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 | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 35 | 32 | 21 | 28 | 65 | 19 | 0 | 20 |
N.S. |
1 | 1.25 | 1.14 | 0.75 | 1.00 | 2.32 | 0.68 | 0.00 | 0.71 |
time (sec) |
N/A | 0.590 | 0.146 | 1.497 | 0.291 | 0.268 | 0.154 | 0.000 | 13.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 28 | 28 | 34 | 49 | 31 | 38 | 45 |
N.S. |
1 | 0.00 | 0.97 | 0.97 | 1.17 | 1.69 | 1.07 | 1.31 | 1.55 |
time (sec) |
N/A | 0.000 | 4.461 | 0.503 | 0.328 | 0.266 | 0.084 | 0.287 | 14.224 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 19 | 19 | 39 | 20 | 33 | 34 | 0 | 34 |
N.S. |
1 | 0.70 | 0.70 | 1.44 | 0.74 | 1.22 | 1.26 | 0.00 | 1.26 |
time (sec) |
N/A | 0.496 | 0.116 | 1.545 | 0.315 | 0.286 | 0.221 | 0.000 | 35.784 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 404 | 63 | 43 | 683 | 42 | 49 | 60 | 0 |
N.S. |
1 | 15.54 | 2.42 | 1.65 | 26.27 | 1.62 | 1.88 | 2.31 | 0.00 |
time (sec) |
N/A | 1.203 | 0.168 | 0.232 | 0.356 | 0.269 | 0.430 | 0.296 | 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 | 26 | 37 | 25 | 28 | 32 | 41 | 27 | 32 | 32 |
N.S. |
1 | 1.42 | 0.96 | 1.08 | 1.23 | 1.58 | 1.04 | 1.23 | 1.23 |
time (sec) |
N/A | 0.439 | 0.030 | 0.133 | 0.207 | 0.260 | 0.120 | 0.267 | 0.127 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | C | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 22 | 45 | 87 | 50 | 63 | 53 | 19 |
N.S. |
1 | 0.00 | 0.88 | 1.80 | 3.48 | 2.00 | 2.52 | 2.12 | 0.76 |
time (sec) |
N/A | 0.000 | 0.190 | 0.466 | 0.265 | 0.265 | 0.225 | 0.289 | 13.616 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 61 | 64 | 41 | 48 | 48 | 71 | 61 | 52 |
N.S. |
1 | 2.35 | 2.46 | 1.58 | 1.85 | 1.85 | 2.73 | 2.35 | 2.00 |
time (sec) |
N/A | 13.043 | 0.146 | 14.223 | 0.408 | 0.294 | 0.209 | 0.290 | 13.160 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 46 | 19 | 17 | 21 | 21 | 22 | 21 | 16 |
N.S. |
1 | 2.19 | 0.90 | 0.81 | 1.00 | 1.00 | 1.05 | 1.00 | 0.76 |
time (sec) |
N/A | 0.369 | 0.146 | 0.085 | 0.225 | 0.257 | 0.074 | 0.275 | 0.156 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 32 | 24 | 31 | 40 | 32 | 30 | 38 |
N.S. |
1 | 0.00 | 1.23 | 0.92 | 1.19 | 1.54 | 1.23 | 1.15 | 1.46 |
time (sec) |
N/A | 0.000 | 0.178 | 0.281 | 0.327 | 0.265 | 0.098 | 0.469 | 3.235 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 34 | 31 | 43 | 30 | 37 | 30 | 29 |
N.S. |
1 | 0.00 | 1.13 | 1.03 | 1.43 | 1.00 | 1.23 | 1.00 | 0.97 |
time (sec) |
N/A | 0.000 | 3.515 | 0.161 | 0.311 | 0.277 | 0.701 | 0.298 | 0.183 |
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 | 13 | 11 | 9 | 7 | 6 | 6 | 7 | 6 | 7 |
N.S. |
1 | 0.85 | 0.69 | 0.54 | 0.46 | 0.46 | 0.54 | 0.46 | 0.54 |
time (sec) |
N/A | 0.148 | 0.026 | 0.063 | 0.191 | 0.240 | 0.032 | 0.268 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 27 | 27 | 37 | 37 | 19 | 37 | 28 |
N.S. |
1 | 0.00 | 0.84 | 0.84 | 1.16 | 1.16 | 0.59 | 1.16 | 0.88 |
time (sec) |
N/A | 0.000 | 5.597 | 0.287 | 0.234 | 0.258 | 0.049 | 0.289 | 13.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | B | B | B | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 0 | 43 | 88 | 56 | 61 | 216 | 134 |
N.S. |
1 | 0.00 | 0.00 | 1.72 | 3.52 | 2.24 | 2.44 | 8.64 | 5.36 |
time (sec) |
N/A | 0.000 | 0.000 | 21.911 | 0.756 | 0.257 | 0.397 | 0.633 | 13.432 |
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 | 14 | 14 | 14 | 13 | 17 | 12 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 1.21 | 0.86 | 0.86 | 0.86 | 0.86 |
time (sec) |
N/A | 0.262 | 0.027 | 0.134 | 0.336 | 0.263 | 0.081 | 0.294 | 12.620 |
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 | 12 | 11 | 11 | 11 | 10 | 10 | 5 | 10 | 10 |
N.S. |
1 | 0.92 | 0.92 | 0.92 | 0.83 | 0.83 | 0.42 | 0.83 | 0.83 |
time (sec) |
N/A | 0.138 | 0.007 | 0.038 | 0.199 | 0.254 | 0.031 | 0.278 | 0.075 |
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 | 21 | 22 | 21 | 21 | 33 | 23 | 27 | 33 | 38 |
N.S. |
1 | 1.05 | 1.00 | 1.00 | 1.57 | 1.10 | 1.29 | 1.57 | 1.81 |
time (sec) |
N/A | 0.181 | 0.636 | 0.189 | 0.340 | 0.257 | 7.899 | 0.280 | 12.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 31 | 35 | 57 | 54 | 42 | 40 | 0 |
N.S. |
1 | 0.00 | 1.29 | 1.46 | 2.38 | 2.25 | 1.75 | 1.67 | 0.00 |
time (sec) |
N/A | 0.000 | 0.105 | 1.652 | 0.321 | 0.265 | 0.152 | 0.351 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 29 | 52 | 28 | 28 | 14 | 17 | 42 |
N.S. |
1 | 0.00 | 0.94 | 1.68 | 0.90 | 0.90 | 0.45 | 0.55 | 1.35 |
time (sec) |
N/A | 0.000 | 0.225 | 9.102 | 0.240 | 0.254 | 0.072 | 0.310 | 13.443 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 19 | 19 | 21 | 22 | 20 | 22 | 22 | 0 |
N.S. |
1 | 1.12 | 1.12 | 1.24 | 1.29 | 1.18 | 1.29 | 1.29 | 0.00 |
time (sec) |
N/A | 0.369 | 0.044 | 4.908 | 0.330 | 0.256 | 2.368 | 0.289 | 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 | 13 | 19 | 13 | 11 | 10 | 10 | 8 | 10 | 10 |
N.S. |
1 | 1.46 | 1.00 | 0.85 | 0.77 | 0.77 | 0.62 | 0.77 | 0.77 |
time (sec) |
N/A | 0.153 | 0.022 | 0.034 | 0.204 | 0.272 | 0.043 | 0.272 | 13.117 |
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 | 18 | 18 | 16 | 13 | 13 | 12 | 17 | 13 | 12 |
N.S. |
1 | 1.00 | 0.89 | 0.72 | 0.72 | 0.67 | 0.94 | 0.72 | 0.67 |
time (sec) |
N/A | 0.148 | 0.004 | 0.050 | 0.208 | 0.233 | 0.049 | 0.269 | 12.954 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | F(-1) | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 22 | 50 | 55 | 55 | 60 | 0 | 0 |
N.S. |
1 | 0.00 | 0.96 | 2.17 | 2.39 | 2.39 | 2.61 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 1.386 | 1.253 | 0.389 | 0.262 | 0.209 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 19 | 19 | 15 | 18 | 17 | 15 | 17 | 14 |
N.S. |
1 | 0.76 | 0.76 | 0.60 | 0.72 | 0.68 | 0.60 | 0.68 | 0.56 |
time (sec) |
N/A | 0.191 | 0.076 | 0.214 | 0.226 | 0.250 | 0.052 | 0.297 | 0.061 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 30 | 29 | 59 | 58 | 34 | 62 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.97 | 1.97 | 1.93 | 1.13 | 2.07 | 0.00 |
time (sec) |
N/A | 0.000 | 5.271 | 0.213 | 0.271 | 0.272 | 0.124 | 0.308 | 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 | 21 | 35 | 23 | 19 | 30 | 30 | 31 | 30 | 30 |
N.S. |
1 | 1.67 | 1.10 | 0.90 | 1.43 | 1.43 | 1.48 | 1.43 | 1.43 |
time (sec) |
N/A | 0.172 | 0.009 | 0.092 | 0.221 | 0.266 | 0.027 | 0.279 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 34 | 38 | 199 | 53 | 122 | 154 | 0 |
N.S. |
1 | 0.00 | 1.21 | 1.36 | 7.11 | 1.89 | 4.36 | 5.50 | 0.00 |
time (sec) |
N/A | 0.000 | 7.428 | 1.468 | 0.396 | 0.255 | 0.213 | 0.411 | 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 | 29 | 55 | 47 | 47 | 51 | 48 | 46 | 48 | 51 |
N.S. |
1 | 1.90 | 1.62 | 1.62 | 1.76 | 1.66 | 1.59 | 1.66 | 1.76 |
time (sec) |
N/A | 0.382 | 0.132 | 0.108 | 0.187 | 0.278 | 0.092 | 0.291 | 0.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 13 | 13 | 14 | 0 | 111 | 58 | 542 | 337 |
N.S. |
1 | 0.81 | 0.81 | 0.88 | 0.00 | 6.94 | 3.62 | 33.88 | 21.06 |
time (sec) |
N/A | 0.771 | 0.191 | 0.397 | 0.000 | 0.254 | 0.100 | 0.324 | 13.758 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 25 | 26 | 53 | 35 | 24 | 25 | 25 |
N.S. |
1 | 0.00 | 1.39 | 1.44 | 2.94 | 1.94 | 1.33 | 1.39 | 1.39 |
time (sec) |
N/A | 0.000 | 0.156 | 0.398 | 0.316 | 0.250 | 0.191 | 0.297 | 13.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | A | A | A | A | F | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 40 | 0 | 43 | 43 | 42 | 41 | 0 | 46 |
N.S. |
1 | 1.25 | 0.00 | 1.34 | 1.34 | 1.31 | 1.28 | 0.00 | 1.44 |
time (sec) |
N/A | 2.539 | 0.000 | 34.003 | 0.358 | 0.267 | 0.210 | 0.000 | 13.873 |
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 | 28 | 56 | 18 | 30 | 28 | 19 | 22 | 29 | 19 |
N.S. |
1 | 2.00 | 0.64 | 1.07 | 1.00 | 0.68 | 0.79 | 1.04 | 0.68 |
time (sec) |
N/A | 0.789 | 0.382 | 0.349 | 0.325 | 0.253 | 0.173 | 0.292 | 13.999 |
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 | 25 | 20 | 20 | 21 | 20 | 28 | 15 | 21 | 20 |
N.S. |
1 | 0.80 | 0.80 | 0.84 | 0.80 | 1.12 | 0.60 | 0.84 | 0.80 |
time (sec) |
N/A | 0.240 | 0.012 | 0.046 | 0.200 | 0.233 | 0.037 | 0.288 | 0.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | A | A | F(-2) | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 1104 | 57 | 34 | 0 | 42 | 100 | 1602 | 32 |
N.S. |
1 | 30.67 | 1.58 | 0.94 | 0.00 | 1.17 | 2.78 | 44.50 | 0.89 |
time (sec) |
N/A | 7.296 | 10.146 | 0.578 | 0.000 | 0.260 | 3.035 | 0.372 | 13.776 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 46 | 160 | 62 | 201 | 92 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.59 | 5.52 | 2.14 | 6.93 | 3.17 | 0.00 |
time (sec) |
N/A | 0.000 | 5.105 | 4.596 | 0.339 | 0.251 | 0.343 | 0.343 | 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 | 14 | 14 | 14 | 12 | 11 | 11 | 14 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.79 | 0.79 | 1.00 | 0.79 | 0.79 |
time (sec) |
N/A | 0.129 | 0.000 | 0.049 | 0.199 | 0.249 | 0.024 | 0.300 | 12.987 |
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 | 25 | 17 | 17 | 21 | 24 | 24 | 21 | 25 |
N.S. |
1 | 1.14 | 0.77 | 0.77 | 0.95 | 1.09 | 1.09 | 0.95 | 1.14 |
time (sec) |
N/A | 0.372 | 0.080 | 0.072 | 0.305 | 0.253 | 0.072 | 0.284 | 13.078 |
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 | 23 | 37 | 43 | 41 | 30 | 36 | 37 | 30 | 48 |
N.S. |
1 | 1.61 | 1.87 | 1.78 | 1.30 | 1.57 | 1.61 | 1.30 | 2.09 |
time (sec) |
N/A | 0.161 | 0.011 | 0.231 | 0.195 | 0.260 | 0.029 | 0.271 | 0.155 |
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 | 16 | 18 | 16 | 12 | 14 | 14 | 15 | 14 | 11 |
N.S. |
1 | 1.12 | 1.00 | 0.75 | 0.88 | 0.88 | 0.94 | 0.88 | 0.69 |
time (sec) |
N/A | 0.174 | 0.002 | 0.252 | 0.186 | 0.246 | 0.026 | 0.278 | 0.026 |
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 | 26 | 44 | 24 | 27 | 44 | 31 | 31 | 42 | 26 |
N.S. |
1 | 1.69 | 0.92 | 1.04 | 1.69 | 1.19 | 1.19 | 1.62 | 1.00 |
time (sec) |
N/A | 0.414 | 0.134 | 0.184 | 0.213 | 0.267 | 0.123 | 0.298 | 12.932 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 35 | 36 | 34 | 35 | 31 | 35 | 34 |
N.S. |
1 | 0.00 | 1.25 | 1.29 | 1.21 | 1.25 | 1.11 | 1.25 | 1.21 |
time (sec) |
N/A | 0.000 | 0.093 | 35.858 | 0.250 | 0.262 | 0.482 | 0.673 | 13.616 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 51 | 48 | 58 | 58 | 42 | 4300 | 0 |
N.S. |
1 | 0.00 | 1.89 | 1.78 | 2.15 | 2.15 | 1.56 | 159.26 | 0.00 |
time (sec) |
N/A | 0.000 | 0.181 | 5.159 | 0.425 | 0.266 | 0.339 | 6.875 | 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 | 15 | 15 | 15 | 14 | 13 | 13 | 14 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 0.93 | 0.87 | 0.87 |
time (sec) |
N/A | 0.165 | 0.010 | 0.060 | 0.213 | 0.251 | 0.051 | 0.278 | 12.811 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 265 | 90 | 1473 | 420 | 405 | 3734 | 0 |
N.S. |
1 | 0.00 | 8.55 | 2.90 | 47.52 | 13.55 | 13.06 | 120.45 | 0.00 |
time (sec) |
N/A | 0.000 | 0.335 | 2.326 | 0.422 | 0.298 | 85.758 | 0.502 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 24 | 38 | 22 | 36 | 36 | 20 | 36 | 0 |
N.S. |
1 | 0.83 | 1.31 | 0.76 | 1.24 | 1.24 | 0.69 | 1.24 | 0.00 |
time (sec) |
N/A | 0.778 | 0.481 | 0.441 | 0.311 | 0.282 | 0.067 | 0.282 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | C | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 32 | 21 | 50 | 20 | 17 | 20 | 16 |
N.S. |
1 | 0.00 | 1.52 | 1.00 | 2.38 | 0.95 | 0.81 | 0.95 | 0.76 |
time (sec) |
N/A | 0.000 | 0.171 | 0.044 | 0.238 | 0.243 | 0.043 | 0.282 | 13.610 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 29 | 29 | 27 | 49 | 34 | 22 | 28 | 24 |
N.S. |
1 | 1.16 | 1.16 | 1.08 | 1.96 | 1.36 | 0.88 | 1.12 | 0.96 |
time (sec) |
N/A | 0.387 | 0.067 | 0.178 | 0.233 | 0.260 | 0.054 | 0.293 | 12.841 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 46 | 76 | 110 | 123 | 105 | 127 | 42 |
N.S. |
1 | 0.00 | 1.70 | 2.81 | 4.07 | 4.56 | 3.89 | 4.70 | 1.56 |
time (sec) |
N/A | 0.000 | 10.109 | 0.337 | 0.263 | 0.253 | 0.125 | 0.350 | 13.649 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 192 | 26 | 27 | 162 | 27 | 24 | 27 | 20 |
N.S. |
1 | 6.00 | 0.81 | 0.84 | 5.06 | 0.84 | 0.75 | 0.84 | 0.62 |
time (sec) |
N/A | 1.580 | 0.242 | 0.158 | 0.232 | 0.263 | 0.147 | 0.294 | 12.973 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 25 | 25 | 24 | 30 | 22 | 24 | 24 |
N.S. |
1 | 0.00 | 0.89 | 0.89 | 0.86 | 1.07 | 0.79 | 0.86 | 0.86 |
time (sec) |
N/A | 0.000 | 0.090 | 0.116 | 0.229 | 0.278 | 0.128 | 0.275 | 12.804 |
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 | 20 | 16 | 16 | 13 | 13 | 13 | 14 | 13 | 13 |
N.S. |
1 | 0.80 | 0.80 | 0.65 | 0.65 | 0.65 | 0.70 | 0.65 | 0.65 |
time (sec) |
N/A | 0.166 | 0.270 | 0.140 | 0.196 | 0.239 | 0.055 | 0.267 | 0.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 28 | 25 | 26 | 25 | 26 | 26 | 46 |
N.S. |
1 | 0.00 | 1.17 | 1.04 | 1.08 | 1.04 | 1.08 | 1.08 | 1.92 |
time (sec) |
N/A | 0.000 | 0.199 | 70.375 | 0.319 | 0.261 | 0.285 | 0.344 | 12.902 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 25 | 38 | 22 | 35 | 31 | 26 | 33 |
N.S. |
1 | 0.00 | 0.76 | 1.15 | 0.67 | 1.06 | 0.94 | 0.79 | 1.00 |
time (sec) |
N/A | 0.000 | 1.799 | 0.177 | 0.396 | 0.253 | 0.105 | 0.355 | 13.205 |
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 | 11 | 11 | 10 | 9 | 9 | 10 | 10 | 9 |
N.S. |
1 | 0.50 | 0.50 | 0.45 | 0.41 | 0.41 | 0.45 | 0.45 | 0.41 |
time (sec) |
N/A | 0.155 | 0.003 | 0.092 | 0.194 | 0.248 | 0.050 | 0.285 | 12.984 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 46 | 32 | 38 | 30 | 48 | 32 | 58 | 37 |
N.S. |
1 | 1.44 | 1.00 | 1.19 | 0.94 | 1.50 | 1.00 | 1.81 | 1.16 |
time (sec) |
N/A | 0.320 | 3.884 | 0.599 | 0.248 | 0.248 | 0.172 | 0.303 | 12.275 |
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 | 20 | 27 | 18 | 17 | 19 | 17 | 17 | 19 |
N.S. |
1 | 0.91 | 1.23 | 0.82 | 0.77 | 0.86 | 0.77 | 0.77 | 0.86 |
time (sec) |
N/A | 0.130 | 0.000 | 0.033 | 0.186 | 0.232 | 0.020 | 0.277 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 72 | 59 | 161 | 82 | 70 | 95 | 63 |
N.S. |
1 | 0.00 | 2.40 | 1.97 | 5.37 | 2.73 | 2.33 | 3.17 | 2.10 |
time (sec) |
N/A | 0.000 | 0.109 | 0.890 | 0.258 | 0.258 | 0.237 | 0.297 | 12.661 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 25 | 25 | 17 | 21 | 21 | 14 | 24 | 19 |
N.S. |
1 | 1.09 | 1.09 | 0.74 | 0.91 | 0.91 | 0.61 | 1.04 | 0.83 |
time (sec) |
N/A | 0.370 | 0.243 | 0.089 | 0.217 | 0.256 | 0.045 | 0.271 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 72 | 25 | 22 | 26 | 22 | 24 | 0 |
N.S. |
1 | 0.00 | 2.48 | 0.86 | 0.76 | 0.90 | 0.76 | 0.83 | 0.00 |
time (sec) |
N/A | 0.000 | 1.402 | 0.618 | 0.343 | 0.250 | 0.153 | 0.333 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 72 | 74 | 58 | 78 | 54 | 61 | 57 | 64 |
N.S. |
1 | 2.88 | 2.96 | 2.32 | 3.12 | 2.16 | 2.44 | 2.28 | 2.56 |
time (sec) |
N/A | 0.303 | 0.014 | 0.049 | 0.200 | 0.270 | 0.106 | 0.260 | 13.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 31 | 32 | 34 | 33 | 27 | 171 | 0 |
N.S. |
1 | 0.00 | 1.03 | 1.07 | 1.13 | 1.10 | 0.90 | 5.70 | 0.00 |
time (sec) |
N/A | 0.000 | 0.052 | 1.470 | 0.317 | 0.248 | 0.100 | 0.546 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 31 | 29 | 28 | 80 | 41 | 34 | 47 | 25 |
N.S. |
1 | 1.11 | 1.04 | 1.00 | 2.86 | 1.46 | 1.21 | 1.68 | 0.89 |
time (sec) |
N/A | 0.503 | 0.070 | 0.117 | 0.239 | 0.247 | 0.199 | 0.280 | 0.155 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 18 | 21 | 17 | 20 | 19 | 20 | 0 |
N.S. |
1 | 0.00 | 0.82 | 0.95 | 0.77 | 0.91 | 0.86 | 0.91 | 0.00 |
time (sec) |
N/A | 0.000 | 0.195 | 0.708 | 0.210 | 0.244 | 0.086 | 0.291 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 58 | 58 | 45 | 58 | 44 | 44 | 45 | 26 |
N.S. |
1 | 2.64 | 2.64 | 2.05 | 2.64 | 2.00 | 2.00 | 2.05 | 1.18 |
time (sec) |
N/A | 0.343 | 0.030 | 0.076 | 0.193 | 0.245 | 0.090 | 0.274 | 13.163 |
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 | 23 | 20 | 20 | 25 | 42 | 40 | 17 | 24 | 29 |
N.S. |
1 | 0.87 | 0.87 | 1.09 | 1.83 | 1.74 | 0.74 | 1.04 | 1.26 |
time (sec) |
N/A | 0.572 | 0.029 | 0.068 | 0.228 | 0.243 | 0.057 | 0.531 | 13.337 |
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 | 14 | 17 | 20 | 10 | 13 | 13 | 14 | 13 | 9 |
N.S. |
1 | 1.21 | 1.43 | 0.71 | 0.93 | 0.93 | 1.00 | 0.93 | 0.64 |
time (sec) |
N/A | 0.136 | 0.004 | 0.026 | 0.194 | 0.232 | 0.024 | 0.289 | 12.714 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | A | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 31 | 87 | 56 | 33 | 51 | 75 | 0 |
N.S. |
1 | 0.00 | 1.07 | 3.00 | 1.93 | 1.14 | 1.76 | 2.59 | 0.00 |
time (sec) |
N/A | 0.000 | 5.093 | 239.818 | 0.269 | 0.253 | 0.238 | 0.354 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | B | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 22 | 21 | 20 | 61 | 17 | 38 | 20 |
N.S. |
1 | 0.00 | 0.96 | 0.91 | 0.87 | 2.65 | 0.74 | 1.65 | 0.87 |
time (sec) |
N/A | 0.000 | 0.309 | 0.372 | 0.180 | 0.247 | 0.099 | 0.336 | 0.326 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | F(-2) | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 28 | 39 | 49 | 27 | 0 | 41 | 0 |
N.S. |
1 | 0.00 | 1.27 | 1.77 | 2.23 | 1.23 | 0.00 | 1.86 | 0.00 |
time (sec) |
N/A | 0.000 | 0.051 | 3.556 | 0.322 | 0.253 | 0.000 | 0.307 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | F | A | F(-1) | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 0 | 28 | 0 | 49 | 0 | 0 | 26 |
N.S. |
1 | 0.00 | 0.00 | 0.88 | 0.00 | 1.53 | 0.00 | 0.00 | 0.81 |
time (sec) |
N/A | 0.000 | 0.000 | 0.348 | 0.000 | 0.257 | 0.000 | 0.000 | 13.108 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 29 | 21 | 21 | 34 | 19 | 17 | 23 | 21 |
N.S. |
1 | 1.81 | 1.31 | 1.31 | 2.12 | 1.19 | 1.06 | 1.44 | 1.31 |
time (sec) |
N/A | 0.495 | 0.050 | 0.225 | 0.232 | 0.244 | 0.069 | 0.290 | 13.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 63 | 41 | 47 | 48 | 48 | 51 | 48 | 49 |
N.S. |
1 | 3.15 | 2.05 | 2.35 | 2.40 | 2.40 | 2.55 | 2.40 | 2.45 |
time (sec) |
N/A | 0.183 | 0.030 | 0.073 | 0.203 | 0.246 | 0.030 | 0.275 | 0.118 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 25 | 17 | 16 | 23 | 16 | 19 | 34 | 16 |
N.S. |
1 | 1.32 | 0.89 | 0.84 | 1.21 | 0.84 | 1.00 | 1.79 | 0.84 |
time (sec) |
N/A | 0.251 | 0.146 | 0.133 | 0.233 | 0.232 | 0.055 | 0.277 | 12.533 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 34 | 37 | 52 | 52 | 31 | 67 | 0 |
N.S. |
1 | 0.00 | 1.26 | 1.37 | 1.93 | 1.93 | 1.15 | 2.48 | 0.00 |
time (sec) |
N/A | 0.000 | 0.093 | 11.460 | 0.261 | 0.268 | 0.130 | 0.503 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 20 | 22 | 22 | 26 | 29 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.87 | 0.96 | 0.96 | 1.13 | 1.26 | 0.00 |
time (sec) |
N/A | 0.000 | 2.311 | 0.247 | 0.256 | 0.260 | 0.093 | 0.296 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | F | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 0 | 34 | 36 | 36 | 34 | 0 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.36 | 1.44 | 1.44 | 1.36 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.574 | 0.329 | 0.248 | 0.154 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | B | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 34 | 28 | 51 | 0 | 66 | 54 | 0 | 63 |
N.S. |
1 | 1.13 | 0.93 | 1.70 | 0.00 | 2.20 | 1.80 | 0.00 | 2.10 |
time (sec) |
N/A | 4.792 | 0.184 | 1.118 | 0.000 | 0.285 | 3.068 | 0.000 | 13.493 |
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 | 20 | 23 | 20 | 18 | 17 | 17 | 15 | 17 | 18 |
N.S. |
1 | 1.15 | 1.00 | 0.90 | 0.85 | 0.85 | 0.75 | 0.85 | 0.90 |
time (sec) |
N/A | 0.337 | 0.028 | 0.221 | 0.215 | 0.251 | 0.050 | 0.281 | 13.201 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 20 | 38 | 37 | 36 | 36 | 37 | 42 |
N.S. |
1 | 0.00 | 0.91 | 1.73 | 1.68 | 1.64 | 1.64 | 1.68 | 1.91 |
time (sec) |
N/A | 0.000 | 0.944 | 0.306 | 0.259 | 0.244 | 0.136 | 0.607 | 13.669 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 23 | 34 | 0 | 35 | 29 | 36 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.48 | 0.00 | 1.52 | 1.26 | 1.57 | 0.00 |
time (sec) |
N/A | 0.000 | 5.086 | 1.528 | 0.000 | 0.256 | 4.559 | 0.519 | 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 | 19 | 13 | 13 | 14 | 13 | 13 | 10 | 13 | 13 |
N.S. |
1 | 0.68 | 0.68 | 0.74 | 0.68 | 0.68 | 0.53 | 0.68 | 0.68 |
time (sec) |
N/A | 0.194 | 0.007 | 0.176 | 0.189 | 0.239 | 0.036 | 0.285 | 0.318 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 27 | 30 | 59 | 28 | 24 | 0 | 29 |
N.S. |
1 | 0.00 | 1.00 | 1.11 | 2.19 | 1.04 | 0.89 | 0.00 | 1.07 |
time (sec) |
N/A | 0.000 | 0.946 | 44.168 | 0.309 | 0.242 | 0.713 | 0.000 | 13.831 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 15 | 13 | 13 | 89 | 14 | 14 | 14 | 16 |
N.S. |
1 | 0.83 | 0.72 | 0.72 | 4.94 | 0.78 | 0.78 | 0.78 | 0.89 |
time (sec) |
N/A | 0.176 | 0.078 | 0.047 | 0.308 | 0.239 | 0.047 | 0.286 | 0.092 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | B | B | F(-1) | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 76 | 56 | 61 | 64 | 83 | 0 | 0 |
N.S. |
1 | 0.00 | 2.30 | 1.70 | 1.85 | 1.94 | 2.52 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.169 | 4.053 | 0.312 | 0.275 | 0.891 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 183 | 27 | 29 | 46 | 44 | 44 | 30 | 43 |
N.S. |
1 | 7.96 | 1.17 | 1.26 | 2.00 | 1.91 | 1.91 | 1.30 | 1.87 |
time (sec) |
N/A | 0.408 | 0.018 | 0.142 | 0.187 | 0.236 | 0.473 | 0.299 | 0.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 15 | 15 | 17 | 18 | 18 | 12 | 43 | 16 |
N.S. |
1 | 0.94 | 0.94 | 1.06 | 1.12 | 1.12 | 0.75 | 2.69 | 1.00 |
time (sec) |
N/A | 0.402 | 0.069 | 0.293 | 0.241 | 0.250 | 0.083 | 0.295 | 12.886 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 32 | 28 | 31 | 27 | 24 | 27 | 29 |
N.S. |
1 | 0.00 | 1.07 | 0.93 | 1.03 | 0.90 | 0.80 | 0.90 | 0.97 |
time (sec) |
N/A | 0.000 | 0.110 | 0.108 | 0.236 | 0.263 | 0.106 | 0.358 | 13.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | F(-1) | F | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 0 | 21 | 26 | 26 | 0 | 0 | 25 |
N.S. |
1 | 0.00 | 0.00 | 0.88 | 1.08 | 1.08 | 0.00 | 0.00 | 1.04 |
time (sec) |
N/A | 0.000 | 0.000 | 1.353 | 0.367 | 0.258 | 0.000 | 0.000 | 14.786 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 146 | 39 | 41 | 71 | 39 | 0 | 31 | 37 |
N.S. |
1 | 5.41 | 1.44 | 1.52 | 2.63 | 1.44 | 0.00 | 1.15 | 1.37 |
time (sec) |
N/A | 2.063 | 0.193 | 0.861 | 0.413 | 0.233 | 0.000 | 0.541 | 14.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 36 | 68 | 70 | 64 | 42 | 78 | 30 |
N.S. |
1 | 0.00 | 1.20 | 2.27 | 2.33 | 2.13 | 1.40 | 2.60 | 1.00 |
time (sec) |
N/A | 0.000 | 0.080 | 2.001 | 0.307 | 0.268 | 0.088 | 0.438 | 14.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 43 | 15 | 13 | 12 | 12 | 12 | 12 | 14 |
N.S. |
1 | 2.87 | 1.00 | 0.87 | 0.80 | 0.80 | 0.80 | 0.80 | 0.93 |
time (sec) |
N/A | 0.513 | 0.105 | 0.319 | 0.209 | 0.243 | 0.052 | 0.278 | 13.695 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 72 | 49 | 46 | 51 | 42 | 51 | 67 | 31 |
N.S. |
1 | 2.25 | 1.53 | 1.44 | 1.59 | 1.31 | 1.59 | 2.09 | 0.97 |
time (sec) |
N/A | 0.311 | 0.811 | 0.169 | 0.264 | 0.257 | 0.175 | 0.271 | 0.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 18 | 38 | 17 | 15 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 1.73 | 0.77 | 0.68 | 0.68 | 0.68 |
time (sec) |
N/A | 0.189 | 0.012 | 0.123 | 0.202 | 0.257 | 0.082 | 0.284 | 13.297 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 30 | 22 | 29 | 27 | 27 | 29 | 22 |
N.S. |
1 | 0.00 | 1.20 | 0.88 | 1.16 | 1.08 | 1.08 | 1.16 | 0.88 |
time (sec) |
N/A | 0.000 | 2.730 | 0.526 | 0.264 | 0.251 | 0.099 | 0.284 | 13.346 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 27 | 29 | 34 | 28 | 27 | 1134 | 28 |
N.S. |
1 | 0.00 | 1.00 | 1.07 | 1.26 | 1.04 | 1.00 | 42.00 | 1.04 |
time (sec) |
N/A | 0.000 | 0.149 | 7.144 | 0.368 | 0.253 | 3.763 | 1.343 | 18.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 29 | 31 | 28 | 24 | 29 | 28 |
N.S. |
1 | 0.00 | 0.00 | 0.97 | 1.03 | 0.93 | 0.80 | 0.97 | 0.93 |
time (sec) |
N/A | 0.000 | 0.000 | 8.042 | 0.343 | 0.264 | 0.409 | 0.369 | 13.551 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | F | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 26 | 0 | 23 | 24 | 24 | 19 | 25 | 0 |
N.S. |
1 | 0.96 | 0.00 | 0.85 | 0.89 | 0.89 | 0.70 | 0.93 | 0.00 |
time (sec) |
N/A | 1.267 | 0.000 | 0.613 | 0.318 | 0.249 | 0.118 | 0.303 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 23 | 17 | 17 | 0 | 16 | 26 | 24 | 0 |
N.S. |
1 | 1.15 | 0.85 | 0.85 | 0.00 | 0.80 | 1.30 | 1.20 | 0.00 |
time (sec) |
N/A | 0.880 | 0.192 | 3.132 | 0.000 | 0.237 | 0.187 | 0.302 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 28 | 25 | 24 | 28 | 22 | 24 | 24 |
N.S. |
1 | 0.00 | 0.90 | 0.81 | 0.77 | 0.90 | 0.71 | 0.77 | 0.77 |
time (sec) |
N/A | 0.000 | 0.143 | 0.246 | 0.216 | 0.261 | 0.155 | 0.301 | 13.813 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 22 | 25 | 52 | 47 | 20 | 24 | 23 |
N.S. |
1 | 0.00 | 1.16 | 1.32 | 2.74 | 2.47 | 1.05 | 1.26 | 1.21 |
time (sec) |
N/A | 0.000 | 0.054 | 0.149 | 0.234 | 0.253 | 0.085 | 0.532 | 13.584 |
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 | 18 | 36 | 33 | 18 | 23 | 23 | 26 | 23 | 33 |
N.S. |
1 | 2.00 | 1.83 | 1.00 | 1.28 | 1.28 | 1.44 | 1.28 | 1.83 |
time (sec) |
N/A | 0.403 | 1.237 | 0.116 | 0.189 | 0.260 | 0.087 | 0.289 | 0.146 |