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 | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 211 | 233 | 128 | 128 | 0 | 249 | 0 | 0 | 0 |
N.S. |
1 | 1.10 | 0.61 | 0.61 | 0.00 | 1.18 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.169 | 0.151 | 0.470 | 0.000 | 0.256 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 77 | 91 | 98 | 60 | 99 | 71 | 158 | 239 | 83 |
N.S. |
1 | 1.18 | 1.27 | 0.78 | 1.29 | 0.92 | 2.05 | 3.10 | 1.08 |
time (sec) |
N/A | 0.270 | 0.106 | 0.305 | 0.177 | 0.258 | 0.764 | 0.303 | 4.304 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 105 | 61 | 78 | 179 | 95 | 0 | 0 | 150 |
N.S. |
1 | 1.05 | 0.61 | 0.78 | 1.79 | 0.95 | 0.00 | 0.00 | 1.50 |
time (sec) |
N/A | 0.351 | 0.111 | 0.245 | 0.186 | 0.255 | 0.000 | 0.000 | 4.121 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 82 | 88 | 60 | 82 | 71 | 158 | 239 | 105 |
N.S. |
1 | 1.09 | 1.17 | 0.80 | 1.09 | 0.95 | 2.11 | 3.19 | 1.40 |
time (sec) |
N/A | 0.248 | 0.083 | 0.258 | 0.177 | 0.239 | 0.741 | 0.283 | 4.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 94 | 99 | 65 | 90 | 182 | 97 | 0 | 0 | 154 |
N.S. |
1 | 1.05 | 0.69 | 0.96 | 1.94 | 1.03 | 0.00 | 0.00 | 1.64 |
time (sec) |
N/A | 0.317 | 0.088 | 0.306 | 0.205 | 0.241 | 0.000 | 0.000 | 4.634 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 195 | 81 | 234 | 268 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.51 | 0.63 | 1.81 | 2.08 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.085 | 0.213 | 0.385 | 0.199 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 123 | 205 | 94 | 198 | 204 | 161 | 549 | 0 | 183 |
N.S. |
1 | 1.67 | 0.76 | 1.61 | 1.66 | 1.31 | 4.46 | 0.00 | 1.49 |
time (sec) |
N/A | 1.263 | 0.166 | 0.312 | 0.196 | 0.254 | 1.456 | 0.000 | 4.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 144 | 71 | 90 | 226 | 99 | 0 | 250 | 372 |
N.S. |
1 | 1.13 | 0.56 | 0.71 | 1.78 | 0.78 | 0.00 | 1.97 | 2.93 |
time (sec) |
N/A | 0.627 | 0.128 | 0.250 | 0.192 | 0.261 | 0.000 | 0.287 | 4.489 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 163 | 316 | 121 | 120 | 388 | 136 | 0 | 0 | 350 |
N.S. |
1 | 1.94 | 0.74 | 0.74 | 2.38 | 0.83 | 0.00 | 0.00 | 2.15 |
time (sec) |
N/A | 0.987 | 0.146 | 0.819 | 0.195 | 0.258 | 0.000 | 0.000 | 5.314 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 132 | 71 | 90 | 206 | 99 | 0 | 251 | 319 |
N.S. |
1 | 1.06 | 0.57 | 0.72 | 1.65 | 0.79 | 0.00 | 2.01 | 2.55 |
time (sec) |
N/A | 0.448 | 0.101 | 0.252 | 0.190 | 0.240 | 0.000 | 0.284 | 4.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 151 | 206 | 127 | 120 | 392 | 137 | 0 | 0 | 358 |
N.S. |
1 | 1.36 | 0.84 | 0.79 | 2.60 | 0.91 | 0.00 | 0.00 | 2.37 |
time (sec) |
N/A | 0.554 | 0.122 | 0.540 | 0.203 | 0.247 | 0.000 | 0.000 | 4.944 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 196 | 303 | 129 | 1305 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.55 | 0.66 | 6.66 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.182 | 0.469 | 0.943 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 209 | 385 | 127 | 3143 | 534 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.84 | 0.61 | 15.04 | 2.56 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.983 | 0.472 | 0.902 | 0.201 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 192 | 264 | 135 | 120 | 437 | 140 | 0 | 341 | 414 |
N.S. |
1 | 1.38 | 0.70 | 0.62 | 2.28 | 0.73 | 0.00 | 1.78 | 2.16 |
time (sec) |
N/A | 0.846 | 0.148 | 0.575 | 0.202 | 0.273 | 0.000 | 0.293 | 6.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 215 | 420 | 107 | 142 | 657 | 161 | 0 | 0 | 831 |
N.S. |
1 | 1.95 | 0.50 | 0.66 | 3.06 | 0.75 | 0.00 | 0.00 | 3.87 |
time (sec) |
N/A | 1.772 | 0.140 | 0.529 | 0.200 | 0.252 | 0.000 | 0.000 | 6.614 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 188 | 239 | 148 | 120 | 422 | 140 | 0 | 342 | 414 |
N.S. |
1 | 1.27 | 0.79 | 0.64 | 2.24 | 0.74 | 0.00 | 1.82 | 2.20 |
time (sec) |
N/A | 0.691 | 0.112 | 0.276 | 0.190 | 0.249 | 0.000 | 0.295 | 5.710 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 203 | 283 | 111 | 150 | 663 | 166 | 0 | 0 | 736 |
N.S. |
1 | 1.39 | 0.55 | 0.74 | 3.27 | 0.82 | 0.00 | 0.00 | 3.63 |
time (sec) |
N/A | 1.103 | 0.311 | 0.517 | 0.207 | 0.253 | 0.000 | 0.000 | 5.316 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD |
size | 277 | 484 | 189 | 1446 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.75 | 0.68 | 5.22 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.550 | 0.414 | 0.844 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 281 | 522 | 218 | 351 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.86 | 0.78 | 1.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 4.915 | 0.552 | 3.398 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 168 | 151 | 152 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 0.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.448 | 0.424 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 22 | 22 | 24 | 22 | 25 | 40 | 49 | 24 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.14 | 1.82 | 2.23 | 1.09 | 1.14 |
time (sec) |
N/A | 0.238 | 7.292 | 0.081 | 0.279 | 0.256 | 1.475 | 0.741 | 3.797 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 22 | 22 | 24 | 22 | 25 | 40 | 49 | 24 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.14 | 1.82 | 2.23 | 1.09 | 1.14 |
time (sec) |
N/A | 0.237 | 5.890 | 0.222 | 0.274 | 0.267 | 1.445 | 0.706 | 3.725 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 36 | 31 | 31 | 0 | 118 | 0 | 0 | 0 |
N.S. |
1 | 0.88 | 0.76 | 0.76 | 0.00 | 2.88 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.342 | 0.165 | 0.257 | 0.000 | 0.252 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 27 | 24 | 24 | 0 | 102 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.83 | 0.83 | 0.00 | 3.52 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.330 | 0.149 | 0.329 | 0.000 | 0.243 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 25 | 22 | 22 | 0 | 88 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.81 | 0.81 | 0.00 | 3.26 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.330 | 0.140 | 0.363 | 0.000 | 0.246 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 27 | 24 | 24 | 0 | 102 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.83 | 0.83 | 0.00 | 3.52 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.319 | 0.136 | 0.327 | 0.000 | 0.244 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 36 | 33 | 31 | 0 | 118 | 0 | 0 | 0 |
N.S. |
1 | 0.88 | 0.80 | 0.76 | 0.00 | 2.88 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.312 | 0.086 | 0.327 | 0.000 | 0.248 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 22 | 22 | 24 | 22 | 25 | 39 | 49 | 24 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.14 | 1.77 | 2.23 | 1.09 | 1.14 |
time (sec) |
N/A | 0.239 | 1.016 | 0.207 | 0.258 | 0.244 | 2.049 | 0.586 | 3.746 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 22 | 22 | 24 | 22 | 151 | 40 | 56 | 24 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 6.86 | 1.82 | 2.55 | 1.09 | 1.14 |
time (sec) |
N/A | 3.160 | 8.003 | 0.154 | 0.283 | 0.244 | 2.158 | 0.342 | 3.806 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 55 | 49 | 62 | 0 | 232 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.92 | 1.17 | 0.00 | 4.38 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.481 | 0.207 | 0.293 | 0.000 | 0.242 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 172 | 80 | 54 | 0 | 231 | 0 | 0 | 0 |
N.S. |
1 | 3.13 | 1.45 | 0.98 | 0.00 | 4.20 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.785 | 0.146 | 0.347 | 0.000 | 0.247 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 97 | 56 | 38 | 0 | 164 | 0 | 0 | 0 |
N.S. |
1 | 2.37 | 1.37 | 0.93 | 0.00 | 4.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.802 | 0.224 | 0.421 | 0.000 | 0.251 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 53 | 87 | 75 | 54 | 0 | 225 | 0 | 0 | 0 |
N.S. |
1 | 1.64 | 1.42 | 1.02 | 0.00 | 4.25 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.935 | 0.134 | 0.378 | 0.000 | 0.243 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 49 | 52 | 43 | 60 | 0 | 222 | 0 | 0 | 0 |
N.S. |
1 | 1.06 | 0.88 | 1.22 | 0.00 | 4.53 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.424 | 0.145 | 0.283 | 0.000 | 0.249 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 22 | 22 | 24 | 22 | 153 | 39 | 56 | 24 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 6.95 | 1.77 | 2.55 | 1.09 | 1.14 |
time (sec) |
N/A | 2.374 | 3.568 | 0.233 | 0.288 | 0.241 | 2.477 | 0.330 | 3.698 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 206 | 60 | 90 | 0 | 256 | 0 | 0 | 0 |
N.S. |
1 | 2.06 | 0.60 | 0.90 | 0.00 | 2.56 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.005 | 0.220 | 0.335 | 0.000 | 0.257 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 270 | 66 | 82 | 0 | 267 | 0 | 0 | 0 |
N.S. |
1 | 2.52 | 0.62 | 0.77 | 0.00 | 2.50 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.261 | 0.239 | 0.374 | 0.000 | 0.251 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 86 | 229 | 56 | 51 | 0 | 193 | 0 | 0 | 0 |
N.S. |
1 | 2.66 | 0.65 | 0.59 | 0.00 | 2.24 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.122 | 0.180 | 0.407 | 0.000 | 0.239 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 100 | 188 | 96 | 82 | 0 | 256 | 0 | 0 | 0 |
N.S. |
1 | 1.88 | 0.96 | 0.82 | 0.00 | 2.56 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.469 | 0.199 | 0.431 | 0.000 | 0.253 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 116 | 86 | 88 | 0 | 241 | 0 | 0 | 0 |
N.S. |
1 | 1.68 | 1.25 | 1.28 | 0.00 | 3.49 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.081 | 0.336 | 0.268 | 0.000 | 0.254 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 22 | 22 | 24 | 22 | 255 | 39 | 56 | 24 | 25 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 11.59 | 1.77 | 2.55 | 1.09 | 1.14 |
time (sec) |
N/A | 2.916 | 4.239 | 0.238 | 0.316 | 0.253 | 2.757 | 0.378 | 3.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 219 | 108 | 122 | 0 | 272 | 0 | 0 | 0 |
N.S. |
1 | 1.75 | 0.86 | 0.98 | 0.00 | 2.18 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.613 | 0.220 | 0.365 | 0.000 | 0.265 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 170 | 409 | 132 | 152 | 0 | 303 | 0 | 0 | 0 |
N.S. |
1 | 2.41 | 0.78 | 0.89 | 0.00 | 1.78 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 3.707 | 0.154 | 0.540 | 0.000 | 0.254 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 257 | 621 | 166 | 182 | 0 | 341 | 0 | 0 | 0 |
N.S. |
1 | 2.42 | 0.65 | 0.71 | 0.00 | 1.33 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 4.723 | 0.422 | 0.624 | 0.000 | 0.264 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 134 | 144 | 81 | 124 | 240 | 131 | 0 | 0 | 206 |
N.S. |
1 | 1.07 | 0.60 | 0.93 | 1.79 | 0.98 | 0.00 | 0.00 | 1.54 |
time (sec) |
N/A | 0.438 | 0.189 | 0.430 | 0.191 | 0.254 | 0.000 | 0.000 | 4.270 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 214 | 334 | 157 | 168 | 516 | 179 | 0 | 0 | 493 |
N.S. |
1 | 1.56 | 0.73 | 0.79 | 2.41 | 0.84 | 0.00 | 0.00 | 2.30 |
time (sec) |
N/A | 0.884 | 0.226 | 0.921 | 0.207 | 0.253 | 0.000 | 0.000 | 5.734 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 291 | 484 | 143 | 212 | 871 | 216 | 0 | 0 | 1041 |
N.S. |
1 | 1.66 | 0.49 | 0.73 | 2.99 | 0.74 | 0.00 | 0.00 | 3.58 |
time (sec) |
N/A | 2.247 | 0.090 | 0.696 | 0.211 | 0.262 | 0.000 | 0.000 | 6.152 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 252 | 226 | 257 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.562 | 0.497 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 22 | 22 | 24 | 22 | 23 | 47 | 22 | 23 | 23 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.05 | 2.14 | 1.00 | 1.05 | 1.05 |
time (sec) |
N/A | 0.239 | 7.742 | 0.175 | 0.271 | 0.250 | 1.359 | 0.738 | 3.847 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 22 | 22 | 24 | 22 | 23 | 47 | 22 | 23 | 23 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.05 | 2.14 | 1.00 | 1.05 | 1.05 |
time (sec) |
N/A | 0.238 | 17.535 | 0.114 | 0.268 | 0.239 | 1.387 | 0.763 | 3.915 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 47 | 40 | 40 | 0 | 220 | 0 | 0 | 0 |
N.S. |
1 | 0.85 | 0.73 | 0.73 | 0.00 | 4.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.354 | 0.126 | 0.303 | 0.000 | 0.244 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 38 | 33 | 33 | 0 | 200 | 0 | 0 | 0 |
N.S. |
1 | 0.88 | 0.77 | 0.77 | 0.00 | 4.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.348 | 0.132 | 0.350 | 0.000 | 0.240 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 47 | 40 | 40 | 0 | 216 | 0 | 0 | 0 |
N.S. |
1 | 0.85 | 0.73 | 0.73 | 0.00 | 3.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.368 | 0.108 | 0.315 | 0.000 | 0.261 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 27 | 24 | 24 | 0 | 136 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 0.83 | 0.83 | 0.00 | 4.69 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.349 | 0.111 | 0.305 | 0.000 | 0.245 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 47 | 55 | 40 | 0 | 216 | 0 | 0 | 0 |
N.S. |
1 | 0.85 | 1.00 | 0.73 | 0.00 | 3.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.367 | 0.220 | 0.318 | 0.000 | 0.261 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 38 | 43 | 33 | 0 | 200 | 0 | 0 | 0 |
N.S. |
1 | 0.88 | 1.00 | 0.77 | 0.00 | 4.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.323 | 0.225 | 0.306 | 0.000 | 0.238 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 47 | 40 | 40 | 0 | 216 | 0 | 0 | 0 |
N.S. |
1 | 0.85 | 0.73 | 0.73 | 0.00 | 3.93 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.322 | 0.197 | 0.331 | 0.000 | 0.252 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 22 | 22 | 24 | 22 | 23 | 44 | 22 | 23 | 23 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.05 | 2.00 | 1.00 | 1.05 | 1.05 |
time (sec) |
N/A | 0.243 | 1.146 | 0.053 | 0.268 | 0.244 | 1.792 | 0.583 | 4.005 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 22 | 22 | 24 | 22 | 23 | 46 | 24 | 23 | 23 |
N.S. |
1 | 1.00 | 1.09 | 1.00 | 1.05 | 2.09 | 1.09 | 1.05 | 1.05 |
time (sec) |
N/A | 0.237 | 2.419 | 0.068 | 0.263 | 0.241 | 2.179 | 0.627 | 3.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 67 | 120 | 56 | 78 | 0 | 418 | 0 | 0 | 0 |
N.S. |
1 | 1.79 | 0.84 | 1.16 | 0.00 | 6.24 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.957 | 0.140 | 0.509 | 0.000 | 0.262 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 63 | 56 | 86 | 0 | 413 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.85 | 1.30 | 0.00 | 6.26 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.432 | 0.268 | 0.315 | 0.000 | 0.259 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 114 | 227 | 73 | 121 | 0 | 447 | 0 | 0 | 0 |
N.S. |
1 | 1.99 | 0.64 | 1.06 | 0.00 | 3.92 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.327 | 0.254 | 0.536 | 0.000 | 0.269 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 149 | 83 | 131 | 0 | 435 | 0 | 0 | 0 |
N.S. |
1 | 1.67 | 0.93 | 1.47 | 0.00 | 4.89 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.100 | 0.141 | 0.293 | 0.000 | 0.243 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 139 | 218 | 79 | 120 | 163 | 91 | 0 | 0 | 0 |
N.S. |
1 | 1.57 | 0.57 | 0.86 | 1.17 | 0.65 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.684 | 0.070 | 0.271 | 0.279 | 0.258 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 197 | 234 | 160 | 175 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.19 | 0.81 | 0.89 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.679 | 0.391 | 0.250 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 109 | 60 | 99 | 88 | 72 | 0 | 0 | 0 |
N.S. |
1 | 1.25 | 0.69 | 1.14 | 1.01 | 0.83 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.411 | 0.051 | 0.181 | 0.277 | 0.255 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 146 | 150 | 125 | 154 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.86 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.390 | 0.198 | 0.240 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 29 | 124 | 30 | 58 | 0 | 47 | 0 |
N.S. |
1 | 1.00 | 0.91 | 3.88 | 0.94 | 1.81 | 0.00 | 1.47 | 0.00 |
time (sec) |
N/A | 0.225 | 0.025 | 0.258 | 0.268 | 0.257 | 0.000 | 0.292 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 76 | 113 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.80 | 1.19 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.234 | 0.086 | 0.202 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 57 | 99 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.76 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.262 | 0.103 | 0.257 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 48 | 73 | 51 | 58 | 0 | 111 | 0 |
N.S. |
1 | 1.00 | 1.14 | 1.74 | 1.21 | 1.38 | 0.00 | 2.64 | 0.00 |
time (sec) |
N/A | 0.269 | 0.041 | 0.250 | 0.278 | 0.249 | 0.000 | 0.300 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 130 | 126 | 141 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.95 | 0.92 | 1.03 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.421 | 0.547 | 0.202 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 205 | 321 | 160 | 175 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.57 | 0.78 | 0.85 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.062 | 0.371 | 0.253 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 161 | 158 | 188 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.98 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.059 | 0.611 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 126 | 104 | 214 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.05 | 0.87 | 1.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.362 | 0.203 | 0.175 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 103 | 90 | 119 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.87 | 1.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.456 | 0.103 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 80 | 100 | 158 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.18 | 1.47 | 2.32 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.487 | 0.104 | 0.172 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 105 | 104 | 89 | 134 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 0.85 | 1.28 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.410 | 0.419 | 0.233 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 152 | 157 | 188 | 231 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 1.24 | 1.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.079 | 1.041 | 0.208 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 219 | 317 | 215 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.45 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 2.680 | 0.699 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 305 | 303 | 570 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.87 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.591 | 3.169 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 128 | 117 | 157 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.91 | 1.23 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.632 | 0.168 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 153 | 138 | 451 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.90 | 2.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.587 | 0.311 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 102 | 122 | 146 | 215 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.20 | 1.43 | 2.11 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.621 | 0.133 | 0.155 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 107 | 131 | 195 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 1.34 | 1.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.688 | 0.320 | 0.238 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 267 | 264 | 301 | 386 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.99 | 1.13 | 1.45 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.567 | 6.621 | 0.197 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 22 | 22 | 24 | 20 | 22 | 41 | 24 | 22 | 22 |
N.S. |
1 | 1.00 | 1.09 | 0.91 | 1.00 | 1.86 | 1.09 | 1.00 | 1.00 |
time (sec) |
N/A | 0.247 | 2.475 | 0.357 | 0.377 | 0.249 | 45.011 | 0.372 | 4.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | A | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 85 | 76 | 123 | 96 | 94 | 0 | 0 | 0 |
N.S. |
1 | 1.15 | 1.03 | 1.66 | 1.30 | 1.27 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.424 | 0.051 | 0.173 | 0.268 | 0.267 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 137 | 143 | 121 | 190 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.04 | 0.88 | 1.39 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.390 | 0.257 | 0.238 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 27 | 38 | 39 | 51 | 0 | 61 | 0 |
N.S. |
1 | 1.00 | 0.63 | 0.88 | 0.91 | 1.19 | 0.00 | 1.42 | 0.00 |
time (sec) |
N/A | 0.233 | 0.029 | 0.223 | 0.180 | 0.254 | 0.000 | 0.314 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 27 | 38 | 36 | 47 | 0 | 59 | 0 |
N.S. |
1 | 1.00 | 0.68 | 0.95 | 0.90 | 1.18 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.207 | 0.023 | 0.221 | 0.190 | 0.254 | 0.000 | 0.325 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 112 | 122 | 97 | 157 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.09 | 0.87 | 1.40 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.568 | 0.181 | 0.166 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 82 | 86 | 89 | 182 | 84 | 107 | 0 | 155 | 0 |
N.S. |
1 | 1.05 | 1.09 | 2.22 | 1.02 | 1.30 | 0.00 | 1.89 | 0.00 |
time (sec) |
N/A | 0.539 | 0.079 | 0.226 | 0.199 | 0.263 | 0.000 | 0.331 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 179 | 256 | 182 | 344 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.43 | 1.02 | 1.92 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.256 | 1.186 | 0.237 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
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 |
size | 24 | 24 | 26 | 22 | 24 | 43 | 26 | 24 | 24 |
N.S. |
1 | 1.00 | 1.08 | 0.92 | 1.00 | 1.79 | 1.08 | 1.00 | 1.00 |
time (sec) |
N/A | 0.273 | 0.485 | 0.244 | 0.440 | 0.264 | 40.842 | 0.329 | 4.415 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | F | F | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 186 | 206 | 165 | 343 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.11 | 0.89 | 1.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.788 | 0.324 | 0.182 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 171 | 159 | 193 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 0.93 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.959 | 0.280 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 68 | 70 | 34 | 45 | 62 | 69 | 0 | 0 | 0 |
N.S. |
1 | 1.03 | 0.50 | 0.66 | 0.91 | 1.01 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.353 | 0.041 | 0.174 | 0.185 | 0.266 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 63 | 63 | 38 | 49 | 57 | 69 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.60 | 0.78 | 0.90 | 1.10 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.234 | 0.033 | 0.230 | 0.188 | 0.265 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 127 | 155 | 159 | 232 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.22 | 1.25 | 1.83 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 1.165 | 0.211 | 0.247 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |