 155 | 226 | 0 | 167 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.37 | 0.84 | 1.22 | 0.00 | 0.90 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.683 | 10.169 | 6.501 | 0.000 | 0.076 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 248 | 146 | 226 | 0 | 171 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.31 | 0.77 | 1.19 | 0.00 | 0.90 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.664 | 10.106 | 4.194 | 0.000 | 0.081 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 0 | 147 | 271 | 0 | 226 | 83 | 0 | 69 | 0 |
N.S. |
1 | 0.00 | 0.77 | 1.43 | 0.00 | 1.19 | 0.44 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.000 | 10.087 | 2.253 | 0.000 | 0.078 | 6.452 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 119 | 90 | 127 | 0 | 107 | 39 | 0 | 52 | 46 |
N.S. |
1 | 1.07 | 0.81 | 1.14 | 0.00 | 0.96 | 0.35 | 0.00 | 0.47 | 0.41 |
time (sec) |
N/A | 0.366 | 10.035 | 0.759 | 0.000 | 0.073 | 0.528 | 0.000 | 0.168 | 17.929 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 361 | 163 | 339 | 0 | 330 | 0 | 0 | 91 | 0 |
N.S. |
1 | 1.60 | 0.72 | 1.50 | 0.00 | 1.46 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.949 | 10.758 | 1.328 | 0.000 | 0.089 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 259 | 400 | 174 | 373 | 0 | 391 | 0 | 0 | 92 | 0 |
N.S. |
1 | 1.54 | 0.67 | 1.44 | 0.00 | 1.51 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 1.076 | 10.950 | 1.770 | 0.000 | 0.087 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 439 | 185 | 407 | 0 | 440 | 0 | 0 | 92 | 0 |
N.S. |
1 | 1.50 | 0.63 | 1.39 | 0.00 | 1.51 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 1.116 | 11.035 | 2.387 | 0.000 | 0.090 | 0.000 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 4 | 4 | 36 | 27 | 0 | 34 | 61 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 9.00 | 6.75 | 0.00 | 8.50 | 15.25 | 0.00 | 5.00 | 0.00 |
time (sec) |
N/A | 0.243 | 0.003 | 0.687 | 0.000 | 0.070 | 0.694 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 34 | 38 | 88 | 0 | 31 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.06 | 1.19 | 2.75 | 0.00 | 0.97 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.268 | 10.135 | 0.888 | 0.000 | 0.072 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | C | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 126 | 58 | 63 | 0 | 29 | 53 | 0 | 16 | 0 |
N.S. |
1 | 5.04 | 2.32 | 2.52 | 0.00 | 1.16 | 2.12 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.362 | 10.046 | 0.867 | 0.000 | 0.069 | 0.655 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 121 | 36 | 93 | 0 | 32 | 0 | 0 | 24 | 0 |
N.S. |
1 | 2.42 | 0.72 | 1.86 | 0.00 | 0.64 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.320 | 10.109 | 1.036 | 0.000 | 0.073 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 86 | 158 | 0 | 102 | 70 | 0 | 58 | 0 |
N.S. |
1 | 1.00 | 1.59 | 2.93 | 0.00 | 1.89 | 1.30 | 0.00 | 1.07 | 0.00 |
time (sec) |
N/A | 0.357 | 10.055 | 1.298 | 0.000 | 0.085 | 0.891 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 85 | 165 | 0 | 119 | 76 | 0 | 63 | 0 |
N.S. |
1 | 1.00 | 1.63 | 3.17 | 0.00 | 2.29 | 1.46 | 0.00 | 1.21 | 0.00 |
time (sec) |
N/A | 0.358 | 10.046 | 2.395 | 0.000 | 0.112 | 0.873 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 233 | 71 | 121 | 0 | 85 | 0 | 0 | 36 | 0 |
N.S. |
1 | 3.24 | 0.99 | 1.68 | 0.00 | 1.18 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.758 | 10.071 | 3.968 | 0.000 | 0.077 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 233 | 100 | 121 | 0 | 85 | 0 | 0 | 36 | 0 |
N.S. |
1 | 3.19 | 1.37 | 1.66 | 0.00 | 1.16 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.716 | 0.264 | 1.704 | 0.000 | 0.074 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | C | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 233 | 100 | 121 | 0 | 85 | 0 | 0 | 36 | 0 |
N.S. |
1 | 3.24 | 1.39 | 1.68 | 0.00 | 1.18 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.750 | 10.242 | 2.645 | 0.000 | 0.077 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 306 | 143 | 194 | 0 | 148 | 184 | 0 | 159 | 0 |
N.S. |
1 | 1.49 | 0.70 | 0.95 | 0.00 | 0.72 | 0.90 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.834 | 8.634 | 7.982 | 0.000 | 0.079 | 1.732 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 277 | 122 | 183 | 0 | 136 | 133 | 0 | 135 | 0 |
N.S. |
1 | 1.56 | 0.69 | 1.03 | 0.00 | 0.76 | 0.75 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.766 | 7.657 | 5.727 | 0.000 | 0.073 | 1.461 | 0.000 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 0 | 88 | 172 | 0 | 126 | 85 | 0 | 111 | 0 |
N.S. |
1 | 0.00 | 0.56 | 1.10 | 0.00 | 0.81 | 0.54 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.000 | 0.014 | 3.969 | 0.000 | 0.076 | 1.035 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 84 | 86 | 82 | 0 | 54 | 39 | 0 | 52 | 46 |
N.S. |
1 | 1.00 | 1.02 | 0.98 | 0.00 | 0.64 | 0.46 | 0.00 | 0.62 | 0.55 |
time (sec) |
N/A | 0.324 | 0.158 | 0.870 | 0.000 | 0.069 | 0.451 | 0.000 | 0.176 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 78 | 67 | 138 | 0 | 90 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.32 | 1.14 | 2.34 | 0.00 | 1.53 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.351 | 0.045 | 1.215 | 0.000 | 0.077 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 234 | 134 | 124 | 0 | 92 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.58 | 0.91 | 0.84 | 0.00 | 0.62 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.723 | 0.104 | 1.699 | 0.000 | 0.075 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 193 | 253 | 175 | 226 | 0 | 167 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.31 | 0.91 | 1.17 | 0.00 | 0.87 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.679 | 10.579 | 2.278 | 0.000 | 0.075 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 287 | 190 | 261 | 0 | 228 | 0 | 0 | 58 | 0 |
N.S. |
1 | 1.26 | 0.84 | 1.15 | 0.00 | 1.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.778 | 10.779 | 2.976 | 0.000 | 0.079 | 0.000 | 0.000 | 0.265 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 331 | 151 | 296 | 0 | 281 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.27 | 0.58 | 1.13 | 0.00 | 1.08 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.871 | 10.869 | 3.896 | 0.000 | 0.081 | 0.000 | 0.000 | 0.272 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 374 | 135 | 216 | 0 | 169 | 279 | 0 | 207 | 0 |
N.S. |
1 | 1.56 | 0.56 | 0.90 | 0.00 | 0.71 | 1.17 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 1.031 | 10.159 | 7.985 | 0.000 | 0.078 | 2.567 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 212 | 341 | 126 | 205 | 0 | 159 | 180 | 0 | 183 | 0 |
N.S. |
1 | 1.61 | 0.59 | 0.97 | 0.00 | 0.75 | 0.85 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.913 | 9.641 | 5.754 | 0.000 | 0.077 | 1.790 | 0.000 | 0.283 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | A | F | A | A | F | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 0 | 91 | 194 | 0 | 147 | 180 | 0 | 159 | 0 |
N.S. |
1 | 0.00 | 0.48 | 1.02 | 0.00 | 0.77 | 0.95 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.000 | 8.500 | 4.009 | 0.000 | 0.076 | 1.763 | 0.000 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 113 | 58 | 96 | 0 | 70 | 41 | 0 | 76 | 46 |
N.S. |
1 | 1.05 | 0.54 | 0.89 | 0.00 | 0.65 | 0.38 | 0.00 | 0.70 | 0.43 |
time (sec) |
N/A | 0.374 | 0.004 | 0.885 | 0.000 | 0.073 | 0.489 | 0.000 | 0.244 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F(-2) | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 243 | 87 | 172 | 0 | 126 | 85 | 0 | 111 | 0 |
N.S. |
1 | 1.56 | 0.56 | 1.10 | 0.00 | 0.81 | 0.54 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.667 | 0.018 | 2.626 | 0.000 | 0.074 | 2.116 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 209 | 142 | 160 | 0 | 111 | 0 | 0 | 60 | 0 |
N.S. |
1 | 1.45 | 0.99 | 1.11 | 0.00 | 0.77 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.589 | 10.466 | 3.083 | 0.000 | 0.081 | 0.000 | 0.000 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 201 | 130 | 184 | 0 | 144 | 0 | 0 | 141 | 0 |
N.S. |
1 | 1.34 | 0.87 | 1.23 | 0.00 | 0.96 | 0.00 | 0.00 | 0.94 | 0.00 |
time (sec) |
N/A | 0.567 | 10.489 | 2.272 | 0.000 | 0.078 | 0.000 | 0.000 | 0.266 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 138 | 91 | 94 | 0 | 83 | 0 | 0 | 383 | 0 |
N.S. |
1 | 1.47 | 0.97 | 1.00 | 0.00 | 0.88 | 0.00 | 0.00 | 4.07 | 0.00 |
time (sec) |
N/A | 0.434 | 10.587 | 3.072 | 0.000 | 0.073 | 0.000 | 0.000 | 0.299 | 0.000 |