Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 89 | 96 | 112 | 0 | 0 | 0 | 66 | 0 |
N.S. |
1 | 1.00 | 1.16 | 1.25 | 1.45 | 0.00 | 0.00 | 0.00 | 0.86 | 0.00 |
time (sec) |
N/A | 0.313 | 0.043 | 0.396 | 0.031 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 83 | 80 | 71 | 81 | 88 | 265 | 88 | 70 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.86 | 0.98 | 1.06 | 3.19 | 1.06 | 0.84 |
time (sec) |
N/A | 0.347 | 0.032 | 0.343 | 0.025 | 0.073 | 0.515 | 0.126 | 0.181 | 3.695 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 202 | 138 | 233 | 214 | 0 | 0 | 0 | 151 | 0 |
N.S. |
1 | 1.00 | 0.68 | 1.15 | 1.06 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 1.218 | 1.322 | 1.164 | 0.034 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 108 | 140 | 170 | 133 | 153 | 683 | 142 | 221 |
N.S. |
1 | 1.00 | 0.69 | 0.90 | 1.09 | 0.85 | 0.98 | 4.38 | 0.91 | 1.42 |
time (sec) |
N/A | 1.067 | 0.037 | 0.579 | 0.032 | 0.081 | 0.676 | 0.136 | 0.166 | 4.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 178 | 178 | 121 | 213 | 198 | 0 | 0 | 0 | 131 | 0 |
N.S. |
1 | 1.00 | 0.68 | 1.20 | 1.11 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 1.000 | 0.849 | 0.710 | 0.034 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 144 | 82 | 119 | 93 | 116 | 133 | 473 | 122 | 111 |
N.S. |
1 | 1.04 | 0.59 | 0.86 | 0.67 | 0.84 | 0.96 | 3.43 | 0.88 | 0.80 |
time (sec) |
N/A | 0.557 | 0.032 | 0.355 | 0.030 | 0.080 | 0.469 | 0.130 | 0.182 | 3.798 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 192 | 99 | 188 | 175 | 0 | 0 | 0 | 109 | 0 |
N.S. |
1 | 1.12 | 0.58 | 1.10 | 1.02 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.877 | 0.509 | 0.460 | 0.035 | 0.000 | 0.000 | 0.000 | 0.173 | 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 | 186 | 186 | 200 | 733 | 0 | 0 | 0 | 0 | 95 | 0 |
N.S. |
1 | 1.00 | 1.08 | 3.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.771 | 0.060 | 7.375 | 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 | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 156 | 156 | 182 | 203 | 200 | 0 | 0 | 0 | 116 | 0 |
N.S. |
1 | 1.00 | 1.17 | 1.30 | 1.28 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.675 | 0.276 | 0.365 | 0.036 | 0.000 | 0.000 | 0.000 | 0.179 | 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 | 162 | 162 | 200 | 779 | 0 | 0 | 0 | 0 | 77 | 0 |
N.S. |
1 | 1.00 | 1.23 | 4.81 | 0.00 | 0.00 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.726 | 0.255 | 6.240 | 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 | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 167 | 153 | 208 | 203 | 0 | 0 | 0 | 99 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.25 | 1.22 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.717 | 0.067 | 0.539 | 0.035 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 214 | 214 | 238 | 1124 | 0 | 0 | 0 | 0 | 130 | 0 |
N.S. |
1 | 1.00 | 1.11 | 5.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.901 | 0.242 | 9.855 | 0.000 | 0.000 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 157 | 118 | 233 | 239 | 0 | 0 | 0 | 118 | 0 |
N.S. |
1 | 1.00 | 0.75 | 1.48 | 1.52 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.829 | 0.530 | 0.565 | 0.036 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 114 | 99 | 149 | 188 | 132 | 148 | 440 | 144 | 335 |
N.S. |
1 | 1.01 | 0.88 | 1.32 | 1.66 | 1.17 | 1.31 | 3.89 | 1.27 | 2.96 |
time (sec) |
N/A | 0.507 | 0.044 | 0.441 | 0.033 | 0.075 | 0.686 | 0.134 | 0.176 | 4.316 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 183 | 140 | 253 | 254 | 0 | 0 | 0 | 138 | 0 |
N.S. |
1 | 1.00 | 0.77 | 1.38 | 1.39 | 0.00 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 1.066 | 0.947 | 0.575 | 0.037 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 170 | 124 | 169 | 204 | 148 | 168 | 651 | 164 | 357 |
N.S. |
1 | 1.00 | 0.73 | 0.99 | 1.20 | 0.87 | 0.99 | 3.83 | 0.96 | 2.10 |
time (sec) |
N/A | 1.130 | 0.047 | 0.456 | 0.035 | 0.090 | 0.993 | 0.132 | 0.167 | 5.122 |
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 | 248 | 298 | 183 | 858 | 0 | 0 | 0 | 0 | 152 | 0 |
N.S. |
1 | 1.20 | 0.74 | 3.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 1.589 | 0.412 | 6.514 | 0.000 | 0.000 | 0.000 | 0.000 | 0.169 | 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 | 21 | 26 | 20 | 21 | 44 | 21 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.05 | 1.30 | 1.00 | 1.05 | 2.20 | 1.05 |
time (sec) |
N/A | 0.222 | 0.693 | 0.201 | 0.091 | 0.077 | 1.094 | 0.928 | 0.184 | 3.505 |
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 | 19 | 19 | 21 | 19 | 20 | 26 | 19 | 20 | 102 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 1.05 | 1.37 | 1.00 | 1.05 | 5.37 | 1.05 |
time (sec) |
N/A | 0.206 | 0.367 | 0.188 | 0.091 | 0.072 | 1.092 | 0.877 | 0.177 | 3.282 |
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 | 22 | 22 | 24 | 22 | 23 | 29 | 20 | 23 | 44 | 23 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.05 | 1.32 | 0.91 | 1.05 | 2.00 | 1.05 |
time (sec) |
N/A | 0.236 | 0.938 | 0.388 | 0.110 | 0.069 | 2.062 | 0.893 | 0.174 | 3.812 |
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 | 102 | 26 | 22 | 21 | 44 | 21 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 5.10 | 1.30 | 1.10 | 1.05 | 2.20 | 1.05 |
time (sec) |
N/A | 0.235 | 0.599 | 0.199 | 0.116 | 0.071 | 1.255 | 0.193 | 0.176 | 3.787 |
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 | 19 | 19 | 21 | 19 | 90 | 26 | 20 | 20 | 42 | 20 |
N.S. |
1 | 1.00 | 1.11 | 1.00 | 4.74 | 1.37 | 1.05 | 1.05 | 2.21 | 1.05 |
time (sec) |
N/A | 0.203 | 0.753 | 0.179 | 0.092 | 0.074 | 1.129 | 0.169 | 0.175 | 3.824 |
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 | 22 | 22 | 24 | 22 | 108 | 29 | 22 | 23 | 44 | 23 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 4.91 | 1.32 | 1.00 | 1.05 | 2.00 | 1.05 |
time (sec) |
N/A | 0.239 | 0.785 | 0.387 | 0.129 | 0.069 | 2.542 | 0.195 | 0.177 | 3.508 |
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 | 144 | 156 | 79 | 84 | 82 | 88 | 97 | 303 | 92 | 80 |
N.S. |
1 | 1.08 | 0.55 | 0.58 | 0.57 | 0.61 | 0.67 | 2.10 | 0.64 | 0.56 |
time (sec) |
N/A | 0.522 | 0.033 | 0.349 | 0.025 | 0.076 | 0.455 | 0.144 | 0.174 | 3.583 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 227 | 271 | 124 | 222 | 199 | 0 | 0 | 0 | 144 | 0 |
N.S. |
1 | 1.19 | 0.55 | 0.98 | 0.88 | 0.00 | 0.00 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 1.164 | 0.826 | 1.079 | 0.034 | 0.000 | 0.000 | 0.000 | 0.168 | 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 | 338 | 466 | 231 | 978 | 0 | 0 | 0 | 0 | 200 | 0 |
N.S. |
1 | 1.38 | 0.68 | 2.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 2.651 | 0.816 | 19.283 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 101 | 60 | 131 | 120 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.16 | 0.69 | 1.51 | 1.38 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.639 | 0.145 | 0.292 | 0.033 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 44 | 42 | 37 | 85 | 56 | 41 | 0 | 38 | 82 |
N.S. |
1 | 1.05 | 1.00 | 0.88 | 2.02 | 1.33 | 0.98 | 0.00 | 0.90 | 1.95 |
time (sec) |
N/A | 0.397 | 0.076 | 0.256 | 0.036 | 0.078 | 0.358 | 0.000 | 0.170 | 3.570 |
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 | 54 | 59 | 44 | 90 | 125 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.09 | 0.81 | 1.67 | 2.31 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.391 | 0.082 | 0.282 | 0.033 | 0.000 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 65 | 22 | 10 | 22 | 11 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 5.00 | 1.69 | 0.77 | 1.69 | 0.85 | 1.77 |
time (sec) |
N/A | 0.200 | 0.005 | 0.197 | 0.034 | 0.070 | 0.462 | 0.109 | 0.177 | 3.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 43 | 109 | 132 | 0 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 0.96 | 2.42 | 2.93 | 0.00 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.378 | 0.108 | 0.259 | 0.035 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 44 | 41 | 46 | 82 | 63 | 37 | 0 | 49 | 80 |
N.S. |
1 | 1.07 | 1.00 | 1.12 | 2.00 | 1.54 | 0.90 | 0.00 | 1.20 | 1.95 |
time (sec) |
N/A | 0.395 | 0.101 | 0.306 | 0.026 | 0.080 | 0.568 | 0.000 | 0.175 | 3.659 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 78 | 60 | 170 | 162 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 0.93 | 0.71 | 2.02 | 1.93 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.609 | 0.246 | 0.381 | 0.035 | 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 | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 135 | 160 | 112 | 750 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.19 | 0.83 | 5.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 1.387 | 0.154 | 14.624 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 90 | 59 | 5330 | 200 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.20 | 0.79 | 71.07 | 2.67 | 0.00 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.719 | 0.179 | 10.532 | 0.035 | 0.000 | 0.000 | 0.000 | 0.168 | 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 | 78 | 89 | 68 | 638 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.14 | 0.87 | 8.18 | 0.00 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.592 | 0.098 | 9.964 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 127 | 22 | 10 | 22 | 11 | 68 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 9.77 | 1.69 | 0.77 | 1.69 | 0.85 | 5.23 |
time (sec) |
N/A | 0.192 | 0.006 | 1.216 | 0.040 | 0.069 | 0.521 | 0.113 | 0.182 | 3.806 |
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 | 66 | 78 | 60 | 1108 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.18 | 0.91 | 16.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.569 | 0.312 | 16.303 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 71 | 61 | 4380 | 237 | 0 | 0 | 0 | 47 | 0 |
N.S. |
1 | 1.08 | 0.92 | 66.36 | 3.59 | 0.00 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.691 | 0.245 | 13.467 | 0.038 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 142 | 133 | 1316 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.03 | 0.96 | 9.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 1.408 | 0.333 | 23.335 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 235 | 142 | 217 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.15 | 0.69 | 1.06 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 1.980 | 0.247 | 22.132 | 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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 120 | 78 | 736 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.17 | 0.76 | 7.15 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 1.002 | 0.231 | 16.364 | 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 | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 116 | 87 | 670 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.07 | 0.81 | 6.20 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.748 | 0.102 | 16.602 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 209 | 22 | 10 | 22 | 11 | 90 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 16.08 | 1.69 | 0.77 | 1.69 | 0.85 | 6.92 |
time (sec) |
N/A | 0.198 | 0.005 | 1.553 | 0.040 | 0.069 | 0.523 | 0.113 | 0.175 | 3.561 |
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 | 91 | 104 | 83 | 1165 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.14 | 0.91 | 12.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.755 | 0.378 | 21.546 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 104 | 93 | 810 | 0 | 0 | 0 | 0 | 49 | 0 |
N.S. |
1 | 1.16 | 1.03 | 9.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 1.020 | 0.231 | 16.441 | 0.000 | 0.000 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 200 | 198 | 165 | 369 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.99 | 0.82 | 1.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 1.934 | 0.359 | 35.397 | 0.000 | 0.000 | 0.000 | 0.000 | 0.189 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 0 | 25 | 14 | 25 | 14 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.00 | 1.67 | 0.93 | 1.67 | 0.93 | 0.73 |
time (sec) |
N/A | 0.202 | 0.007 | 0.299 | 0.000 | 0.066 | 0.671 | 0.116 | 0.171 | 3.492 |
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 | 23 | 22 | 20 | 22 | 26 | 23 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 1.15 | 1.10 | 1.00 | 1.10 | 1.30 | 1.15 |
time (sec) |
N/A | 0.228 | 0.967 | 0.972 | 0.090 | 0.070 | 0.781 | 0.443 | 0.163 | 3.625 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 10 | 21 | 20 | 7 | 21 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 2.33 | 2.22 | 0.78 | 2.33 | 1.00 | 1.00 |
time (sec) |
N/A | 0.200 | 0.079 | 0.211 | 0.031 | 0.078 | 0.264 | 0.123 | 0.171 | 3.570 |
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 | 22 | 22 | 24 | 22 | 25 | 23 | 22 | 24 | 25 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.14 | 1.05 | 1.00 | 1.09 | 1.14 | 1.14 |
time (sec) |
N/A | 0.253 | 0.239 | 1.344 | 0.098 | 0.084 | 1.144 | 0.417 | 0.178 | 3.473 |
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 | 52 | 22 | 24 | 22 | 30 | 23 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 2.60 | 1.10 | 1.20 | 1.10 | 1.50 | 1.15 |
time (sec) |
N/A | 0.287 | 0.145 | 0.965 | 0.082 | 0.073 | 0.878 | 0.125 | 0.192 | 3.455 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 12 | 23 | 22 | 8 | 22 | 11 | 23 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 2.09 | 2.00 | 0.73 | 2.00 | 1.00 | 2.09 |
time (sec) |
N/A | 0.200 | 0.006 | 0.217 | 0.031 | 0.072 | 0.401 | 0.114 | 0.184 | 3.358 |
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 | 22 | 22 | 24 | 22 | 59 | 23 | 26 | 24 | 29 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 2.68 | 1.05 | 1.18 | 1.09 | 1.32 | 1.14 |
time (sec) |
N/A | 0.317 | 0.177 | 0.945 | 0.093 | 0.072 | 1.342 | 0.125 | 0.181 | 3.459 |
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 | 113 | 22 | 24 | 22 | 30 | 23 |
N.S. |
1 | 1.00 | 1.10 | 1.00 | 5.65 | 1.10 | 1.20 | 1.10 | 1.50 | 1.15 |
time (sec) |
N/A | 0.273 | 0.451 | 0.938 | 0.085 | 0.075 | 1.008 | 0.139 | 0.184 | 3.509 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 12 | 42 | 22 | 12 | 22 | 11 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 3.23 | 1.69 | 0.92 | 1.69 | 0.85 | 1.77 |
time (sec) |
N/A | 0.237 | 0.006 | 0.239 | 0.036 | 0.081 | 0.540 | 0.114 | 0.179 | 3.420 |
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 | 22 | 22 | 24 | 22 | 134 | 23 | 26 | 24 | 29 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 6.09 | 1.05 | 1.18 | 1.09 | 1.32 | 1.14 |
time (sec) |
N/A | 0.330 | 0.599 | 0.607 | 0.097 | 0.071 | 1.683 | 0.141 | 0.189 | 3.471 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 18 | 0 | 84 | 26 | 30 | 19 | 33 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 0.00 | 4.94 | 1.53 | 1.76 | 1.12 | 1.94 |
time (sec) |
N/A | 0.213 | 0.010 | 1.073 | 0.000 | 0.082 | 0.914 | 0.112 | 0.191 | 3.748 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 129 | 64 | 159 | 177 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.18 | 0.59 | 1.46 | 1.62 | 0.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.754 | 0.125 | 0.512 | 0.034 | 0.000 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 45 | 55 | 126 | 65 | 0 | 0 | 52 | 110 |
N.S. |
1 | 1.00 | 0.79 | 0.96 | 2.21 | 1.14 | 0.00 | 0.00 | 0.91 | 1.93 |
time (sec) |
N/A | 0.321 | 0.123 | 0.595 | 0.032 | 0.075 | 0.000 | 0.000 | 0.183 | 3.628 |
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 | 55 | 60 | 66 | 37 | 62 | 48 | 61 | 154 | 86 | 37 |
N.S. |
1 | 1.09 | 1.20 | 0.67 | 1.13 | 0.87 | 1.11 | 2.80 | 1.56 | 0.67 |
time (sec) |
N/A | 0.242 | 0.093 | 0.375 | 0.032 | 0.075 | 0.443 | 0.116 | 0.187 | 3.532 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 44 | 54 | 122 | 64 | 0 | 255 | 53 | 106 |
N.S. |
1 | 1.00 | 0.81 | 1.00 | 2.26 | 1.19 | 0.00 | 4.72 | 0.98 | 1.96 |
time (sec) |
N/A | 0.223 | 0.101 | 0.574 | 0.032 | 0.072 | 0.000 | 1.105 | 0.189 | 3.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 109 | 63 | 190 | 206 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.20 | 0.69 | 2.09 | 2.26 | 0.00 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.681 | 0.138 | 0.463 | 0.040 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 102 | 77 | 127 | 150 | 118 | 253 | 0 | 134 | 132 |
N.S. |
1 | 1.24 | 0.94 | 1.55 | 1.83 | 1.44 | 3.09 | 0.00 | 1.63 | 1.61 |
time (sec) |
N/A | 0.708 | 0.149 | 0.529 | 0.032 | 0.078 | 0.885 | 0.000 | 0.166 | 3.843 |
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 | 123 | 191 | 83 | 213 | 233 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.55 | 0.67 | 1.73 | 1.89 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 1.634 | 0.254 | 0.660 | 0.036 | 0.000 | 0.000 | 0.000 | 0.163 | 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 | 161 | 184 | 103 | 735 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.14 | 0.64 | 4.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 1.320 | 0.141 | 24.043 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 105 | 93 | 72 | 273 | 96 | 0 | 0 | 121 | 231 |
N.S. |
1 | 1.12 | 0.99 | 0.77 | 2.90 | 1.02 | 0.00 | 0.00 | 1.29 | 2.46 |
time (sec) |
N/A | 0.391 | 0.164 | 22.652 | 0.036 | 0.083 | 0.000 | 0.000 | 0.182 | 4.406 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 85 | 43 | 52 | 146 | 66 | 0 | 140 | 55 | 198 |
N.S. |
1 | 1.04 | 0.52 | 0.63 | 1.78 | 0.80 | 0.00 | 1.71 | 0.67 | 2.41 |
time (sec) |
N/A | 0.351 | 0.052 | 0.502 | 0.031 | 0.075 | 0.000 | 0.119 | 0.172 | 3.793 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 100 | 93 | 72 | 268 | 95 | 0 | 88 | 121 | 213 |
N.S. |
1 | 1.14 | 1.06 | 0.82 | 3.05 | 1.08 | 0.00 | 1.00 | 1.38 | 2.42 |
time (sec) |
N/A | 0.340 | 0.125 | 23.138 | 0.037 | 0.079 | 0.000 | 1.220 | 0.178 | 4.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 167 | 106 | 1203 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.23 | 0.78 | 8.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 1.248 | 0.233 | 42.651 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 175 | 97 | 3005 | 406 | 0 | 0 | 0 | 207 | 0 |
N.S. |
1 | 1.23 | 0.68 | 21.16 | 2.86 | 0.00 | 0.00 | 0.00 | 1.46 | 0.00 |
time (sec) |
N/A | 1.497 | 0.298 | 20.664 | 0.041 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 313 | 146 | 1415 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.53 | 0.71 | 6.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 3.692 | 0.686 | 43.704 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 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 | 227 | 259 | 139 | 806 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.14 | 0.61 | 3.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 1.919 | 0.139 | 27.717 | 0.000 | 0.000 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 132 | 72 | 87 | 465 | 114 | 0 | 0 | 85 | 410 |
N.S. |
1 | 1.09 | 0.60 | 0.72 | 3.84 | 0.94 | 0.00 | 0.00 | 0.70 | 3.39 |
time (sec) |
N/A | 0.488 | 0.068 | 22.721 | 0.048 | 0.075 | 0.000 | 0.000 | 0.173 | 4.504 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 133 | 91 | 72 | 298 | 97 | 0 | 192 | 121 | 239 |
N.S. |
1 | 1.12 | 0.76 | 0.61 | 2.50 | 0.82 | 0.00 | 1.61 | 1.02 | 2.01 |
time (sec) |
N/A | 0.488 | 0.057 | 32.194 | 0.038 | 0.070 | 0.000 | 0.122 | 0.174 | 4.431 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 127 | 71 | 86 | 459 | 113 | 0 | 122 | 86 | 378 |
N.S. |
1 | 1.10 | 0.62 | 0.75 | 3.99 | 0.98 | 0.00 | 1.06 | 0.75 | 3.29 |
time (sec) |
N/A | 0.454 | 0.048 | 24.033 | 0.044 | 0.076 | 0.000 | 1.394 | 0.173 | 4.266 |
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 | 193 | 241 | 135 | 1300 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.25 | 0.70 | 6.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 1.811 | 0.276 | 65.895 | 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 | C | A | F(-2) | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 191 | 235 | 144 | 271 | 0 | 0 | 0 | 0 | 175 | 0 |
N.S. |
1 | 1.23 | 0.75 | 1.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.92 | 0.00 |
time (sec) |
N/A | 2.166 | 0.259 | 36.934 | 0.000 | 0.000 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 302 | 443 | 215 | 447 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.47 | 0.71 | 1.48 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 4.824 | 0.472 | 90.923 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | F | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 111 | 87 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.08 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.637 | 0.182 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 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 | 22 | 22 | 24 | 22 | 23 | 31 | 22 | 23 | 36 | 23 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.05 | 1.41 | 1.00 | 1.05 | 1.64 | 1.05 |
time (sec) |
N/A | 0.241 | 3.279 | 1.761 | 0.102 | 0.091 | 0.791 | 0.542 | 0.161 | 3.522 |
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 | 22 | 22 | 24 | 22 | 23 | 31 | 22 | 23 | 36 | 23 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.05 | 1.41 | 1.00 | 1.05 | 1.64 | 1.05 |
time (sec) |
N/A | 0.254 | 1.083 | 2.177 | 0.105 | 0.080 | 0.763 | 0.504 | 0.165 | 3.501 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 25 | 27 | 22 | 0 | 58 | 0 | 0 | 46 | 0 |
N.S. |
1 | 0.93 | 1.00 | 0.81 | 0.00 | 2.15 | 0.00 | 0.00 | 1.70 | 0.00 |
time (sec) |
N/A | 0.343 | 0.152 | 1.009 | 0.000 | 0.072 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 13 | 0 | 38 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.00 | 2.71 | 0.00 | 0.00 | 2.43 | 0.00 |
time (sec) |
N/A | 0.321 | 0.117 | 0.968 | 0.000 | 0.072 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 25 | 27 | 22 | 0 | 54 | 0 | 0 | 32 | 0 |
N.S. |
1 | 0.93 | 1.00 | 0.81 | 0.00 | 2.00 | 0.00 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 0.295 | 0.108 | 1.000 | 0.000 | 0.080 | 0.000 | 0.000 | 0.174 | 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 | 22 | 22 | 24 | 22 | 23 | 28 | 22 | 23 | 34 | 23 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.05 | 1.27 | 1.00 | 1.05 | 1.55 | 1.05 |
time (sec) |
N/A | 0.242 | 0.711 | 1.684 | 0.115 | 0.078 | 1.089 | 0.421 | 0.169 | 3.528 |
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 | 22 | 22 | 24 | 22 | 117 | 31 | 24 | 23 | 42 | 23 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 5.32 | 1.41 | 1.09 | 1.05 | 1.91 | 1.05 |
time (sec) |
N/A | 1.406 | 2.303 | 1.731 | 0.132 | 0.067 | 0.968 | 0.150 | 0.165 | 3.606 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 36 | 36 | 0 | 111 | 0 | 0 | 111 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.95 | 0.00 | 2.92 | 0.00 | 0.00 | 2.92 | 0.00 |
time (sec) |
N/A | 0.512 | 0.175 | 1.271 | 0.000 | 0.093 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 75 | 32 | 28 | 0 | 106 | 0 | 0 | 40 | 0 |
N.S. |
1 | 2.08 | 0.89 | 0.78 | 0.00 | 2.94 | 0.00 | 0.00 | 1.11 | 0.00 |
time (sec) |
N/A | 0.885 | 0.070 | 1.471 | 0.000 | 0.085 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 30 | 36 | 0 | 102 | 0 | 0 | 112 | 0 |
N.S. |
1 | 1.00 | 0.86 | 1.03 | 0.00 | 2.91 | 0.00 | 0.00 | 3.20 | 0.00 |
time (sec) |
N/A | 0.443 | 0.117 | 1.319 | 0.000 | 0.084 | 0.000 | 0.000 | 0.164 | 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 | 22 | 22 | 24 | 22 | 123 | 28 | 24 | 23 | 40 | 23 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 5.59 | 1.27 | 1.09 | 1.05 | 1.82 | 1.05 |
time (sec) |
N/A | 1.382 | 2.960 | 1.792 | 0.128 | 0.074 | 1.314 | 0.143 | 0.164 | 3.544 |
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 | 22 | 22 | 24 | 22 | 209 | 31 | 24 | 23 | 42 | 23 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 9.50 | 1.41 | 1.09 | 1.05 | 1.91 | 1.05 |
time (sec) |
N/A | 0.952 | 5.993 | 1.743 | 0.149 | 0.074 | 1.014 | 0.176 | 0.170 | 3.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 108 | 47 | 51 | 0 | 131 | 0 | 0 | 128 | 0 |
N.S. |
1 | 1.69 | 0.73 | 0.80 | 0.00 | 2.05 | 0.00 | 0.00 | 2.00 | 0.00 |
time (sec) |
N/A | 1.086 | 0.093 | 1.487 | 0.000 | 0.071 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 66 | 43 | 0 | 135 | 0 | 0 | 221 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.60 | 0.00 | 1.88 | 0.00 | 0.00 | 3.07 | 0.00 |
time (sec) |
N/A | 0.522 | 0.059 | 1.503 | 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 | A | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 103 | 58 | 51 | 0 | 122 | 0 | 0 | 129 | 0 |
N.S. |
1 | 1.78 | 1.00 | 0.88 | 0.00 | 2.10 | 0.00 | 0.00 | 2.22 | 0.00 |
time (sec) |
N/A | 1.068 | 0.061 | 1.399 | 0.000 | 0.077 | 0.000 | 0.000 | 0.169 | 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 | 22 | 22 | 24 | 22 | 217 | 28 | 24 | 23 | 40 | 23 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 9.86 | 1.27 | 1.09 | 1.05 | 1.82 | 1.05 |
time (sec) |
N/A | 1.044 | 2.685 | 1.549 | 0.150 | 0.072 | 1.429 | 0.173 | 0.166 | 3.604 |
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 | 97 | 103 | 73 | 68 | 0 | 151 | 0 | 0 | 238 | 0 |
N.S. |
1 | 1.06 | 0.75 | 0.70 | 0.00 | 1.56 | 0.00 | 0.00 | 2.45 | 0.00 |
time (sec) |
N/A | 0.690 | 0.152 | 1.451 | 0.000 | 0.083 | 0.000 | 0.000 | 0.172 | 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 | 120 | 171 | 84 | 83 | 0 | 171 | 0 | 0 | 252 | 0 |
N.S. |
1 | 1.42 | 0.70 | 0.69 | 0.00 | 1.42 | 0.00 | 0.00 | 2.10 | 0.00 |
time (sec) |
N/A | 1.439 | 0.073 | 1.512 | 0.000 | 0.085 | 0.000 | 0.000 | 0.177 | 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 | 168 | 101 | 98 | 0 | 200 | 0 | 0 | 252 | 0 |
N.S. |
1 | 1.09 | 0.66 | 0.64 | 0.00 | 1.30 | 0.00 | 0.00 | 1.64 | 0.00 |
time (sec) |
N/A | 0.933 | 0.138 | 1.615 | 0.000 | 0.076 | 0.000 | 0.000 | 0.184 | 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 | 177 | 236 | 112 | 113 | 0 | 220 | 0 | 0 | 252 | 0 |
N.S. |
1 | 1.33 | 0.63 | 0.64 | 0.00 | 1.24 | 0.00 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 1.710 | 0.075 | 1.683 | 0.000 | 0.074 | 0.000 | 0.000 | 0.174 | 0.000 |