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 | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 75 | 107 | 116 | 276 | 1516 | 483 | 325 | 267 |
N.S. |
1 | 1.00 | 0.69 | 0.99 | 1.07 | 2.56 | 14.04 | 4.47 | 3.01 | 2.47 |
time (sec) |
N/A | 0.429 | 0.042 | 0.234 | 0.040 | 0.091 | 0.393 | 0.133 | 0.231 | 8.873 |
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 | 73 | 73 | 47 | 72 | 70 | 133 | 658 | 230 | 145 | 161 |
N.S. |
1 | 1.00 | 0.64 | 0.99 | 0.96 | 1.82 | 9.01 | 3.15 | 1.99 | 2.21 |
time (sec) |
N/A | 0.341 | 0.049 | 0.046 | 0.039 | 0.089 | 0.295 | 0.132 | 0.241 | 8.809 |
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 | 35 | 35 | 25 | 34 | 34 | 35 | 105 | 51 | 36 | 35 |
N.S. |
1 | 1.00 | 0.71 | 0.97 | 0.97 | 1.00 | 3.00 | 1.46 | 1.03 | 1.00 |
time (sec) |
N/A | 0.304 | 0.011 | 0.035 | 0.028 | 0.076 | 0.192 | 0.124 | 0.240 | 9.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 70 | 0 | 0 | 0 | 146 | 0 | 284 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 1.60 | 0.00 | 3.12 | 0.00 |
time (sec) |
N/A | 0.408 | 0.037 | 0.000 | 0.000 | 0.000 | 1.171 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 115 | 75 | 0 | 0 | 0 | 678 | 0 | 882 | 0 |
N.S. |
1 | 1.06 | 0.69 | 0.00 | 0.00 | 0.00 | 6.22 | 0.00 | 8.09 | 0.00 |
time (sec) |
N/A | 0.428 | 0.025 | 0.000 | 0.000 | 0.000 | 2.338 | 0.000 | 0.286 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 154 | 87 | 0 | 0 | 0 | 1991 | 0 | 0 | 0 |
N.S. |
1 | 1.16 | 0.65 | 0.00 | 0.00 | 0.00 | 14.97 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.495 | 0.028 | 0.000 | 0.000 | 0.000 | 3.481 | 0.000 | 0.285 | 0.000 |
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 | 215 | 215 | 161 | 214 | 264 | 1085 | 6928 | 1802 | 1305 | 741 |
N.S. |
1 | 1.00 | 0.75 | 1.00 | 1.23 | 5.05 | 32.22 | 8.38 | 6.07 | 3.45 |
time (sec) |
N/A | 0.685 | 0.097 | 0.308 | 0.059 | 0.100 | 0.787 | 0.155 | 0.308 | 9.245 |
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 | 168 | 168 | 121 | 167 | 190 | 669 | 4094 | 1129 | 800 | 558 |
N.S. |
1 | 1.00 | 0.72 | 0.99 | 1.13 | 3.98 | 24.37 | 6.72 | 4.76 | 3.32 |
time (sec) |
N/A | 0.572 | 0.065 | 0.286 | 0.049 | 0.117 | 0.585 | 0.142 | 0.272 | 9.077 |
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 | 121 | 121 | 74 | 120 | 116 | 343 | 2014 | 586 | 395 | 371 |
N.S. |
1 | 1.00 | 0.61 | 0.99 | 0.96 | 2.83 | 16.64 | 4.84 | 3.26 | 3.07 |
time (sec) |
N/A | 0.451 | 0.085 | 0.240 | 0.044 | 0.084 | 0.434 | 0.131 | 0.267 | 8.858 |
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 | 58 | 58 | 41 | 57 | 56 | 87 | 330 | 135 | 94 | 95 |
N.S. |
1 | 1.00 | 0.71 | 0.98 | 0.97 | 1.50 | 5.69 | 2.33 | 1.62 | 1.64 |
time (sec) |
N/A | 0.317 | 0.026 | 0.231 | 0.038 | 0.077 | 0.346 | 0.125 | 0.250 | 8.768 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 163 | 163 | 122 | 0 | 0 | 0 | 233 | 0 | 1057 | 0 |
N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 1.43 | 0.00 | 6.48 | 0.00 |
time (sec) |
N/A | 0.592 | 0.102 | 0.000 | 0.000 | 0.000 | 1.856 | 0.000 | 0.295 | 0.000 |
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 | 181 | 192 | 130 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.940 | 0.100 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.249 | 0.000 |
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 | 216 | 244 | 145 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.13 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.262 | 0.066 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.307 | 0.000 |
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 | 169 | 169 | 101 | 168 | 162 | 649 | 4398 | 1102 | 749 | 695 |
N.S. |
1 | 1.00 | 0.60 | 0.99 | 0.96 | 3.84 | 26.02 | 6.52 | 4.43 | 4.11 |
time (sec) |
N/A | 0.561 | 0.245 | 0.267 | 0.048 | 0.094 | 0.625 | 0.132 | 0.303 | 9.053 |
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 | 217 | 217 | 128 | 1255 | 208 | 1051 | 8032 | 1778 | 1215 | 1075 |
N.S. |
1 | 1.00 | 0.59 | 5.78 | 0.96 | 4.84 | 37.01 | 8.19 | 5.60 | 4.95 |
time (sec) |
N/A | 0.631 | 0.290 | 0.312 | 0.055 | 0.092 | 0.886 | 0.152 | 0.249 | 9.693 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 170 | 128 | 0 | 0 | 0 | 405 | 0 | 452 | 0 |
N.S. |
1 | 1.01 | 0.76 | 0.00 | 0.00 | 0.00 | 2.41 | 0.00 | 2.69 | 0.00 |
time (sec) |
N/A | 0.461 | 0.060 | 0.000 | 0.000 | 0.000 | 3.015 | 0.000 | 0.258 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 129 | 132 | 107 | 0 | 0 | 0 | 299 | 0 | 178 | 0 |
N.S. |
1 | 1.02 | 0.83 | 0.00 | 0.00 | 0.00 | 2.32 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 0.268 | 0.036 | 0.000 | 0.000 | 0.000 | 2.276 | 0.000 | 0.243 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 82 | 0 | 0 | 0 | 189 | 0 | 57 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 2.08 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.202 | 0.023 | 0.000 | 0.000 | 0.000 | 1.541 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 42 | 0 | 0 | 0 | 95 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 2.16 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.161 | 0.005 | 0.000 | 0.000 | 0.000 | 0.557 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 170 | 127 | 0 | 0 | 0 | 983 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.75 | 0.00 | 0.00 | 0.00 | 5.78 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.333 | 0.068 | 0.000 | 0.000 | 0.000 | 5.349 | 0.000 | 0.254 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 233 | 233 | 178 | 0 | 0 | 0 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.00 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.425 | 0.084 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.256 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 315 | 315 | 241 | 0 | 0 | 0 | 0 | 0 | 80 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.561 | 0.242 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.272 | 0.000 |
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 | 205 | 200 | 177 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.376 | 0.079 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.305 | 0.000 |
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 | 155 | 166 | 132 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.07 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.301 | 0.042 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 82 | 0 | 0 | 0 | 770 | 0 | 410 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 8.46 | 0.00 | 4.51 | 0.00 |
time (sec) |
N/A | 0.207 | 0.028 | 0.000 | 0.000 | 0.000 | 15.833 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 42 | 0 | 0 | 0 | 398 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 9.05 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.164 | 0.005 | 0.000 | 0.000 | 0.000 | 2.902 | 0.000 | 0.246 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 294 | 294 | 216 | 0 | 0 | 0 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.00 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.451 | 0.095 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.255 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 372 | 372 | 289 | 0 | 0 | 0 | 0 | 0 | 97 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.580 | 0.145 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.274 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 82 | 0 | 0 | 0 | 2530 | 0 | 846 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.00 | 0.00 | 0.00 | 27.80 | 0.00 | 9.30 | 0.00 |
time (sec) |
N/A | 0.206 | 0.031 | 0.000 | 0.000 | 0.000 | 58.826 | 0.000 | 0.289 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 166 | 119 | 0 | 0 | 0 | 277 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.71 | 0.00 | 0.00 | 0.00 | 1.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.304 | 0.493 | 0.000 | 0.000 | 0.000 | 9.068 | 0.000 | 0.403 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 166 | 119 | 0 | 0 | 0 | 178 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.71 | 0.00 | 0.00 | 0.00 | 1.06 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.294 | 0.369 | 0.000 | 0.000 | 0.000 | 4.121 | 0.000 | 0.362 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 168 | 166 | 119 | 0 | 0 | 0 | 87 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.71 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.297 | 0.280 | 0.000 | 0.000 | 0.000 | 1.757 | 0.000 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 164 | 119 | 0 | 0 | 0 | 83 | 0 | 1169 | 0 |
N.S. |
1 | 0.99 | 0.72 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 | 7.04 | 0.00 |
time (sec) |
N/A | 0.293 | 0.254 | 0.000 | 0.000 | 0.000 | 1.592 | 0.000 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 159 | 162 | 119 | 0 | 0 | 0 | 83 | 0 | 0 | 0 |
N.S. |
1 | 1.02 | 0.75 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.313 | 0.324 | 0.000 | 0.000 | 0.000 | 2.552 | 0.000 | 0.335 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 174 | 118 | 0 | 0 | 0 | 83 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.74 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.329 | 0.361 | 0.000 | 0.000 | 0.000 | 5.853 | 0.000 | 0.345 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 386 | 363 | 205 | 0 | 0 | 0 | 435 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.53 | 0.00 | 0.00 | 0.00 | 1.13 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.714 | 1.217 | 0.000 | 0.000 | 0.000 | 16.486 | 0.000 | 0.475 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 386 | 363 | 205 | 0 | 0 | 0 | 282 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.53 | 0.00 | 0.00 | 0.00 | 0.73 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.704 | 0.600 | 0.000 | 0.000 | 0.000 | 8.371 | 0.000 | 0.468 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 386 | 363 | 205 | 0 | 0 | 0 | 138 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.53 | 0.00 | 0.00 | 0.00 | 0.36 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.686 | 0.420 | 0.000 | 0.000 | 0.000 | 3.075 | 0.000 | 0.377 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 384 | 361 | 205 | 0 | 0 | 0 | 133 | 0 | 0 | 0 |
N.S. |
1 | 0.94 | 0.53 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.694 | 0.417 | 0.000 | 0.000 | 0.000 | 2.581 | 0.000 | 0.388 | 0.000 |
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 | 357 | 354 | 205 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.874 | 0.544 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.440 | 0.000 |
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 | 337 | 337 | 205 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.847 | 0.897 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.493 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 158 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.363 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 3.072 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 154 | 0 | 0 | 0 | 0 | 0 | 0 | 274 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.78 | 0.00 |
time (sec) |
N/A | 0.338 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.260 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 152 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.336 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.590 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 152 | 152 | 0 | 0 | 0 | 0 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.332 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.552 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 158 | 0 | 0 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.354 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 158 | 158 | 0 | 0 | 0 | 0 | 0 | 0 | 86 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.344 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.657 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 526 | 315 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.585 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 38.999 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 437 | 315 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.602 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 19.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 307 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.26 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.593 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 7.840 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 303 | 0 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.573 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 3.819 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 377 | 303 | 0 | 0 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 0.80 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.578 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 3.106 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 531 | 315 | 0 | 0 | 0 | 0 | 0 | 0 | 103 | 0 |
N.S. |
1 | 0.59 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.618 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 3.652 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | No | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 670 | 315 | 0 | 0 | 0 | 0 | 0 | 0 | 144 | 0 |
N.S. |
1 | 0.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.629 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 5.745 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 268 | 184 | 0 | 0 | 0 | 243 | 0 | 88 | 0 |
N.S. |
1 | 1.09 | 0.75 | 0.00 | 0.00 | 0.00 | 0.99 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.605 | 0.150 | 0.000 | 0.000 | 0.000 | 3.020 | 0.000 | 22.861 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 206 | 160 | 0 | 0 | 0 | 178 | 0 | 63 | 0 |
N.S. |
1 | 1.07 | 0.83 | 0.00 | 0.00 | 0.00 | 0.93 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.331 | 0.068 | 0.000 | 0.000 | 0.000 | 2.152 | 0.000 | 0.427 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 108 | 0 | 0 | 0 | 114 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.248 | 0.043 | 0.000 | 0.000 | 0.000 | 1.508 | 0.000 | 0.342 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 66 | 0 | 0 | 0 | 58 | 0 | 18 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.183 | 0.011 | 0.000 | 0.000 | 0.000 | 0.596 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 168 | 0 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.341 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.351 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 248 | 0 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.480 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.525 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 264 | 270 | 185 | 0 | 0 | 0 | 495 | 0 | 24 | 0 |
N.S. |
1 | 1.02 | 0.70 | 0.00 | 0.00 | 0.00 | 1.88 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.607 | 0.145 | 0.000 | 0.000 | 0.000 | 8.136 | 0.000 | 200.043 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 202 | 208 | 161 | 0 | 0 | 0 | 364 | 0 | 132 | 0 |
N.S. |
1 | 1.03 | 0.80 | 0.00 | 0.00 | 0.00 | 1.80 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.339 | 0.069 | 0.000 | 0.000 | 0.000 | 5.543 | 0.000 | 1.137 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 141 | 141 | 109 | 0 | 0 | 0 | 233 | 0 | 80 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 1.65 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.255 | 0.042 | 0.000 | 0.000 | 0.000 | 3.551 | 0.000 | 0.549 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 67 | 0 | 0 | 0 | 58 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.84 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.188 | 0.015 | 0.000 | 0.000 | 0.000 | 1.594 | 0.000 | 0.263 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 170 | 0 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.364 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.036 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 255 | 251 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.500 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 3.508 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 246 | 260 | 184 | 0 | 0 | 0 | 236 | 0 | 96 | 0 |
N.S. |
1 | 1.06 | 0.75 | 0.00 | 0.00 | 0.00 | 0.96 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.614 | 0.142 | 0.000 | 0.000 | 0.000 | 3.188 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 192 | 198 | 160 | 0 | 0 | 0 | 173 | 0 | 69 | 0 |
N.S. |
1 | 1.03 | 0.83 | 0.00 | 0.00 | 0.00 | 0.90 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.349 | 0.073 | 0.000 | 0.000 | 0.000 | 1.918 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 139 | 108 | 0 | 0 | 0 | 110 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.248 | 0.043 | 0.000 | 0.000 | 0.000 | 1.350 | 0.000 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 68 | 66 | 0 | 0 | 0 | 56 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.182 | 0.016 | 0.000 | 0.000 | 0.000 | 0.520 | 0.000 | 0.224 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 168 | 0 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.347 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.257 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 248 | 0 | 0 | 0 | 0 | 0 | 0 | 64 | 0 |
N.S. |
1 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.464 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.548 | 0.000 |
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 | 251 | 242 | 187 | 0 | 0 | 0 | 0 | 0 | 160 | 0 |
N.S. |
1 | 0.96 | 0.75 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.394 | 0.151 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.305 | 0.000 |
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 | 199 | 210 | 163 | 0 | 0 | 0 | 0 | 0 | 117 | 0 |
N.S. |
1 | 1.06 | 0.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.332 | 0.071 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.290 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 111 | 0 | 0 | 0 | 110 | 0 | 74 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.76 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.247 | 0.042 | 0.000 | 0.000 | 0.000 | 5.036 | 0.000 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 69 | 0 | 0 | 0 | 56 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.183 | 0.015 | 0.000 | 0.000 | 0.000 | 0.684 | 0.000 | 0.261 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 174 | 0 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.343 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.035 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 257 | 0 | 0 | 0 | 0 | 0 | 0 | 105 | 0 |
N.S. |
1 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.497 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.843 | 0.000 |
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 | 278 | 258 | 187 | 0 | 0 | 0 | 0 | 0 | 236 | 0 |
N.S. |
1 | 0.93 | 0.67 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.407 | 0.155 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.440 | 0.000 |
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 | 211 | 226 | 163 | 0 | 0 | 0 | 0 | 0 | 174 | 0 |
N.S. |
1 | 1.07 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.82 | 0.00 |
time (sec) |
N/A | 0.352 | 0.072 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.394 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 145 | 111 | 0 | 0 | 0 | 110 | 0 | 112 | 0 |
N.S. |
1 | 1.00 | 0.77 | 0.00 | 0.00 | 0.00 | 0.76 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.263 | 0.048 | 0.000 | 0.000 | 0.000 | 66.227 | 0.000 | 0.383 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 69 | 0 | 0 | 0 | 56 | 0 | 55 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.79 | 0.00 | 0.77 | 0.00 |
time (sec) |
N/A | 0.185 | 0.017 | 0.000 | 0.000 | 0.000 | 1.289 | 0.000 | 0.240 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 174 | 0 | 0 | 0 | 0 | 0 | 0 | 104 | 0 |
N.S. |
1 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.349 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.806 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 261 | 257 | 0 | 0 | 0 | 0 | 0 | 0 | 146 | 0 |
N.S. |
1 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.486 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.127 | 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 | 171 | 171 | 145 | 402 | 286 | 519 | 6999 | 882 | 568 | 486 |
N.S. |
1 | 1.00 | 0.85 | 2.35 | 1.67 | 3.04 | 40.93 | 5.16 | 3.32 | 2.84 |
time (sec) |
N/A | 0.328 | 0.062 | 0.309 | 0.042 | 0.097 | 1.829 | 0.130 | 0.221 | 9.181 |
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 | 135 | 135 | 114 | 318 | 210 | 368 | 4134 | 624 | 397 | 363 |
N.S. |
1 | 1.00 | 0.84 | 2.36 | 1.56 | 2.73 | 30.62 | 4.62 | 2.94 | 2.69 |
time (sec) |
N/A | 0.287 | 0.041 | 0.302 | 0.049 | 0.090 | 1.229 | 0.132 | 0.220 | 8.601 |
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 | 102 | 102 | 112 | 195 | 146 | 252 | 2181 | 410 | 256 | 255 |
N.S. |
1 | 1.00 | 1.10 | 1.91 | 1.43 | 2.47 | 21.38 | 4.02 | 2.51 | 2.50 |
time (sec) |
N/A | 0.251 | 0.065 | 0.288 | 0.038 | 0.092 | 0.772 | 0.127 | 0.225 | 8.501 |
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 | 70 | 70 | 59 | 100 | 89 | 149 | 952 | 237 | 142 | 163 |
N.S. |
1 | 1.00 | 0.84 | 1.43 | 1.27 | 2.13 | 13.60 | 3.39 | 2.03 | 2.33 |
time (sec) |
N/A | 0.209 | 0.034 | 0.289 | 0.037 | 0.085 | 0.485 | 0.122 | 0.227 | 8.383 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 64 | 0 | 0 | 0 | 279 | 0 | 213 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.00 | 0.00 | 0.00 | 3.62 | 0.00 | 2.77 | 0.00 |
time (sec) |
N/A | 0.220 | 0.021 | 0.000 | 0.000 | 0.000 | 2.220 | 0.000 | 0.213 | 0.000 |
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 | 56 | 82 | 48 | 0 | 0 | 0 | 173 | 0 | 118 | 0 |
N.S. |
1 | 1.46 | 0.86 | 0.00 | 0.00 | 0.00 | 3.09 | 0.00 | 2.11 | 0.00 |
time (sec) |
N/A | 0.199 | 0.014 | 0.000 | 0.000 | 0.000 | 1.651 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 106 | 62 | 0 | 0 | 0 | 860 | 0 | 149 | 0 |
N.S. |
1 | 1.06 | 0.62 | 0.00 | 0.00 | 0.00 | 8.60 | 0.00 | 1.49 | 0.00 |
time (sec) |
N/A | 0.225 | 0.012 | 0.000 | 0.000 | 0.000 | 3.568 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 115 | 62 | 0 | 0 | 0 | 2926 | 0 | 216 | 0 |
N.S. |
1 | 1.06 | 0.57 | 0.00 | 0.00 | 0.00 | 27.09 | 0.00 | 2.00 | 0.00 |
time (sec) |
N/A | 0.226 | 0.014 | 0.000 | 0.000 | 0.000 | 11.666 | 0.000 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 117 | 65 | 0 | 0 | 0 | 6387 | 0 | 364 | 0 |
N.S. |
1 | 1.05 | 0.59 | 0.00 | 0.00 | 0.00 | 57.54 | 0.00 | 3.28 | 0.00 |
time (sec) |
N/A | 0.235 | 0.013 | 0.000 | 0.000 | 0.000 | 85.806 | 0.000 | 0.233 | 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 | 232 | 232 | 199 | 751 | 447 | 1031 | 14317 | 1750 | 1174 | 932 |
N.S. |
1 | 1.00 | 0.86 | 3.24 | 1.93 | 4.44 | 61.71 | 7.54 | 5.06 | 4.02 |
time (sec) |
N/A | 0.402 | 0.099 | 0.362 | 0.047 | 0.100 | 3.281 | 0.153 | 0.235 | 9.031 |
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 | 185 | 185 | 355 | 598 | 335 | 762 | 8940 | 1266 | 840 | 723 |
N.S. |
1 | 1.00 | 1.92 | 3.23 | 1.81 | 4.12 | 48.32 | 6.84 | 4.54 | 3.91 |
time (sec) |
N/A | 0.351 | 0.366 | 0.336 | 0.043 | 0.094 | 2.108 | 0.134 | 0.261 | 9.021 |
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 | 140 | 176 | 420 | 235 | 520 | 5097 | 851 | 554 | 496 |
N.S. |
1 | 1.00 | 1.26 | 3.00 | 1.68 | 3.71 | 36.41 | 6.08 | 3.96 | 3.54 |
time (sec) |
N/A | 0.288 | 0.138 | 0.375 | 0.044 | 0.085 | 1.379 | 0.134 | 0.219 | 8.814 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 148 | 148 | 132 | 0 | 0 | 0 | 1608 | 0 | 697 | 0 |
N.S. |
1 | 1.00 | 0.89 | 0.00 | 0.00 | 0.00 | 10.86 | 0.00 | 4.71 | 0.00 |
time (sec) |
N/A | 0.299 | 0.084 | 0.000 | 0.000 | 0.000 | 3.151 | 0.000 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 145 | 114 | 0 | 0 | 0 | 785 | 0 | 459 | 0 |
N.S. |
1 | 1.27 | 1.00 | 0.00 | 0.00 | 0.00 | 6.89 | 0.00 | 4.03 | 0.00 |
time (sec) |
N/A | 0.364 | 0.049 | 0.000 | 0.000 | 0.000 | 2.193 | 0.000 | 0.215 | 0.000 |
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 | 149 | 168 | 99 | 0 | 0 | 0 | 1090 | 0 | 526 | 0 |
N.S. |
1 | 1.13 | 0.66 | 0.00 | 0.00 | 0.00 | 7.32 | 0.00 | 3.53 | 0.00 |
time (sec) |
N/A | 0.412 | 0.036 | 0.000 | 0.000 | 0.000 | 3.764 | 0.000 | 0.235 | 0.000 |
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 | 133 | 193 | 78 | 0 | 0 | 0 | 3016 | 0 | 431 | 0 |
N.S. |
1 | 1.45 | 0.59 | 0.00 | 0.00 | 0.00 | 22.68 | 0.00 | 3.24 | 0.00 |
time (sec) |
N/A | 0.400 | 0.014 | 0.000 | 0.000 | 0.000 | 11.600 | 0.000 | 0.255 | 0.000 |