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 | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 87 | 61 | 73 | 72 | 88 | 0 | 128 | 0 |
N.S. |
1 | 0.90 | 0.63 | 0.75 | 0.74 | 0.91 | 0.00 | 1.32 | 0.00 |
time (sec) |
N/A | 0.279 | 0.329 | 0.448 | 0.186 | 0.278 | 0.000 | 0.312 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 135 | 69 | 75 | 0 | 172 | 0 | 201 | 0 |
N.S. |
1 | 1.06 | 0.54 | 0.59 | 0.00 | 1.35 | 0.00 | 1.58 | 0.00 |
time (sec) |
N/A | 0.677 | 0.329 | 0.414 | 0.000 | 0.288 | 0.000 | 0.455 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 66 | 51 | 56 | 55 | 68 | 0 | 99 | 0 |
N.S. |
1 | 0.90 | 0.70 | 0.77 | 0.75 | 0.93 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.266 | 0.179 | 0.375 | 0.189 | 0.287 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 99 | 59 | 65 | 0 | 132 | 0 | 147 | 0 |
N.S. |
1 | 1.04 | 0.62 | 0.68 | 0.00 | 1.39 | 0.00 | 1.55 | 0.00 |
time (sec) |
N/A | 0.504 | 0.159 | 0.346 | 0.000 | 0.338 | 0.000 | 0.386 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 45 | 41 | 39 | 38 | 46 | 0 | 70 | 0 |
N.S. |
1 | 0.92 | 0.84 | 0.80 | 0.78 | 0.94 | 0.00 | 1.43 | 0.00 |
time (sec) |
N/A | 0.254 | 0.131 | 0.403 | 0.192 | 0.272 | 0.000 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 49 | 55 | 0 | 92 | 0 | 93 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.87 | 0.00 | 1.46 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.362 | 0.124 | 0.350 | 0.000 | 0.271 | 0.000 | 0.313 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 21 | 20 | 25 | 58 | 38 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.83 | 1.04 | 2.42 | 1.58 | 0.83 |
time (sec) |
N/A | 0.210 | 0.067 | 0.145 | 0.183 | 0.282 | 0.134 | 0.297 | 5.981 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 32 | 40 | 32 | 58 | 92 | 0 | 59 | 0 |
N.S. |
1 | 0.80 | 1.00 | 0.80 | 1.45 | 2.30 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.238 | 0.105 | 0.270 | 0.287 | 0.376 | 0.000 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 46 | 83 | 0 | 159 | 0 | 102 | 0 |
N.S. |
1 | 1.00 | 0.64 | 1.15 | 0.00 | 2.21 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.337 | 0.212 | 0.417 | 0.000 | 0.279 | 0.000 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 89 | 42 | 90 | 117 | 99 | 0 | 112 | 0 |
N.S. |
1 | 0.94 | 0.44 | 0.95 | 1.23 | 1.04 | 0.00 | 1.18 | 0.00 |
time (sec) |
N/A | 0.404 | 0.152 | 0.403 | 0.270 | 0.281 | 0.000 | 0.293 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 142 | 54 | 157 | 0 | 188 | 0 | 178 | 0 |
N.S. |
1 | 1.04 | 0.39 | 1.15 | 0.00 | 1.37 | 0.00 | 1.30 | 0.00 |
time (sec) |
N/A | 0.604 | 0.203 | 0.386 | 0.000 | 0.297 | 0.000 | 0.532 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 149 | 153 | 44 | 118 | 168 | 121 | 0 | 146 | 0 |
N.S. |
1 | 1.03 | 0.30 | 0.79 | 1.13 | 0.81 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.535 | 0.172 | 0.579 | 0.281 | 0.351 | 0.000 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 197 | 212 | 61 | 254 | 0 | 210 | 0 | 239 | 0 |
N.S. |
1 | 1.08 | 0.31 | 1.29 | 0.00 | 1.07 | 0.00 | 1.21 | 0.00 |
time (sec) |
N/A | 0.951 | 0.239 | 0.427 | 0.000 | 0.299 | 0.000 | 0.355 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 87 | 61 | 73 | 72 | 110 | 0 | 132 | 0 |
N.S. |
1 | 0.90 | 0.63 | 0.75 | 0.74 | 1.13 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.272 | 0.250 | 0.392 | 0.186 | 0.287 | 0.000 | 0.298 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 171 | 79 | 87 | 0 | 210 | 0 | 162 | 0 |
N.S. |
1 | 1.08 | 0.50 | 0.55 | 0.00 | 1.32 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.809 | 0.396 | 0.355 | 0.000 | 0.287 | 0.000 | 0.322 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 66 | 51 | 56 | 55 | 88 | 0 | 102 | 0 |
N.S. |
1 | 0.90 | 0.70 | 0.77 | 0.75 | 1.21 | 0.00 | 1.40 | 0.00 |
time (sec) |
N/A | 0.254 | 0.110 | 0.355 | 0.200 | 0.275 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 135 | 69 | 77 | 0 | 166 | 0 | 132 | 0 |
N.S. |
1 | 1.06 | 0.54 | 0.61 | 0.00 | 1.31 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.623 | 0.111 | 0.327 | 0.000 | 0.280 | 0.000 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 45 | 41 | 39 | 38 | 66 | 252 | 72 | 0 |
N.S. |
1 | 0.92 | 0.84 | 0.80 | 0.78 | 1.35 | 5.14 | 1.47 | 0.00 |
time (sec) |
N/A | 0.249 | 0.061 | 0.355 | 0.196 | 0.279 | 4.236 | 0.434 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 99 | 59 | 67 | 0 | 122 | 0 | 102 | 0 |
N.S. |
1 | 1.04 | 0.62 | 0.71 | 0.00 | 1.28 | 0.00 | 1.07 | 0.00 |
time (sec) |
N/A | 0.476 | 0.105 | 0.327 | 0.000 | 0.280 | 0.000 | 0.306 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 21 | 20 | 40 | 90 | 38 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.83 | 1.67 | 3.75 | 1.58 | 0.83 |
time (sec) |
N/A | 0.201 | 0.033 | 0.166 | 0.195 | 0.297 | 1.186 | 0.488 | 6.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 52 | 62 | 49 | 80 | 72 | 0 | 73 | 0 |
N.S. |
1 | 0.84 | 1.00 | 0.79 | 1.29 | 1.16 | 0.00 | 1.18 | 0.00 |
time (sec) |
N/A | 0.238 | 0.081 | 0.336 | 0.272 | 0.282 | 0.000 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 26 | 37 | 98 | 26 | 0 | 38 | 37 |
N.S. |
1 | 1.00 | 1.00 | 1.42 | 3.77 | 1.00 | 0.00 | 1.46 | 1.42 |
time (sec) |
N/A | 0.240 | 0.168 | 0.303 | 0.326 | 0.328 | 0.000 | 0.327 | 4.790 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 65 | 72 | 70 | 94 | 99 | 0 | 91 | 0 |
N.S. |
1 | 0.89 | 0.99 | 0.96 | 1.29 | 1.36 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.373 | 0.131 | 0.390 | 0.267 | 0.293 | 0.000 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-1) | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 51 | 107 | 0 | 215 | 0 | 95 | 0 |
N.S. |
1 | 1.00 | 0.48 | 1.00 | 0.00 | 2.01 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.457 | 0.118 | 0.441 | 0.000 | 0.309 | 0.000 | 0.311 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 124 | 44 | 101 | 151 | 155 | 0 | 128 | 0 |
N.S. |
1 | 0.98 | 0.35 | 0.80 | 1.19 | 1.22 | 0.00 | 1.01 | 0.00 |
time (sec) |
N/A | 0.510 | 0.048 | 0.543 | 0.267 | 0.296 | 0.000 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 169 | 177 | 54 | 176 | 0 | 248 | 0 | 143 | 0 |
N.S. |
1 | 1.05 | 0.32 | 1.04 | 0.00 | 1.47 | 0.00 | 0.85 | 0.00 |
time (sec) |
N/A | 0.727 | 0.138 | 0.496 | 0.000 | 0.384 | 0.000 | 0.301 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 66 | 51 | 56 | 55 | 114 | 620 | 108 | 0 |
N.S. |
1 | 0.90 | 0.70 | 0.77 | 0.75 | 1.56 | 8.49 | 1.48 | 0.00 |
time (sec) |
N/A | 0.264 | 0.135 | 72.605 | 0.217 | 0.283 | 129.016 | 0.429 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 171 | 79 | 87 | 0 | 219 | 0 | 172 | 0 |
N.S. |
1 | 1.08 | 0.50 | 0.55 | 0.00 | 1.38 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.803 | 0.208 | 27.346 | 0.000 | 0.295 | 0.000 | 0.335 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 45 | 41 | 39 | 38 | 88 | 335 | 76 | 0 |
N.S. |
1 | 0.92 | 0.84 | 0.80 | 0.78 | 1.80 | 6.84 | 1.55 | 0.00 |
time (sec) |
N/A | 0.250 | 0.082 | 7.518 | 0.205 | 0.289 | 38.091 | 0.314 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 135 | 69 | 77 | 0 | 167 | 0 | 140 | 0 |
N.S. |
1 | 1.06 | 0.54 | 0.61 | 0.00 | 1.31 | 0.00 | 1.10 | 0.00 |
time (sec) |
N/A | 0.627 | 0.178 | 1.777 | 0.000 | 0.284 | 0.000 | 0.329 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 21 | 20 | 61 | 126 | 38 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.83 | 2.54 | 5.25 | 1.58 | 0.83 |
time (sec) |
N/A | 0.206 | 0.040 | 0.463 | 0.225 | 0.277 | 13.551 | 0.297 | 3.809 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 74 | 73 | 66 | 97 | 89 | 0 | 91 | 0 |
N.S. |
1 | 0.86 | 0.85 | 0.77 | 1.13 | 1.03 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.250 | 0.122 | 1.165 | 0.328 | 0.292 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 55 | 36 | 45 | 191 | 41 | 0 | 72 | 88 |
N.S. |
1 | 1.00 | 0.65 | 0.82 | 3.47 | 0.75 | 0.00 | 1.31 | 1.60 |
time (sec) |
N/A | 0.367 | 0.150 | 4.931 | 0.393 | 0.290 | 0.000 | 0.319 | 4.657 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 61 | 75 | 66 | 94 | 102 | 0 | 91 | 0 |
N.S. |
1 | 0.88 | 1.09 | 0.96 | 1.36 | 1.48 | 0.00 | 1.32 | 0.00 |
time (sec) |
N/A | 0.373 | 0.258 | 31.826 | 0.286 | 0.287 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 47 | 184 | 43 | 0 | 38 | 225 |
N.S. |
1 | 1.00 | 1.00 | 1.57 | 6.13 | 1.43 | 0.00 | 1.27 | 7.50 |
time (sec) |
N/A | 0.234 | 0.122 | 109.121 | 0.417 | 0.282 | 0.000 | 0.306 | 6.915 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 100 | 110 | 107 | 134 | 147 | 0 | 112 | 0 |
N.S. |
1 | 0.97 | 1.07 | 1.04 | 1.30 | 1.43 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 0.488 | 0.179 | 0.384 | 0.300 | 0.304 | 0.000 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-1) | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 142 | 51 | 120 | 0 | 263 | 0 | 111 | 0 |
N.S. |
1 | 1.02 | 0.37 | 0.86 | 0.00 | 1.89 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.621 | 0.177 | 0.324 | 0.000 | 0.283 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 44 | 113 | 185 | 208 | 0 | 144 | 0 |
N.S. |
1 | 1.00 | 0.28 | 0.71 | 1.16 | 1.31 | 0.00 | 0.91 | 0.00 |
time (sec) |
N/A | 0.642 | 0.058 | 0.487 | 0.260 | 0.292 | 0.000 | 0.309 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 87 | 64 | 73 | 72 | 154 | 0 | 140 | 0 |
N.S. |
1 | 0.90 | 0.66 | 0.75 | 0.74 | 1.59 | 0.00 | 1.44 | 0.00 |
time (sec) |
N/A | 0.264 | 0.398 | 0.148 | 0.178 | 0.300 | 0.000 | 0.319 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 223 | 243 | 102 | 107 | 0 | 296 | 0 | 236 | 0 |
N.S. |
1 | 1.09 | 0.46 | 0.48 | 0.00 | 1.33 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 1.152 | 0.352 | 153.247 | 0.000 | 0.279 | 0.000 | 0.326 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 66 | 54 | 56 | 55 | 128 | 0 | 108 | 0 |
N.S. |
1 | 0.90 | 0.74 | 0.77 | 0.75 | 1.75 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.253 | 0.176 | 58.254 | 0.173 | 0.279 | 0.000 | 0.311 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 191 | 207 | 92 | 97 | 0 | 244 | 0 | 204 | 0 |
N.S. |
1 | 1.08 | 0.48 | 0.51 | 0.00 | 1.28 | 0.00 | 1.07 | 0.00 |
time (sec) |
N/A | 0.945 | 0.170 | 19.947 | 0.000 | 0.281 | 0.000 | 0.325 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 45 | 44 | 39 | 38 | 102 | 0 | 76 | 0 |
N.S. |
1 | 0.92 | 0.90 | 0.80 | 0.78 | 2.08 | 0.00 | 1.55 | 0.00 |
time (sec) |
N/A | 0.247 | 0.094 | 6.208 | 0.183 | 0.282 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 171 | 82 | 87 | 0 | 192 | 0 | 172 | 0 |
N.S. |
1 | 1.08 | 0.52 | 0.55 | 0.00 | 1.21 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.768 | 0.143 | 1.802 | 0.000 | 0.284 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 21 | 20 | 74 | 156 | 38 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.83 | 3.08 | 6.50 | 1.58 | 0.83 |
time (sec) |
N/A | 0.201 | 0.070 | 0.464 | 0.176 | 0.265 | 130.569 | 0.313 | 4.457 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 110 | 96 | 85 | 83 | 115 | 102 | 0 | 107 | 0 |
N.S. |
1 | 0.87 | 0.77 | 0.75 | 1.05 | 0.93 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.255 | 0.224 | 1.120 | 0.263 | 0.282 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 48 | 55 | 237 | 54 | 0 | 105 | 0 |
N.S. |
1 | 1.00 | 0.54 | 0.62 | 2.66 | 0.61 | 0.00 | 1.18 | 0.00 |
time (sec) |
N/A | 0.496 | 0.231 | 4.855 | 0.307 | 0.266 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 85 | 42 | 83 | 112 | 116 | 0 | 107 | 0 |
N.S. |
1 | 0.93 | 0.46 | 0.91 | 1.23 | 1.27 | 0.00 | 1.18 | 0.00 |
time (sec) |
N/A | 0.371 | 0.056 | 29.891 | 0.262 | 0.298 | 0.000 | 0.316 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 42 | 57 | 320 | 57 | 0 | 76 | 118 |
N.S. |
1 | 1.00 | 0.69 | 0.93 | 5.25 | 0.93 | 0.00 | 1.25 | 1.93 |
time (sec) |
N/A | 0.359 | 0.144 | 92.734 | 0.306 | 0.285 | 0.000 | 0.294 | 8.471 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 106 | 103 | 108 | 75 | 132 | 145 | 0 | 149 | 0 |
N.S. |
1 | 0.97 | 1.02 | 0.71 | 1.25 | 1.37 | 0.00 | 1.41 | 0.00 |
time (sec) |
N/A | 0.484 | 0.192 | 0.364 | 0.263 | 0.301 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 47 | 270 | 54 | 0 | 38 | 86 |
N.S. |
1 | 1.00 | 1.00 | 1.57 | 9.00 | 1.80 | 0.00 | 1.27 | 2.87 |
time (sec) |
N/A | 0.236 | 0.256 | 0.295 | 0.313 | 0.264 | 0.000 | 0.308 | 7.979 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 120 | 144 | 168 | 193 | 0 | 128 | 0 |
N.S. |
1 | 1.00 | 0.89 | 1.07 | 1.24 | 1.43 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.634 | 0.389 | 0.664 | 0.264 | 0.295 | 0.000 | 0.322 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-1) | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 171 | 177 | 64 | 139 | 0 | 312 | 0 | 127 | 0 |
N.S. |
1 | 1.04 | 0.37 | 0.81 | 0.00 | 1.82 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.771 | 0.474 | 0.378 | 0.000 | 0.299 | 0.000 | 0.321 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 191 | 194 | 44 | 129 | 219 | 254 | 0 | 160 | 0 |
N.S. |
1 | 1.02 | 0.23 | 0.68 | 1.15 | 1.33 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.796 | 0.075 | 0.896 | 0.277 | 0.314 | 0.000 | 0.320 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 233 | 247 | 64 | 208 | 0 | 346 | 0 | 175 | 0 |
N.S. |
1 | 1.06 | 0.27 | 0.89 | 0.00 | 1.48 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 1.053 | 0.797 | 0.550 | 0.000 | 0.310 | 0.000 | 0.328 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 87 | 61 | 73 | 281 | 82 | 0 | 112 | 0 |
N.S. |
1 | 0.90 | 0.63 | 0.75 | 2.90 | 0.85 | 0.00 | 1.15 | 0.00 |
time (sec) |
N/A | 0.255 | 0.197 | 0.574 | 0.198 | 0.283 | 0.000 | 0.332 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 99 | 59 | 64 | 0 | 155 | 0 | 84 | 0 |
N.S. |
1 | 1.04 | 0.62 | 0.67 | 0.00 | 1.63 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.464 | 0.168 | 0.568 | 0.000 | 0.303 | 0.000 | 0.343 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 66 | 51 | 56 | 160 | 62 | 0 | 90 | 0 |
N.S. |
1 | 0.90 | 0.70 | 0.77 | 2.19 | 0.85 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.247 | 0.099 | 0.611 | 0.202 | 0.283 | 0.000 | 0.328 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 49 | 54 | 0 | 115 | 0 | 65 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.86 | 0.00 | 1.83 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.333 | 0.056 | 0.636 | 0.000 | 0.273 | 0.000 | 0.339 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 45 | 34 | 39 | 75 | 40 | 0 | 68 | 0 |
N.S. |
1 | 0.92 | 0.69 | 0.80 | 1.53 | 0.82 | 0.00 | 1.39 | 0.00 |
time (sec) |
N/A | 0.235 | 0.049 | 0.566 | 0.247 | 0.298 | 0.000 | 0.333 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 44 | 0 | 71 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.47 | 0.00 | 2.37 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.211 | 0.053 | 0.424 | 0.000 | 0.267 | 0.000 | 0.387 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 21 | 20 | 20 | 32 | 38 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.91 | 0.91 | 1.45 | 1.73 | 0.91 |
time (sec) |
N/A | 0.188 | 0.020 | 0.228 | 0.190 | 0.278 | 0.279 | 0.330 | 4.145 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 54 | 39 | 54 | 78 | 90 | 0 | 123 | 0 |
N.S. |
1 | 0.90 | 0.65 | 0.90 | 1.30 | 1.50 | 0.00 | 2.05 | 0.00 |
time (sec) |
N/A | 0.234 | 0.037 | 0.585 | 0.275 | 0.291 | 0.000 | 0.317 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 107 | 52 | 134 | 0 | 200 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.51 | 1.31 | 0.00 | 1.96 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.412 | 0.130 | 0.613 | 0.000 | 0.298 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 116 | 118 | 42 | 107 | 132 | 145 | 0 | 195 | 0 |
N.S. |
1 | 1.02 | 0.36 | 0.92 | 1.14 | 1.25 | 0.00 | 1.68 | 0.00 |
time (sec) |
N/A | 0.375 | 0.047 | 0.726 | 0.277 | 0.319 | 0.000 | 0.373 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 162 | 177 | 61 | 241 | 0 | 230 | 0 | 144 | 0 |
N.S. |
1 | 1.09 | 0.38 | 1.49 | 0.00 | 1.42 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.720 | 0.094 | 0.734 | 0.000 | 0.310 | 0.000 | 0.376 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 175 | 190 | 44 | 135 | 183 | 167 | 0 | 233 | 0 |
N.S. |
1 | 1.09 | 0.25 | 0.77 | 1.05 | 0.95 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.655 | 0.053 | 0.858 | 0.280 | 0.298 | 0.000 | 0.349 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 221 | 249 | 61 | 330 | 0 | 250 | 0 | 262 | 0 |
N.S. |
1 | 1.13 | 0.28 | 1.49 | 0.00 | 1.13 | 0.00 | 1.19 | 0.00 |
time (sec) |
N/A | 1.105 | 0.128 | 0.828 | 0.000 | 0.306 | 0.000 | 0.377 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 87 | 54 | 73 | 72 | 72 | 0 | 112 | 0 |
N.S. |
1 | 0.90 | 0.56 | 0.75 | 0.74 | 0.74 | 0.00 | 1.15 | 0.00 |
time (sec) |
N/A | 0.271 | 0.159 | 0.595 | 0.193 | 0.263 | 0.000 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 52 | 57 | 0 | 142 | 0 | 68 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.90 | 0.00 | 2.25 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.353 | 0.127 | 0.498 | 0.000 | 0.285 | 0.000 | 0.330 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 66 | 44 | 56 | 55 | 52 | 0 | 90 | 0 |
N.S. |
1 | 0.90 | 0.60 | 0.77 | 0.75 | 0.71 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.266 | 0.073 | 0.558 | 0.187 | 0.273 | 0.000 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 42 | 47 | 0 | 98 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 1.40 | 1.57 | 0.00 | 3.27 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.228 | 0.046 | 0.474 | 0.000 | 0.269 | 0.000 | 0.351 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 43 | 32 | 39 | 36 | 28 | 0 | 65 | 0 |
N.S. |
1 | 0.91 | 0.68 | 0.83 | 0.77 | 0.60 | 0.00 | 1.38 | 0.00 |
time (sec) |
N/A | 0.269 | 0.038 | 0.493 | 0.185 | 0.269 | 0.000 | 0.338 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 84 | 94 | 0 | 196 | 0 | 114 | 0 |
N.S. |
1 | 1.00 | 1.11 | 1.24 | 0.00 | 2.58 | 0.00 | 1.50 | 0.00 |
time (sec) |
N/A | 0.323 | 0.104 | 0.875 | 0.000 | 0.275 | 0.000 | 0.330 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 21 | 20 | 33 | 34 | 40 | 50 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.91 | 1.50 | 1.55 | 1.82 | 2.27 |
time (sec) |
N/A | 0.215 | 0.026 | 0.216 | 0.182 | 0.283 | 0.547 | 0.363 | 4.613 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | B | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 83 | 41 | 71 | 91 | 132 | 0 | 142 | 0 |
N.S. |
1 | 0.93 | 0.46 | 0.80 | 1.02 | 1.48 | 0.00 | 1.60 | 0.00 |
time (sec) |
N/A | 0.258 | 0.050 | 0.556 | 0.288 | 0.295 | 0.000 | 0.399 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 142 | 60 | 212 | 0 | 240 | 0 | 199 | 0 |
N.S. |
1 | 1.06 | 0.45 | 1.58 | 0.00 | 1.79 | 0.00 | 1.49 | 0.00 |
time (sec) |
N/A | 0.574 | 0.152 | 0.635 | 0.000 | 0.301 | 0.000 | 0.396 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 150 | 155 | 42 | 124 | 146 | 187 | 0 | 211 | 0 |
N.S. |
1 | 1.03 | 0.28 | 0.83 | 0.97 | 1.25 | 0.00 | 1.41 | 0.00 |
time (sec) |
N/A | 0.530 | 0.051 | 0.705 | 0.275 | 0.292 | 0.000 | 0.326 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 195 | 214 | 58 | 311 | 0 | 270 | 0 | 220 | 0 |
N.S. |
1 | 1.10 | 0.30 | 1.59 | 0.00 | 1.38 | 0.00 | 1.13 | 0.00 |
time (sec) |
N/A | 0.908 | 0.149 | 0.747 | 0.000 | 0.293 | 0.000 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 211 | 227 | 44 | 152 | 197 | 207 | 0 | 249 | 0 |
N.S. |
1 | 1.08 | 0.21 | 0.72 | 0.93 | 0.98 | 0.00 | 1.18 | 0.00 |
time (sec) |
N/A | 0.835 | 0.057 | 0.855 | 0.279 | 0.306 | 0.000 | 0.324 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-1) | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 256 | 286 | 61 | 394 | 0 | 290 | 0 | 271 | 0 |
N.S. |
1 | 1.12 | 0.24 | 1.54 | 0.00 | 1.13 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 1.396 | 0.172 | 0.755 | 0.000 | 0.323 | 0.000 | 0.366 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 99 | 59 | 67 | 0 | 201 | 0 | 90 | 0 |
N.S. |
1 | 1.04 | 0.62 | 0.71 | 0.00 | 2.12 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.495 | 0.436 | 0.675 | 0.000 | 0.284 | 0.000 | 0.371 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 108 | 64 | 90 | 89 | 82 | 0 | 134 | 0 |
N.S. |
1 | 0.89 | 0.53 | 0.74 | 0.74 | 0.68 | 0.00 | 1.11 | 0.00 |
time (sec) |
N/A | 0.286 | 0.189 | 0.604 | 0.203 | 0.284 | 0.000 | 0.394 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 52 | 57 | 0 | 161 | 0 | 68 | 0 |
N.S. |
1 | 1.00 | 0.83 | 0.90 | 0.00 | 2.56 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.356 | 0.208 | 0.598 | 0.000 | 0.277 | 0.000 | 0.295 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 97 | 87 | 54 | 73 | 72 | 62 | 0 | 112 | 0 |
N.S. |
1 | 0.90 | 0.56 | 0.75 | 0.74 | 0.64 | 0.00 | 1.15 | 0.00 |
time (sec) |
N/A | 0.268 | 0.115 | 0.602 | 0.195 | 0.269 | 0.000 | 0.321 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 42 | 47 | 0 | 117 | 0 | 40 | 0 |
N.S. |
1 | 1.00 | 1.40 | 1.57 | 0.00 | 3.90 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.226 | 0.078 | 0.633 | 0.000 | 0.280 | 0.000 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 71 | 64 | 44 | 56 | 55 | 40 | 0 | 88 | 0 |
N.S. |
1 | 0.90 | 0.62 | 0.79 | 0.77 | 0.56 | 0.00 | 1.24 | 0.00 |
time (sec) |
N/A | 0.261 | 0.057 | 0.514 | 0.200 | 0.270 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 114 | 96 | 112 | 0 | 215 | 0 | 140 | 0 |
N.S. |
1 | 1.06 | 0.89 | 1.04 | 0.00 | 1.99 | 0.00 | 1.30 | 0.00 |
time (sec) |
N/A | 0.464 | 0.133 | 0.658 | 0.000 | 0.278 | 0.000 | 0.388 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 45 | 41 | 30 | 37 | 42 | 41 | 245 | 64 | 0 |
N.S. |
1 | 0.91 | 0.67 | 0.82 | 0.93 | 0.91 | 5.44 | 1.42 | 0.00 |
time (sec) |
N/A | 0.256 | 0.043 | 0.526 | 0.204 | 0.280 | 1.968 | 0.294 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 100 | 123 | 0 | 252 | 0 | 139 | 0 |
N.S. |
1 | 1.00 | 1.33 | 1.64 | 0.00 | 3.36 | 0.00 | 1.85 | 0.00 |
time (sec) |
N/A | 0.321 | 0.171 | 0.635 | 0.000 | 0.302 | 0.000 | 0.312 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 21 | 20 | 48 | 65 | 40 | 72 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.83 | 2.00 | 2.71 | 1.67 | 3.00 |
time (sec) |
N/A | 0.209 | 0.030 | 0.226 | 0.200 | 0.276 | 2.039 | 0.358 | 7.627 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 113 | 112 | 41 | 88 | 114 | 169 | 0 | 158 | 0 |
N.S. |
1 | 0.99 | 0.36 | 0.78 | 1.01 | 1.50 | 0.00 | 1.40 | 0.00 |
time (sec) |
N/A | 0.272 | 0.057 | 0.659 | 0.285 | 0.300 | 0.000 | 0.304 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 167 | 177 | 52 | 288 | 0 | 280 | 0 | 218 | 0 |
N.S. |
1 | 1.06 | 0.31 | 1.72 | 0.00 | 1.68 | 0.00 | 1.31 | 0.00 |
time (sec) |
N/A | 0.758 | 0.161 | 0.706 | 0.000 | 0.303 | 0.000 | 0.305 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 185 | 192 | 42 | 141 | 167 | 225 | 0 | 227 | 0 |
N.S. |
1 | 1.04 | 0.23 | 0.76 | 0.90 | 1.22 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 0.693 | 0.063 | 0.724 | 0.267 | 0.301 | 0.000 | 0.370 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 233 | 251 | 54 | 381 | 0 | 308 | 0 | 255 | 0 |
N.S. |
1 | 1.08 | 0.23 | 1.64 | 0.00 | 1.32 | 0.00 | 1.09 | 0.00 |
time (sec) |
N/A | 1.185 | 0.131 | 0.760 | 0.000 | 0.317 | 0.000 | 0.312 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 130 | 64 | 231 | 0 | 116 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.52 | 1.86 | 0.00 | 0.94 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.549 | 0.277 | 5.837 | 0.000 | 0.121 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 96 | 64 | 214 | 0 | 111 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.67 | 2.25 | 0.00 | 1.17 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.441 | 0.209 | 4.292 | 0.000 | 0.113 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 96 | 64 | 179 | 0 | 95 | 0 | 0 | 0 |
N.S. |
1 | 1.01 | 0.67 | 1.88 | 0.00 | 1.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.414 | 0.163 | 2.954 | 0.000 | 0.100 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 64 | 120 | 0 | 85 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.02 | 1.90 | 0.00 | 1.35 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.313 | 0.160 | 2.303 | 0.000 | 0.103 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | C | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 61 | 61 | 62 | 75 | 0 | 75 | 0 | 0 | 45 |
N.S. |
1 | 1.00 | 1.02 | 1.23 | 0.00 | 1.23 | 0.00 | 0.00 | 0.74 |
time (sec) |
N/A | 0.316 | 0.292 | 1.496 | 0.000 | 0.092 | 0.000 | 0.000 | 0.588 |