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 | C | F | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 84 | 82 | 37 | 0 | 53 | 44 | 0 | 10 | 0 |
N.S. |
1 | 0.98 | 0.95 | 0.43 | 0.00 | 0.62 | 0.51 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.329 | 0.041 | 0.875 | 0.000 | 0.087 | 0.595 | 0.000 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 69 | 50 | 23 | 48 | 49 | 61 | 49 | 54 | 0 |
N.S. |
1 | 1.10 | 0.79 | 0.37 | 0.76 | 0.78 | 0.97 | 0.78 | 0.86 | 0.00 |
time (sec) |
N/A | 0.489 | 0.029 | 0.694 | 0.035 | 0.092 | 0.712 | 0.109 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 51 | 41 | 43 | 39 | 39 | 46 | 38 | 42 | 0 |
N.S. |
1 | 1.04 | 0.84 | 0.88 | 0.80 | 0.80 | 0.94 | 0.78 | 0.86 | 0.00 |
time (sec) |
N/A | 0.361 | 0.021 | 0.658 | 0.034 | 0.088 | 0.872 | 0.118 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 35 | 29 | 29 | 30 | 29 | 29 | 30 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.83 | 0.86 | 0.83 | 0.83 | 0.86 | 0.00 |
time (sec) |
N/A | 0.282 | 0.006 | 0.623 | 0.058 | 0.089 | 0.497 | 0.108 | 0.201 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 16 | 16 | 16 | 12 | 15 | 16 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.07 | 1.07 | 0.80 | 1.00 | 1.07 | 0.00 |
time (sec) |
N/A | 0.174 | 0.004 | 0.561 | 0.042 | 0.086 | 0.497 | 0.112 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 43 | 20 | 0 | 0 | 22 | 0 | 10 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.47 | 0.00 | 0.00 | 0.51 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.196 | 0.005 | 0.677 | 0.000 | 0.000 | 0.359 | 0.000 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 30 | 26 | 24 | 36 | 37 | 10 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.20 | 1.04 | 0.96 | 1.44 | 1.48 | 0.40 | 0.00 |
time (sec) |
N/A | 0.306 | 0.009 | 0.704 | 0.104 | 0.088 | 0.590 | 0.113 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 50 | 46 | 47 | 32 | 31 | 41 | 149 | 38 | 0 |
N.S. |
1 | 1.09 | 1.00 | 1.02 | 0.70 | 0.67 | 0.89 | 3.24 | 0.83 | 0.00 |
time (sec) |
N/A | 0.392 | 0.011 | 0.685 | 0.099 | 0.092 | 0.523 | 0.117 | 0.194 | 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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.206 | 1.868 | 0.240 | 0.055 | 0.098 | 1.375 | 0.125 | 0.267 | 3.637 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 232 | 107 | 154 | 0 | 105 | 0 | 117 | 12 | 0 |
N.S. |
1 | 1.56 | 0.72 | 1.03 | 0.00 | 0.70 | 0.00 | 0.79 | 0.08 | 0.00 |
time (sec) |
N/A | 1.435 | 0.090 | 7.199 | 0.000 | 0.091 | 0.000 | 0.132 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 158 | 78 | 84 | 0 | 81 | 0 | 150 | 12 | 0 |
N.S. |
1 | 1.41 | 0.70 | 0.75 | 0.00 | 0.72 | 0.00 | 1.34 | 0.11 | 0.00 |
time (sec) |
N/A | 0.950 | 0.051 | 7.039 | 0.000 | 0.092 | 0.000 | 0.123 | 0.222 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 79 | 58 | 62 | 0 | 56 | 0 | 65 | 10 | 0 |
N.S. |
1 | 1.07 | 0.78 | 0.84 | 0.00 | 0.76 | 0.00 | 0.88 | 0.14 | 0.00 |
time (sec) |
N/A | 0.527 | 0.038 | 6.918 | 0.000 | 0.094 | 0.000 | 0.130 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 37 | 32 | 32 | 0 | 31 | 0 | 49 | 8 | 0 |
N.S. |
1 | 1.16 | 1.00 | 1.00 | 0.00 | 0.97 | 0.00 | 1.53 | 0.25 | 0.00 |
time (sec) |
N/A | 0.360 | 0.010 | 5.924 | 0.000 | 0.098 | 0.000 | 0.117 | 0.215 | 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 | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.193 | 0.294 | 0.116 | 0.079 | 0.076 | 1.080 | 0.115 | 0.197 | 3.697 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.194 | 0.323 | 0.185 | 0.061 | 0.084 | 1.061 | 0.116 | 0.199 | 3.700 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | C | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 12 | 10 | 12 | 74 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 7.40 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.192 | 0.348 | 0.177 | 0.079 | 0.091 | 1.077 | 0.116 | 0.252 | 3.610 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.486 | 2.565 | 0.286 | 0.062 | 0.093 | 0.613 | 0.125 | 0.202 | 4.351 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 164 | 96 | 156 | 123 | 92 | 0 | 338 | 144 | 0 |
N.S. |
1 | 0.89 | 0.52 | 0.85 | 0.67 | 0.50 | 0.00 | 1.84 | 0.78 | 0.00 |
time (sec) |
N/A | 0.630 | 0.142 | 0.840 | 0.121 | 0.085 | 0.000 | 0.135 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 109 | 63 | 99 | 91 | 64 | 0 | 252 | 89 | 0 |
N.S. |
1 | 0.92 | 0.53 | 0.84 | 0.77 | 0.54 | 0.00 | 2.14 | 0.75 | 0.00 |
time (sec) |
N/A | 0.519 | 0.100 | 0.849 | 0.109 | 0.090 | 0.000 | 0.131 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 66 | 50 | 57 | 68 | 48 | 0 | 191 | 56 | 0 |
N.S. |
1 | 1.06 | 0.81 | 0.92 | 1.10 | 0.77 | 0.00 | 3.08 | 0.90 | 0.00 |
time (sec) |
N/A | 0.435 | 0.069 | 0.829 | 0.102 | 0.088 | 0.000 | 0.130 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | C | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 41 | 24 | 23 | 23 | 0 | 303 | 28 | 0 |
N.S. |
1 | 1.00 | 1.58 | 0.92 | 0.88 | 0.88 | 0.00 | 11.65 | 1.08 | 0.00 |
time (sec) |
N/A | 0.187 | 0.027 | 0.743 | 0.037 | 0.082 | 0.000 | 0.119 | 0.193 | 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 | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.199 | 0.360 | 0.322 | 0.265 | 0.091 | 0.370 | 0.122 | 0.195 | 3.871 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 39 | 46 | 0 | 39 | 0 | 181 | 12 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.00 | 0.00 | 0.85 | 0.00 | 3.93 | 0.26 | 0.00 |
time (sec) |
N/A | 0.453 | 0.072 | 0.921 | 0.000 | 0.092 | 0.000 | 0.130 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 92 | 84 | 83 | 0 | 96 | 0 | 809 | 12 | 0 |
N.S. |
1 | 0.83 | 0.76 | 0.75 | 0.00 | 0.86 | 0.00 | 7.29 | 0.11 | 0.00 |
time (sec) |
N/A | 0.567 | 0.233 | 0.957 | 0.000 | 0.119 | 0.000 | 0.139 | 0.220 | 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 | 12 | 12 | 14 | 12 | 14 | 14 | 12 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.00 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.211 | 5.281 | 0.250 | 0.069 | 0.100 | 1.296 | 0.169 | 0.205 | 3.738 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 334 | 435 | 158 | 0 | 0 | 151 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.30 | 0.47 | 0.00 | 0.00 | 0.45 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 4.474 | 1.193 | 0.000 | 0.000 | 0.098 | 0.000 | 0.000 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 187 | 95 | 111 | 0 | 100 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.21 | 0.62 | 0.72 | 0.00 | 0.65 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.608 | 0.322 | 16.528 | 0.000 | 0.092 | 0.000 | 0.000 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 54 | 43 | 45 | 0 | 44 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.10 | 0.88 | 0.92 | 0.00 | 0.90 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.417 | 0.008 | 11.583 | 0.000 | 0.086 | 0.000 | 0.000 | 0.210 | 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 | 12 | 12 | 14 | 12 | 14 | 14 | 10 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 0.83 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.208 | 2.156 | 0.097 | 0.070 | 0.076 | 0.387 | 0.164 | 0.216 | 3.931 |
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 | 12 | 12 | 14 | 12 | 14 | 14 | 12 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.00 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.214 | 3.532 | 0.217 | 0.067 | 0.089 | 0.325 | 0.180 | 0.241 | 3.998 |
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 | 12 | 12 | 14 | 12 | 14 | 14 | 12 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.00 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.215 | 1.596 | 0.198 | 0.092 | 0.090 | 0.388 | 0.181 | 0.212 | 3.948 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 156 | 106 | 0 | 0 | 140 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.14 | 0.77 | 0.00 | 0.00 | 1.02 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.612 | 1.143 | 0.000 | 0.000 | 0.100 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 156 | 106 | 0 | 0 | 140 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.14 | 0.77 | 0.00 | 0.00 | 1.02 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.579 | 1.118 | 0.000 | 0.000 | 0.095 | 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 | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 145 | 102 | 0 | 0 | 127 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.13 | 0.80 | 0.00 | 0.00 | 0.99 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.555 | 1.070 | 0.000 | 0.000 | 0.102 | 0.000 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 53 | 95 | 54 | 49 | 57 | 0 | 59 | 65 | 0 |
N.S. |
1 | 0.98 | 1.76 | 1.00 | 0.91 | 1.06 | 0.00 | 1.09 | 1.20 | 0.00 |
time (sec) |
N/A | 0.276 | 0.058 | 0.717 | 0.031 | 0.089 | 0.000 | 0.112 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 147 | 107 | 0 | 0 | 142 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.12 | 0.82 | 0.00 | 0.00 | 1.08 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.586 | 1.105 | 0.000 | 0.000 | 0.093 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 158 | 111 | 0 | 0 | 147 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.14 | 0.80 | 0.00 | 0.00 | 1.06 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.604 | 1.126 | 0.000 | 0.000 | 0.114 | 0.000 | 0.000 | 0.219 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 244 | 128 | 0 | 0 | 180 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.39 | 0.73 | 0.00 | 0.00 | 1.02 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.680 | 1.995 | 0.000 | 0.000 | 0.098 | 0.000 | 0.000 | 0.268 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 128 | 0 | 0 | 0 | 72 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.33 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 1.062 | 0.000 | 0.000 | 0.000 | 0.086 | 0.000 | 0.000 | 0.204 | 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 | 12 | 12 | 14 | 12 | 14 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.17 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.529 | 0.563 | 0.229 | 0.099 | 0.079 | 1.361 | 0.111 | 0.186 | 4.163 |
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 | 10 | 10 | 10 | 9 | 8 | 8 | 7 | 8 | 8 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.80 | 0.80 | 0.70 | 0.80 | 0.80 | 0.00 |
time (sec) |
N/A | 0.193 | 0.010 | 3.503 | 0.031 | 0.090 | 0.220 | 0.110 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 23 | 0 | 23 | 0 | 41 | 11 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.00 | 0.88 | 0.00 | 1.58 | 0.42 | 0.00 |
time (sec) |
N/A | 0.298 | 0.015 | 3.395 | 0.000 | 0.095 | 0.000 | 0.113 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 66 | 44 | 45 | 0 | 43 | 0 | 55 | 12 | 0 |
N.S. |
1 | 1.08 | 0.72 | 0.74 | 0.00 | 0.70 | 0.00 | 0.90 | 0.20 | 0.00 |
time (sec) |
N/A | 0.484 | 0.058 | 4.506 | 0.000 | 0.090 | 0.000 | 0.113 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 140 | 64 | 69 | 0 | 67 | 0 | 138 | 14 | 0 |
N.S. |
1 | 1.54 | 0.70 | 0.76 | 0.00 | 0.74 | 0.00 | 1.52 | 0.15 | 0.00 |
time (sec) |
N/A | 0.892 | 0.072 | 4.888 | 0.000 | 0.086 | 0.000 | 0.128 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 214 | 93 | 138 | 0 | 92 | 0 | 106 | 14 | 0 |
N.S. |
1 | 1.70 | 0.74 | 1.10 | 0.00 | 0.73 | 0.00 | 0.84 | 0.11 | 0.00 |
time (sec) |
N/A | 1.254 | 0.123 | 5.096 | 0.000 | 0.091 | 0.000 | 0.121 | 0.235 | 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 | 12 | 12 | 14 | 12 | 14 | 14 | 14 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.17 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 1.064 | 0.581 | 0.261 | 0.155 | 0.085 | 1.925 | 0.110 | 0.238 | 4.504 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 48 | 0 | 0 | 0 | 44 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.09 | 0.00 | 0.00 | 0.00 | 1.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.527 | 0.000 | 0.000 | 0.000 | 0.091 | 0.000 | 0.000 | 0.279 | 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 | 12 | 12 | 14 | 12 | 14 | 14 | 12 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.00 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.197 | 0.668 | 0.271 | 0.159 | 0.080 | 1.561 | 0.116 | 0.252 | 4.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 36 | 28 | 0 | 25 | 0 | 33 | 11 | 0 |
N.S. |
1 | 1.00 | 1.06 | 0.82 | 0.00 | 0.74 | 0.00 | 0.97 | 0.32 | 0.00 |
time (sec) |
N/A | 0.305 | 0.016 | 3.499 | 0.000 | 0.081 | 0.000 | 0.112 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 71 | 42 | 44 | 0 | 43 | 0 | 124 | 12 | 0 |
N.S. |
1 | 1.16 | 0.69 | 0.72 | 0.00 | 0.70 | 0.00 | 2.03 | 0.20 | 0.00 |
time (sec) |
N/A | 0.474 | 0.036 | 4.567 | 0.000 | 0.083 | 0.000 | 0.116 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 129 | 72 | 89 | 0 | 73 | 0 | 82 | 14 | 0 |
N.S. |
1 | 1.32 | 0.73 | 0.91 | 0.00 | 0.74 | 0.00 | 0.84 | 0.14 | 0.00 |
time (sec) |
N/A | 0.749 | 0.071 | 4.831 | 0.000 | 0.094 | 0.000 | 0.121 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 234 | 94 | 111 | 0 | 92 | 0 | 180 | 14 | 0 |
N.S. |
1 | 1.83 | 0.73 | 0.87 | 0.00 | 0.72 | 0.00 | 1.41 | 0.11 | 0.00 |
time (sec) |
N/A | 1.399 | 0.076 | 5.909 | 0.000 | 0.105 | 0.000 | 0.123 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 34 | 25 | 24 | 0 | 41 | 0 | 23 | 11 | 0 |
N.S. |
1 | 1.17 | 0.86 | 0.83 | 0.00 | 1.41 | 0.00 | 0.79 | 0.38 | 0.00 |
time (sec) |
N/A | 0.272 | 0.021 | 5.767 | 0.000 | 0.095 | 0.000 | 0.117 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 34 | 25 | 24 | 0 | 42 | 0 | 23 | 11 | 0 |
N.S. |
1 | 1.17 | 0.86 | 0.83 | 0.00 | 1.45 | 0.00 | 0.79 | 0.38 | 0.00 |
time (sec) |
N/A | 0.274 | 0.022 | 5.476 | 0.000 | 0.091 | 0.000 | 0.113 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 212 | 123 | 175 | 0 | 114 | 0 | 398 | 18 | 0 |
N.S. |
1 | 1.21 | 0.70 | 1.00 | 0.00 | 0.65 | 0.00 | 2.27 | 0.10 | 0.00 |
time (sec) |
N/A | 1.811 | 0.241 | 9.980 | 0.000 | 0.103 | 0.000 | 0.162 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 105 | 71 | 82 | 0 | 72 | 0 | 507 | 16 | 0 |
N.S. |
1 | 1.08 | 0.73 | 0.85 | 0.00 | 0.74 | 0.00 | 5.23 | 0.16 | 0.00 |
time (sec) |
N/A | 0.949 | 0.175 | 8.826 | 0.000 | 0.105 | 0.000 | 0.145 | 0.215 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 33 | 31 | 0 | 31 | 0 | 57 | 15 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.91 | 0.00 | 0.91 | 0.00 | 1.68 | 0.44 | 0.00 |
time (sec) |
N/A | 0.343 | 0.014 | 6.481 | 0.000 | 0.093 | 0.000 | 0.121 | 0.200 | 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 | 16 | 16 | 18 | 16 | 18 | 18 | 15 | 18 | 39 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.94 | 1.12 | 2.44 | 1.12 |
time (sec) |
N/A | 0.296 | 2.178 | 0.322 | 0.165 | 0.086 | 1.115 | 0.126 | 0.217 | 6.635 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 199 | 239 | 134 | 212 | 0 | 125 | 0 | 431 | 18 | 0 |
N.S. |
1 | 1.20 | 0.67 | 1.07 | 0.00 | 0.63 | 0.00 | 2.17 | 0.09 | 0.00 |
time (sec) |
N/A | 1.975 | 0.236 | 11.392 | 0.000 | 0.091 | 0.000 | 0.155 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 115 | 74 | 95 | 0 | 77 | 0 | 528 | 16 | 0 |
N.S. |
1 | 1.06 | 0.69 | 0.88 | 0.00 | 0.71 | 0.00 | 4.89 | 0.15 | 0.00 |
time (sec) |
N/A | 0.877 | 0.135 | 8.975 | 0.000 | 0.095 | 0.000 | 0.145 | 0.221 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 45 | 38 | 0 | 37 | 0 | 95 | 15 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.83 | 0.00 | 0.80 | 0.00 | 2.07 | 0.33 | 0.00 |
time (sec) |
N/A | 0.318 | 0.016 | 6.524 | 0.000 | 0.087 | 0.000 | 0.126 | 0.218 | 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 | 16 | 16 | 18 | 16 | 18 | 18 | 15 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.94 | 1.12 | 1.12 | 1.12 |
time (sec) |
N/A | 0.283 | 1.649 | 0.304 | 0.283 | 0.083 | 1.204 | 0.127 | 0.225 | 5.592 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 371 | 377 | 407 | 1212 | 0 | 432 | 0 | 200182 | 16 | 0 |
N.S. |
1 | 1.02 | 1.10 | 3.27 | 0.00 | 1.16 | 0.00 | 539.57 | 0.04 | 0.00 |
time (sec) |
N/A | 1.567 | 3.532 | 5.037 | 0.000 | 0.105 | 0.000 | 4.450 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 160 | 168 | 266 | 0 | 146 | 0 | 9541 | 15 | 0 |
N.S. |
1 | 1.04 | 1.09 | 1.73 | 0.00 | 0.95 | 0.00 | 61.95 | 0.10 | 0.00 |
time (sec) |
N/A | 0.501 | 0.978 | 1.066 | 0.000 | 0.096 | 0.000 | 0.395 | 0.199 | 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 | 16 | 16 | 18 | 16 | 18 | 18 | 15 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.94 | 1.12 | 1.12 | 1.12 |
time (sec) |
N/A | 0.291 | 13.075 | 0.544 | 0.266 | 0.079 | 0.763 | 0.132 | 0.226 | 5.629 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 370 | 378 | 389 | 1208 | 0 | 429 | 0 | 206132 | 16 | 0 |
N.S. |
1 | 1.02 | 1.05 | 3.26 | 0.00 | 1.16 | 0.00 | 557.11 | 0.04 | 0.00 |
time (sec) |
N/A | 1.754 | 3.240 | 1.440 | 0.000 | 0.108 | 0.000 | 4.579 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 160 | 164 | 264 | 0 | 147 | 0 | 9214 | 15 | 0 |
N.S. |
1 | 1.05 | 1.07 | 1.73 | 0.00 | 0.96 | 0.00 | 60.22 | 0.10 | 0.00 |
time (sec) |
N/A | 0.490 | 0.992 | 0.956 | 0.000 | 0.092 | 0.000 | 0.403 | 0.199 | 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 | 16 | 16 | 18 | 16 | 18 | 18 | 15 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.94 | 1.12 | 1.12 | 1.12 |
time (sec) |
N/A | 0.264 | 7.519 | 0.608 | 0.276 | 0.092 | 0.753 | 0.140 | 0.176 | 4.807 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 88 | 78 | 124 | 0 | 109 | 700 | 0 | 10 | 0 |
N.S. |
1 | 0.98 | 0.87 | 1.38 | 0.00 | 1.21 | 7.78 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.347 | 0.055 | 1.058 | 0.000 | 0.113 | 1.058 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 70 | 53 | 54 | 94 | 59 | 85 | 0 | 55 | 0 |
N.S. |
1 | 1.11 | 0.84 | 0.86 | 1.49 | 0.94 | 1.35 | 0.00 | 0.87 | 0.00 |
time (sec) |
N/A | 0.484 | 0.028 | 0.815 | 0.145 | 0.084 | 1.546 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 53 | 44 | 42 | 49 | 54 | 70 | 0 | 43 | 0 |
N.S. |
1 | 1.08 | 0.90 | 0.86 | 1.00 | 1.10 | 1.43 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.381 | 0.021 | 0.811 | 0.052 | 0.083 | 1.333 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 36 | 35 | 28 | 70 | 51 | 53 | 0 | 31 | 0 |
N.S. |
1 | 1.03 | 1.00 | 0.80 | 2.00 | 1.46 | 1.51 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.287 | 0.009 | 0.777 | 0.186 | 0.091 | 1.024 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 17 | 27 | 28 | 31 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.69 | 1.75 | 1.94 | 0.00 | 1.12 | 0.00 |
time (sec) |
N/A | 0.171 | 0.004 | 0.599 | 0.038 | 0.090 | 0.925 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 94 | 158 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.00 | 1.54 | 2.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.211 | 0.025 | 0.795 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 32 | 34 | 25 | 42 | 0 | 10 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.23 | 1.31 | 0.96 | 1.62 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.318 | 0.009 | 0.764 | 0.144 | 0.087 | 0.574 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 49 | 46 | 47 | 61 | 42 | 87 | 0 | 37 | 0 |
N.S. |
1 | 1.07 | 1.00 | 1.02 | 1.33 | 0.91 | 1.89 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.387 | 0.011 | 0.770 | 0.217 | 0.084 | 1.581 | 0.000 | 0.209 | 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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.209 | 1.839 | 0.283 | 0.066 | 0.093 | 3.785 | 0.102 | 0.230 | 3.919 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 232 | 108 | 135 | 0 | 118 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.42 | 0.66 | 0.83 | 0.00 | 0.72 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 1.415 | 0.078 | 7.583 | 0.000 | 0.090 | 0.000 | 0.000 | 0.218 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 156 | 78 | 84 | 0 | 111 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.39 | 0.70 | 0.75 | 0.00 | 0.99 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.946 | 0.061 | 7.717 | 0.000 | 0.099 | 0.000 | 0.000 | 0.243 | 0.000 |
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 | 75 | 79 | 58 | 62 | 0 | 0 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.05 | 0.77 | 0.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.515 | 0.034 | 7.554 | 0.000 | 0.000 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 36 | 31 | 30 | 0 | 59 | 0 | 0 | 8 | 0 |
N.S. |
1 | 1.16 | 1.00 | 0.97 | 0.00 | 1.90 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.346 | 0.010 | 6.786 | 0.000 | 0.088 | 0.000 | 0.000 | 0.207 | 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 | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.186 | 0.278 | 0.145 | 0.067 | 0.098 | 3.531 | 0.105 | 0.202 | 4.148 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.189 | 0.320 | 0.208 | 0.074 | 0.091 | 3.809 | 0.112 | 0.210 | 4.066 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.194 | 0.341 | 0.259 | 0.069 | 0.096 | 3.665 | 0.105 | 0.219 | 3.996 |
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 | 10 | 10 | 12 | 10 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 1.00 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.506 | 2.123 | 0.334 | 0.060 | 0.094 | 0.610 | 0.105 | 0.214 | 4.692 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 184 | 164 | 95 | 153 | 502 | 176 | 0 | 0 | 144 | 0 |
N.S. |
1 | 0.89 | 0.52 | 0.83 | 2.73 | 0.96 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.650 | 0.163 | 1.013 | 1.105 | 0.096 | 0.000 | 0.000 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 108 | 64 | 98 | 423 | 148 | 0 | 0 | 90 | 0 |
N.S. |
1 | 0.92 | 0.54 | 0.83 | 3.58 | 1.25 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.528 | 0.112 | 0.971 | 0.973 | 0.091 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 66 | 49 | 56 | 311 | 104 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.06 | 0.79 | 0.90 | 5.02 | 1.68 | 0.00 | 0.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.454 | 0.078 | 0.895 | 0.818 | 0.102 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 42 | 26 | 44 | 47 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.56 | 0.96 | 1.63 | 1.74 | 0.00 | 0.00 | 1.11 | 0.00 |
time (sec) |
N/A | 0.182 | 0.027 | 0.793 | 0.038 | 0.084 | 0.000 | 0.000 | 0.223 | 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 | 10 | 10 | 12 | 10 | 12 | 12 | 8 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.20 | 1.00 | 1.20 | 1.20 | 0.80 | 1.20 | 1.20 | 1.20 |
time (sec) |
N/A | 0.193 | 0.367 | 0.362 | 0.680 | 0.081 | 0.334 | 0.102 | 0.225 | 4.188 |
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 | 47 | 47 | 40 | 47 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.00 | 0.85 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.454 | 0.050 | 0.898 | 0.000 | 0.000 | 0.000 | 0.000 | 0.212 | 0.000 |
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 | 111 | 92 | 76 | 85 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 0.83 | 0.68 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.562 | 0.276 | 0.983 | 0.000 | 0.000 | 0.000 | 0.000 | 0.225 | 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 | 12 | 12 | 14 | 12 | 14 | 14 | 12 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.00 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.215 | 5.503 | 0.263 | 0.067 | 0.093 | 1.191 | 0.113 | 0.234 | 4.063 |
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 | 334 | 435 | 159 | 0 | 0 | 0 | 0 | 0 | 14 | 0 |
N.S. |
1 | 1.30 | 0.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.04 | 0.00 |
time (sec) |
N/A | 4.542 | 0.830 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.209 | 0.000 |
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 | 155 | 188 | 96 | 113 | 0 | 0 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.21 | 0.62 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 1.705 | 0.237 | 16.652 | 0.000 | 0.000 | 0.000 | 0.000 | 0.213 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 53 | 41 | 43 | 0 | 88 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.10 | 0.85 | 0.90 | 0.00 | 1.83 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.420 | 0.008 | 11.920 | 0.000 | 0.090 | 0.000 | 0.000 | 0.233 | 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 | 12 | 12 | 14 | 12 | 14 | 14 | 10 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 0.83 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.221 | 0.766 | 0.122 | 0.073 | 0.078 | 0.481 | 0.105 | 0.226 | 4.078 |
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 | 12 | 12 | 14 | 12 | 14 | 14 | 12 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.00 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.220 | 1.337 | 0.272 | 0.076 | 0.083 | 0.302 | 0.112 | 0.234 | 4.109 |
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 | 12 | 12 | 14 | 12 | 14 | 14 | 12 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.17 | 1.00 | 1.17 | 1.17 | 1.00 | 1.17 | 1.17 | 1.17 |
time (sec) |
N/A | 0.233 | 1.694 | 0.270 | 0.079 | 0.078 | 0.440 | 0.122 | 0.234 | 4.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 152 | 102 | 0 | 0 | 448 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.14 | 0.77 | 0.00 | 0.00 | 3.37 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.617 | 1.182 | 0.000 | 0.000 | 0.107 | 0.000 | 0.000 | 0.274 | 0.000 |