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 | N/A | B | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 851 | 18 | 117 | 20 | 17 | 20 | 181 | 20 |
N.S. |
1 | 1.00 | 47.28 | 1.00 | 6.50 | 1.11 | 0.94 | 1.11 | 10.06 | 1.11 |
time (sec) |
N/A | 1.004 | 3.710 | 0.058 | 0.733 | 0.095 | 4.391 | 0.147 | 0.178 | 25.203 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 106 | 96 | 547 | 0 | 68 | 0 | 69 | 20 | 0 |
N.S. |
1 | 0.99 | 0.90 | 5.11 | 0.00 | 0.64 | 0.00 | 0.64 | 0.19 | 0.00 |
time (sec) |
N/A | 0.578 | 0.150 | 1.000 | 0.000 | 0.089 | 0.000 | 0.121 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 51 | 272 | 0 | 29 | 0 | 31 | 70 | 0 |
N.S. |
1 | 1.00 | 1.00 | 5.33 | 0.00 | 0.57 | 0.00 | 0.61 | 1.37 | 0.00 |
time (sec) |
N/A | 0.456 | 0.081 | 2.883 | 0.000 | 0.071 | 0.000 | 0.119 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 20 | 18 | 20 | 20 | 15 | 20 | 60 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.83 | 1.11 | 3.33 | 1.11 |
time (sec) |
N/A | 0.297 | 0.220 | 0.026 | 0.097 | 0.100 | 1.809 | 0.113 | 0.184 | 25.136 |
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 | 18 | 18 | 20 | 18 | 20 | 20 | 17 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.94 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.290 | 0.378 | 0.026 | 0.104 | 0.095 | 4.266 | 0.112 | 0.170 | 25.447 |
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 | 18 | 18 | 20 | 18 | 20 | 20 | 15 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.83 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.285 | 0.300 | 0.054 | 0.074 | 0.066 | 1.577 | 0.112 | 0.163 | 24.980 |
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 | 14 | 14 | 16 | 14 | 16 | 16 | 14 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.14 | 1.00 | 1.14 | 1.14 | 1.14 |
time (sec) |
N/A | 0.263 | 0.014 | 0.049 | 0.115 | 0.067 | 1.087 | 0.114 | 0.195 | 25.077 |
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 | 18 | 18 | 20 | 18 | 20 | 20 | 17 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.94 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.286 | 0.433 | 0.044 | 0.069 | 0.096 | 3.170 | 0.118 | 0.165 | 25.117 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 193 | 157 | 1487 | 0 | 141 | 0 | 313 | 20 | 0 |
N.S. |
1 | 1.40 | 1.14 | 10.78 | 0.00 | 1.02 | 0.00 | 2.27 | 0.14 | 0.00 |
time (sec) |
N/A | 0.968 | 0.120 | 1.063 | 0.000 | 0.068 | 0.000 | 0.119 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 79 | 97 | 421 | 0 | 78 | 0 | 141 | 88 | 0 |
N.S. |
1 | 0.95 | 1.17 | 5.07 | 0.00 | 0.94 | 0.00 | 1.70 | 1.06 | 0.00 |
time (sec) |
N/A | 0.486 | 0.049 | 2.825 | 0.000 | 0.066 | 0.000 | 0.118 | 0.172 | 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 | 18 | 18 | 20 | 18 | 69 | 20 | 17 | 20 | 78 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 3.83 | 1.11 | 0.94 | 1.11 | 4.33 | 1.11 |
time (sec) |
N/A | 0.283 | 0.253 | 0.026 | 0.081 | 0.093 | 3.050 | 0.118 | 0.191 | 25.122 |
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 | 18 | 18 | 20 | 18 | 78 | 20 | 19 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 4.33 | 1.11 | 1.06 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.285 | 1.347 | 0.026 | 0.073 | 0.093 | 5.473 | 0.133 | 0.188 | 25.165 |
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 | 18 | 18 | 20 | 18 | 66 | 20 | 17 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 3.67 | 1.11 | 0.94 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.278 | 0.371 | 0.043 | 0.069 | 0.069 | 2.458 | 0.114 | 0.193 | 25.081 |
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 | 14 | 14 | 16 | 14 | 73 | 16 | 15 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 5.21 | 1.14 | 1.07 | 1.14 | 1.14 | 1.14 |
time (sec) |
N/A | 0.256 | 0.274 | 0.046 | 0.063 | 0.070 | 1.902 | 0.110 | 0.254 | 25.101 |
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 | 18 | 18 | 20 | 18 | 79 | 20 | 19 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 4.39 | 1.11 | 1.06 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.278 | 1.114 | 0.049 | 0.071 | 0.075 | 4.264 | 0.119 | 0.186 | 25.605 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 204 | 315 | 185 | 1969 | 0 | 270 | 0 | 874 | 20 | 0 |
N.S. |
1 | 1.54 | 0.91 | 9.65 | 0.00 | 1.32 | 0.00 | 4.28 | 0.10 | 0.00 |
time (sec) |
N/A | 1.588 | 0.169 | 1.218 | 0.000 | 0.085 | 0.000 | 0.138 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 115 | 113 | 716 | 0 | 157 | 0 | 406 | 18 | 0 |
N.S. |
1 | 1.01 | 0.99 | 6.28 | 0.00 | 1.38 | 0.00 | 3.56 | 0.16 | 0.00 |
time (sec) |
N/A | 0.576 | 0.061 | 3.071 | 0.000 | 0.077 | 0.000 | 0.120 | 0.167 | 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 | 18 | 18 | 20 | 18 | 161 | 20 | 17 | 20 | 80 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 8.94 | 1.11 | 0.94 | 1.11 | 4.44 | 1.11 |
time (sec) |
N/A | 0.279 | 0.406 | 0.026 | 0.072 | 0.086 | 4.217 | 0.127 | 0.167 | 25.898 |
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 | 18 | 18 | 20 | 18 | 184 | 20 | 19 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 10.22 | 1.11 | 1.06 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.277 | 3.042 | 0.046 | 0.072 | 0.071 | 7.676 | 0.121 | 0.170 | 25.809 |
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 | 18 | 18 | 20 | 18 | 180 | 20 | 17 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 10.00 | 1.11 | 0.94 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.269 | 0.526 | 0.004 | 0.078 | 0.075 | 4.116 | 0.118 | 0.201 | 25.719 |
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 | 14 | 14 | 16 | 14 | 164 | 16 | 15 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 11.71 | 1.14 | 1.07 | 1.14 | 1.14 | 1.14 |
time (sec) |
N/A | 0.254 | 0.369 | 0.051 | 0.065 | 0.066 | 2.660 | 0.119 | 0.180 | 25.715 |
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 | 18 | 18 | 20 | 18 | 187 | 20 | 19 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 10.39 | 1.11 | 1.06 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.274 | 2.026 | 0.049 | 0.069 | 0.071 | 5.822 | 0.115 | 0.171 | 25.852 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 44 | 0 | 43 | 0 | 54 | 0 | 44 | 19 | 0 |
N.S. |
1 | 0.98 | 0.00 | 0.96 | 0.00 | 1.20 | 0.00 | 0.98 | 0.42 | 0.00 |
time (sec) |
N/A | 0.450 | 0.000 | 2.430 | 0.000 | 0.064 | 0.000 | 0.124 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 23 | 0 | 19 | 27 | 20 | 63 | 18 |
N.S. |
1 | 1.00 | 1.00 | 1.15 | 0.00 | 0.95 | 1.35 | 1.00 | 3.15 | 0.90 |
time (sec) |
N/A | 0.346 | 0.018 | 0.768 | 0.000 | 0.085 | 0.696 | 0.117 | 0.187 | 26.011 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 92 | 0 | 74 | 0 | 99 | 0 | 100 | 19 | 0 |
N.S. |
1 | 1.30 | 0.00 | 1.04 | 0.00 | 1.39 | 0.00 | 1.41 | 0.27 | 0.00 |
time (sec) |
N/A | 0.685 | 0.000 | 2.947 | 0.000 | 0.074 | 0.000 | 0.127 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 43 | 43 | 48 | 0 | 55 | 49 | 47 | 80 | 46 |
N.S. |
1 | 0.91 | 0.91 | 1.02 | 0.00 | 1.17 | 1.04 | 1.00 | 1.70 | 0.98 |
time (sec) |
N/A | 0.392 | 0.024 | 0.731 | 0.000 | 0.061 | 0.724 | 0.117 | 0.176 | 25.666 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 165 | 0 | 105 | 0 | 142 | 0 | 151 | 19 | 0 |
N.S. |
1 | 1.30 | 0.00 | 0.83 | 0.00 | 1.12 | 0.00 | 1.19 | 0.15 | 0.00 |
time (sec) |
N/A | 1.050 | 0.000 | 2.848 | 0.000 | 0.069 | 0.000 | 0.129 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 71 | 55 | 70 | 0 | 79 | 70 | 71 | 17 | 74 |
N.S. |
1 | 0.97 | 0.75 | 0.96 | 0.00 | 1.08 | 0.96 | 0.97 | 0.23 | 1.01 |
time (sec) |
N/A | 0.453 | 0.030 | 0.743 | 0.000 | 0.065 | 0.747 | 0.121 | 0.183 | 25.742 |
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 | 150 | 148 | 105 | 151 | 120 | 148 | 136 | 216 | 126 | 100 |
N.S. |
1 | 0.99 | 0.70 | 1.01 | 0.80 | 0.99 | 0.91 | 1.44 | 0.84 | 0.67 |
time (sec) |
N/A | 0.594 | 0.077 | 6.193 | 0.037 | 0.089 | 3.734 | 0.123 | 0.170 | 25.590 |
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 | 66 | 64 | 63 | 101 | 97 | 96 | 100 | 96 | 85 | 71 |
N.S. |
1 | 0.97 | 0.95 | 1.53 | 1.47 | 1.45 | 1.52 | 1.45 | 1.29 | 1.08 |
time (sec) |
N/A | 0.429 | 0.013 | 1.317 | 0.035 | 0.069 | 1.033 | 0.121 | 0.169 | 25.561 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 76 | 2965 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 0.99 | 38.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.691 | 1.369 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 79 | 99 | 411 | 118 | 0 | 0 | 0 | 109 | 0 |
N.S. |
1 | 0.92 | 1.15 | 4.78 | 1.37 | 0.00 | 0.00 | 0.00 | 1.27 | 0.00 |
time (sec) |
N/A | 0.534 | 0.033 | 1.157 | 0.033 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1294 | 1307 | 1041 | 1957 | 0 | 0 | 0 | 0 | 165 | 0 |
N.S. |
1 | 1.01 | 0.80 | 1.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 3.359 | 0.880 | 1.354 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1304 | 1316 | 1101 | 0 | 0 | 0 | 0 | 0 | 148 | 0 |
N.S. |
1 | 1.01 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 3.295 | 0.835 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1137 | 1153 | 972 | 1787 | 0 | 0 | 0 | 0 | 154 | 0 |
N.S. |
1 | 1.01 | 0.85 | 1.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 2.845 | 0.753 | 1.096 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1170 | 1183 | 766 | 1787 | 0 | 0 | 0 | 0 | 163 | 0 |
N.S. |
1 | 1.01 | 0.65 | 1.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 2.811 | 0.950 | 1.162 | 0.000 | 0.000 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 1328 | 1292 | 912 | 1954 | 0 | 0 | 0 | 0 | 183 | 0 |
N.S. |
1 | 0.97 | 0.69 | 1.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 3.318 | 1.756 | 1.702 | 0.000 | 0.000 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 160 | 146 | 823 | 0 | 116 | 0 | 108 | 20 | 0 |
N.S. |
1 | 0.98 | 0.89 | 5.02 | 0.00 | 0.71 | 0.00 | 0.66 | 0.12 | 0.00 |
time (sec) |
N/A | 0.709 | 0.242 | 1.290 | 0.000 | 0.073 | 0.000 | 0.132 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 106 | 96 | 547 | 0 | 68 | 0 | 69 | 20 | 0 |
N.S. |
1 | 0.99 | 0.90 | 5.11 | 0.00 | 0.64 | 0.00 | 0.64 | 0.19 | 0.00 |
time (sec) |
N/A | 0.583 | 0.124 | 1.120 | 0.000 | 0.076 | 0.000 | 0.128 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 51 | 272 | 0 | 29 | 0 | 31 | 70 | 0 |
N.S. |
1 | 1.00 | 1.00 | 5.33 | 0.00 | 0.57 | 0.00 | 0.61 | 1.37 | 0.00 |
time (sec) |
N/A | 0.454 | 0.073 | 2.914 | 0.000 | 0.082 | 0.000 | 0.116 | 0.272 | 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 | 18 | 18 | 20 | 18 | 20 | 20 | 15 | 20 | 60 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.83 | 1.11 | 3.33 | 1.11 |
time (sec) |
N/A | 0.288 | 0.210 | 0.025 | 0.100 | 0.076 | 8.891 | 0.113 | 0.209 | 25.357 |
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 | 18 | 18 | 20 | 18 | 20 | 20 | 17 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.94 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.283 | 0.366 | 0.023 | 0.100 | 0.086 | 32.415 | 0.113 | 0.186 | 25.521 |
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 | 18 | 18 | 20 | 18 | 20 | 20 | 15 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.83 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.285 | 0.282 | 0.046 | 0.090 | 0.067 | 10.135 | 0.122 | 0.216 | 25.485 |
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 | 14 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 1.12 | 1.12 | 0.88 | 1.12 | 1.12 | 1.12 |
time (sec) |
N/A | 0.273 | 0.263 | 0.049 | 0.090 | 0.066 | 4.797 | 0.117 | 0.182 | 25.641 |
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 | 14 | 14 | 16 | 14 | 16 | 16 | 14 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 1.14 | 1.14 | 1.00 | 1.14 | 1.14 | 1.14 |
time (sec) |
N/A | 0.264 | 0.015 | 0.049 | 0.102 | 0.074 | 4.795 | 0.128 | 0.197 | 25.621 |
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 | 18 | 18 | 20 | 18 | 20 | 20 | 17 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.94 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.295 | 0.410 | 0.050 | 0.092 | 0.089 | 17.853 | 0.111 | 0.173 | 25.605 |
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 | 18 | 18 | 20 | 18 | 20 | 20 | 17 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.11 | 1.11 | 0.94 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.289 | 0.425 | 0.052 | 0.095 | 0.093 | 23.843 | 0.119 | 0.194 | 25.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 195 | 309 | 290 | 2564 | 0 | 211 | 0 | 487 | 20 | 0 |
N.S. |
1 | 1.58 | 1.49 | 13.15 | 0.00 | 1.08 | 0.00 | 2.50 | 0.10 | 0.00 |
time (sec) |
N/A | 1.104 | 0.194 | 1.424 | 0.000 | 0.073 | 0.000 | 0.146 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 193 | 157 | 1487 | 0 | 141 | 0 | 313 | 20 | 0 |
N.S. |
1 | 1.37 | 1.11 | 10.55 | 0.00 | 1.00 | 0.00 | 2.22 | 0.14 | 0.00 |
time (sec) |
N/A | 0.978 | 0.111 | 1.234 | 0.000 | 0.069 | 0.000 | 0.125 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 79 | 97 | 421 | 0 | 78 | 0 | 141 | 88 | 0 |
N.S. |
1 | 0.95 | 1.17 | 5.07 | 0.00 | 0.94 | 0.00 | 1.70 | 1.06 | 0.00 |
time (sec) |
N/A | 0.515 | 0.048 | 3.156 | 0.000 | 0.086 | 0.000 | 0.123 | 0.214 | 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 | 18 | 18 | 20 | 18 | 69 | 20 | 17 | 20 | 78 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 3.83 | 1.11 | 0.94 | 1.11 | 4.33 | 1.11 |
time (sec) |
N/A | 0.282 | 0.242 | 0.026 | 0.112 | 0.083 | 16.041 | 0.115 | 0.204 | 25.731 |
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 | 18 | 18 | 20 | 18 | 78 | 20 | 19 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 4.33 | 1.11 | 1.06 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.288 | 1.314 | 0.026 | 0.113 | 0.075 | 38.405 | 0.125 | 0.238 | 25.587 |
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 | 18 | 18 | 20 | 18 | 66 | 20 | 17 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 3.67 | 1.11 | 0.94 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.284 | 0.341 | 0.004 | 0.113 | 0.093 | 14.732 | 0.111 | 0.198 | 25.537 |
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 | 74 | 18 | 15 | 18 | 18 | 18 |
N.S. |
1 | 1.00 | 1.12 | 1.00 | 4.62 | 1.12 | 0.94 | 1.12 | 1.12 | 1.12 |
time (sec) |
N/A | 0.272 | 0.460 | 0.025 | 0.104 | 0.095 | 8.728 | 0.117 | 0.192 | 25.485 |
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 | 14 | 14 | 16 | 14 | 77 | 16 | 15 | 16 | 16 | 16 |
N.S. |
1 | 1.00 | 1.14 | 1.00 | 5.50 | 1.14 | 1.07 | 1.14 | 1.14 | 1.14 |
time (sec) |
N/A | 0.256 | 0.290 | 0.052 | 0.107 | 0.075 | 8.920 | 0.120 | 0.186 | 25.495 |
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 | 18 | 18 | 20 | 18 | 79 | 20 | 19 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 4.39 | 1.11 | 1.06 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.277 | 1.094 | 0.052 | 0.110 | 0.080 | 21.661 | 0.115 | 0.190 | 25.463 |
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 | 18 | 18 | 20 | 18 | 80 | 20 | 19 | 20 | 20 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 4.44 | 1.11 | 1.06 | 1.11 | 1.11 | 1.11 |
time (sec) |
N/A | 0.279 | 1.106 | 0.004 | 0.104 | 0.085 | 29.381 | 0.112 | 0.191 | 25.509 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | B | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 994 | 20 | 171 | 22 | 19 | 22 | 1504 | 22 |
N.S. |
1 | 1.00 | 49.70 | 1.00 | 8.55 | 1.10 | 0.95 | 1.10 | 75.20 | 1.10 |
time (sec) |
N/A | 0.531 | 3.101 | 0.067 | 0.246 | 0.082 | 109.178 | 0.251 | 0.173 | 25.471 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | B | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 466 | 20 | 126 | 22 | 19 | 22 | 602 | 22 |
N.S. |
1 | 1.00 | 23.30 | 1.00 | 6.30 | 1.10 | 0.95 | 1.10 | 30.10 | 1.10 |
time (sec) |
N/A | 0.500 | 0.903 | 0.063 | 0.214 | 0.154 | 58.003 | 0.183 | 0.183 | 25.436 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 70 | 0 | 0 | 0 | 377 | 0 | 145 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 4.65 | 0.00 | 1.79 | 0.00 |
time (sec) |
N/A | 0.367 | 0.026 | 0.000 | 0.000 | 0.000 | 34.607 | 0.000 | 0.160 | 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 | 20 | 20 | 22 | 20 | 22 | 22 | 17 | 22 | 24 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.10 | 1.10 | 0.85 | 1.10 | 1.20 | 1.10 |
time (sec) |
N/A | 0.299 | 0.837 | 0.054 | 0.116 | 0.091 | 12.390 | 0.114 | 0.164 | 25.546 |
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 | 20 | 20 | 22 | 20 | 97 | 22 | 19 | 22 | 24 | 22 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 4.85 | 1.10 | 0.95 | 1.10 | 1.20 | 1.10 |
time (sec) |
N/A | 0.292 | 1.716 | 0.030 | 0.124 | 0.097 | 30.968 | 0.115 | 0.157 | 25.773 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 372 | 196 | 171 | 0 | 239 | 266 | 0 | 0 | 186 | 0 |
N.S. |
1 | 0.53 | 0.46 | 0.00 | 0.64 | 0.72 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.878 | 0.278 | 0.000 | 0.050 | 0.118 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 164 | 140 | 0 | 200 | 204 | 0 | 0 | 143 | 0 |
N.S. |
1 | 0.64 | 0.55 | 0.00 | 0.78 | 0.80 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.721 | 0.221 | 0.000 | 0.054 | 0.110 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | B | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 78 | 74 | 0 | 146 | 121 | 0 | 0 | 93 | 0 |
N.S. |
1 | 0.77 | 0.73 | 0.00 | 1.45 | 1.20 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 0.529 | 0.029 | 0.000 | 0.051 | 0.076 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 79 | 168 | 614 | 0 | 0 | 0 | 0 | 60 | 0 |
N.S. |
1 | 0.90 | 1.91 | 6.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.707 | 0.163 | 3.916 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
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 | 124 | 95 | 150 | 0 | 0 | 197 | 0 | 0 | 125 | 0 |
N.S. |
1 | 0.77 | 1.21 | 0.00 | 0.00 | 1.59 | 0.00 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.641 | 0.107 | 0.000 | 0.000 | 0.087 | 0.000 | 0.000 | 0.168 | 0.000 |
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 | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 146 | 288 | 0 | 0 | 279 | 0 | 0 | 164 | 0 |
N.S. |
1 | 0.73 | 1.44 | 0.00 | 0.00 | 1.40 | 0.00 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 1.095 | 0.399 | 0.000 | 0.000 | 0.135 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 14 | 0 | 12 | 14 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 0.00 | 0.92 | 1.08 | 0.00 | 3.08 | 0.00 |
time (sec) |
N/A | 0.275 | 0.005 | 1.552 | 0.000 | 0.100 | 1.484 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 24 | 21 | 40 | 0 | 40 | 100 | 0 | 42 | 0 |
N.S. |
1 | 1.14 | 1.00 | 1.90 | 0.00 | 1.90 | 4.76 | 0.00 | 2.00 | 0.00 |
time (sec) |
N/A | 0.387 | 0.006 | 1.546 | 0.000 | 0.115 | 1.638 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 24 | 21 | 41 | 0 | 41 | 100 | 0 | 44 | 0 |
N.S. |
1 | 1.14 | 1.00 | 1.95 | 0.00 | 1.95 | 4.76 | 0.00 | 2.10 | 0.00 |
time (sec) |
N/A | 0.367 | 0.007 | 1.547 | 0.000 | 0.096 | 1.631 | 0.000 | 0.175 | 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 | 41 | 38 | 39 | 38 | 0 | 54 | 0 | 0 | 49 | 0 |
N.S. |
1 | 0.93 | 0.95 | 0.93 | 0.00 | 1.32 | 0.00 | 0.00 | 1.20 | 0.00 |
time (sec) |
N/A | 0.396 | 0.016 | 2.508 | 0.000 | 0.109 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 42 | 43 | 170 | 0 | 60 | 0 | 0 | 55 | 0 |
N.S. |
1 | 0.95 | 0.98 | 3.86 | 0.00 | 1.36 | 0.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.409 | 0.006 | 0.656 | 0.000 | 0.077 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 76 | 164 | 578 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.96 | 2.08 | 7.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.72 | 0.00 |
time (sec) |
N/A | 0.690 | 0.063 | 4.165 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 109 | 270 | 1409 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.96 | 2.39 | 12.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.810 | 0.181 | 5.042 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 131 | 185 | 284 | 214 | 269 | 335 | 573 | 296 | 208 |
N.S. |
1 | 0.94 | 1.32 | 2.03 | 1.53 | 1.92 | 2.39 | 4.09 | 2.11 | 1.49 |
time (sec) |
N/A | 0.500 | 0.227 | 1.719 | 0.034 | 0.087 | 0.974 | 0.133 | 0.166 | 25.766 |
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 | 112 | 107 | 121 | 184 | 136 | 172 | 202 | 316 | 188 | 131 |
N.S. |
1 | 0.96 | 1.08 | 1.64 | 1.21 | 1.54 | 1.80 | 2.82 | 1.68 | 1.17 |
time (sec) |
N/A | 0.442 | 0.118 | 0.891 | 0.032 | 0.105 | 0.564 | 0.121 | 0.161 | 25.730 |
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 | 84 | 83 | 78 | 77 | 74 | 91 | 105 | 136 | 98 | 68 |
N.S. |
1 | 0.99 | 0.93 | 0.92 | 0.88 | 1.08 | 1.25 | 1.62 | 1.17 | 0.81 |
time (sec) |
N/A | 0.406 | 0.052 | 0.656 | 0.028 | 0.067 | 0.354 | 0.125 | 0.154 | 25.711 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 29 | 24 | 32 | 35 | 32 | 36 | 39 | 35 | 29 |
N.S. |
1 | 1.21 | 1.00 | 1.33 | 1.46 | 1.33 | 1.50 | 1.62 | 1.46 | 1.21 |
time (sec) |
N/A | 0.300 | 0.009 | 0.415 | 0.030 | 0.075 | 0.141 | 0.111 | 0.181 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 57 | 98 | 118 | 0 | 0 | 0 | 97 | 0 |
N.S. |
1 | 1.00 | 0.98 | 1.69 | 2.03 | 0.00 | 0.00 | 0.00 | 1.67 | 0.00 |
time (sec) |
N/A | 0.471 | 0.007 | 2.895 | 0.033 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
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 | 68 | 65 | 62 | 66 | 65 | 80 | 236 | 81 | 115 | 70 |
N.S. |
1 | 0.96 | 0.91 | 0.97 | 0.96 | 1.18 | 3.47 | 1.19 | 1.69 | 1.03 |
time (sec) |
N/A | 0.331 | 0.057 | 1.309 | 0.026 | 0.089 | 1.841 | 0.120 | 0.175 | 26.545 |
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 | 105 | 90 | 80 | 88 | 120 | 236 | 1518 | 185 | 429 | 96 |
N.S. |
1 | 0.86 | 0.76 | 0.84 | 1.14 | 2.25 | 14.46 | 1.76 | 4.09 | 0.91 |
time (sec) |
N/A | 0.437 | 0.085 | 1.586 | 0.032 | 0.100 | 6.210 | 0.120 | 0.168 | 26.100 |
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 | 116 | 105 | 111 | 232 | 443 | 4571 | 365 | 898 | 145 |
N.S. |
1 | 0.87 | 0.79 | 0.83 | 1.74 | 3.33 | 34.37 | 2.74 | 6.75 | 1.09 |
time (sec) |
N/A | 0.488 | 0.121 | 2.233 | 0.035 | 0.090 | 18.396 | 0.124 | 0.175 | 26.335 |
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 | 178 | 189 | 249 | 244 | 177 | 498 | 527 | 218 | 254 | 222 |
N.S. |
1 | 1.06 | 1.40 | 1.37 | 0.99 | 2.80 | 2.96 | 1.22 | 1.43 | 1.25 |
time (sec) |
N/A | 0.818 | 0.837 | 2.020 | 0.111 | 0.119 | 17.511 | 0.133 | 0.165 | 26.022 |
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 | 141 | 151 | 211 | 187 | 131 | 320 | 374 | 152 | 178 | 263 |
N.S. |
1 | 1.07 | 1.50 | 1.33 | 0.93 | 2.27 | 2.65 | 1.08 | 1.26 | 1.87 |
time (sec) |
N/A | 0.711 | 0.541 | 1.391 | 0.106 | 0.120 | 8.718 | 0.135 | 0.181 | 28.778 |
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 | 99 | 112 | 83 | 78 | 80 | 198 | 199 | 85 | 90 | 81 |
N.S. |
1 | 1.13 | 0.84 | 0.79 | 0.81 | 2.00 | 2.01 | 0.86 | 0.91 | 0.82 |
time (sec) |
N/A | 0.481 | 0.030 | 0.815 | 0.104 | 0.090 | 4.050 | 0.130 | 0.181 | 26.662 |
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 | 45 | 50 | 45 | 46 | 45 | 107 | 100 | 41 | 44 | 37 |
N.S. |
1 | 1.11 | 1.00 | 1.02 | 1.00 | 2.38 | 2.22 | 0.91 | 0.98 | 0.82 |
time (sec) |
N/A | 0.296 | 0.011 | 0.125 | 0.109 | 0.074 | 2.008 | 0.117 | 0.171 | 25.953 |
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 | 201 | 213 | 201 | 196 | 0 | 0 | 0 | 0 | 108 | 0 |
N.S. |
1 | 1.06 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.817 | 0.095 | 1.679 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 108 | 137 | 99 | 108 | 261 | 0 | 121 | 179 | 337 |
N.S. |
1 | 0.91 | 1.15 | 0.83 | 0.91 | 2.19 | 0.00 | 1.02 | 1.50 | 2.83 |
time (sec) |
N/A | 0.436 | 0.075 | 1.965 | 0.107 | 0.102 | 0.000 | 0.120 | 0.161 | 26.914 |
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 | 174 | 181 | 217 | 147 | 206 | 744 | 0 | 278 | 600 | 272 |
N.S. |
1 | 1.04 | 1.25 | 0.84 | 1.18 | 4.28 | 0.00 | 1.60 | 3.45 | 1.56 |
time (sec) |
N/A | 0.657 | 0.608 | 2.566 | 0.107 | 0.140 | 0.000 | 0.129 | 0.174 | 26.628 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 320 | 327 | 286 | 398 | 332 | 8840 | 265 | 381 | 435 | 536 |
N.S. |
1 | 1.02 | 0.89 | 1.24 | 1.04 | 27.62 | 0.83 | 1.19 | 1.36 | 1.68 |
time (sec) |
N/A | 1.692 | 0.532 | 2.692 | 0.109 | 8.621 | 22.087 | 0.162 | 0.201 | 25.895 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 250 | 262 | 231 | 336 | 249 | 5799 | 173 | 274 | 290 | 358 |
N.S. |
1 | 1.05 | 0.92 | 1.34 | 1.00 | 23.20 | 0.69 | 1.10 | 1.16 | 1.43 |
time (sec) |
N/A | 1.198 | 0.327 | 1.688 | 0.120 | 2.290 | 15.085 | 0.154 | 0.192 | 25.620 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 229 | 242 | 204 | 247 | 187 | 2284 | 112 | 212 | 207 | 210 |
N.S. |
1 | 1.06 | 0.89 | 1.08 | 0.82 | 9.97 | 0.49 | 0.93 | 0.90 | 0.92 |
time (sec) |
N/A | 0.916 | 0.078 | 1.105 | 0.108 | 1.272 | 10.203 | 0.154 | 0.188 | 25.531 |
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 | 133 | 142 | 129 | 122 | 125 | 110 | 165 | 143 | 91 | 134 |
N.S. |
1 | 1.07 | 0.97 | 0.92 | 0.94 | 0.83 | 1.24 | 1.08 | 0.68 | 1.01 |
time (sec) |
N/A | 0.559 | 0.028 | 0.165 | 0.109 | 0.083 | 24.322 | 0.128 | 0.170 | 0.407 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 308 | 322 | 313 | 101 | 0 | 0 | 0 | 0 | 110 | 0 |
N.S. |
1 | 1.05 | 1.02 | 0.33 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 1.190 | 0.183 | 1.879 | 0.000 | 0.000 | 0.000 | 0.000 | 0.220 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 292 | 296 | 254 | 277 | 311 | 7010 | 0 | 363 | 6006 | 736 |
N.S. |
1 | 1.01 | 0.87 | 0.95 | 1.07 | 24.01 | 0.00 | 1.24 | 20.57 | 2.52 |
time (sec) |
N/A | 1.276 | 0.353 | 2.214 | 0.110 | 1.324 | 0.000 | 0.184 | 0.239 | 25.826 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | C | F(-1) | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 391 | 379 | 325 | 347 | 517 | 13236 | 0 | 660 | 16189 | 2227 |
N.S. |
1 | 0.97 | 0.83 | 0.89 | 1.32 | 33.85 | 0.00 | 1.69 | 41.40 | 5.70 |
time (sec) |
N/A | 1.518 | 0.631 | 3.302 | 0.116 | 8.600 | 0.000 | 0.255 | 0.311 | 26.273 |
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 | 139 | 135 | 114 | 244 | 166 | 239 | 355 | 847 | 339 | 184 |
N.S. |
1 | 0.97 | 0.82 | 1.76 | 1.19 | 1.72 | 2.55 | 6.09 | 2.44 | 1.32 |
time (sec) |
N/A | 0.617 | 0.151 | 0.967 | 0.036 | 0.134 | 1.443 | 0.138 | 0.172 | 25.791 |
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 | 102 | 100 | 86 | 168 | 102 | 153 | 216 | 490 | 218 | 111 |
N.S. |
1 | 0.98 | 0.84 | 1.65 | 1.00 | 1.50 | 2.12 | 4.80 | 2.14 | 1.09 |
time (sec) |
N/A | 0.501 | 0.085 | 0.688 | 0.028 | 0.080 | 0.875 | 0.132 | 0.191 | 25.724 |
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 | 78 | 78 | 85 | 65 | 55 | 80 | 112 | 233 | 115 | 57 |
N.S. |
1 | 1.00 | 1.09 | 0.83 | 0.71 | 1.03 | 1.44 | 2.99 | 1.47 | 0.73 |
time (sec) |
N/A | 0.443 | 0.031 | 0.348 | 0.030 | 0.076 | 0.574 | 0.132 | 0.173 | 25.664 |