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 | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 37 | 41 | 102 | 370 | 133 | 82 | 60 |
N.S. |
1 | 1.00 | 0.92 | 1.02 | 2.55 | 9.25 | 3.32 | 2.05 | 1.50 |
time (sec) |
N/A | 0.041 | 0.049 | 6.092 | 0.212 | 0.288 | 0.273 | 0.269 | 1.449 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 502 | 101 | 100 | 362 | 0 | 97 | 132 |
N.S. |
1 | 1.00 | 8.10 | 1.63 | 1.61 | 5.84 | 0.00 | 1.56 | 2.13 |
time (sec) |
N/A | 0.076 | 1.398 | 2.178 | 0.317 | 0.308 | 0.000 | 0.290 | 1.437 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 14 | 13 | 51 | 19 | 22 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 3.92 | 1.46 | 1.69 | 1.08 |
time (sec) |
N/A | 0.018 | 0.020 | 1.356 | 0.234 | 0.293 | 0.189 | 0.271 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 121 | 123 | 149 | 383 | 0 | 186 | 186 |
N.S. |
1 | 1.00 | 1.53 | 1.56 | 1.89 | 4.85 | 0.00 | 2.35 | 2.35 |
time (sec) |
N/A | 0.074 | 0.326 | 13.925 | 0.320 | 0.314 | 0.000 | 0.267 | 2.567 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 93 | 93 | 94 | 138 | 215 | 802 | 0 | 167 | 302 |
N.S. |
1 | 1.00 | 1.01 | 1.48 | 2.31 | 8.62 | 0.00 | 1.80 | 3.25 |
time (sec) |
N/A | 0.121 | 0.197 | 50.269 | 0.290 | 0.299 | 0.000 | 0.301 | 1.741 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 136 | 136 | 260 | 211 | 375 | 2615 | 0 | 295 | 519 |
N.S. |
1 | 1.00 | 1.91 | 1.55 | 2.76 | 19.23 | 0.00 | 2.17 | 3.82 |
time (sec) |
N/A | 0.113 | 1.519 | 95.750 | 0.303 | 0.330 | 0.000 | 0.276 | 6.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 144 | 137 | 266 | 490 | 3044 | 0 | 287 | 476 |
N.S. |
1 | 1.00 | 0.95 | 1.85 | 3.40 | 21.14 | 0.00 | 1.99 | 3.31 |
time (sec) |
N/A | 0.208 | 0.354 | 179.319 | 0.325 | 0.322 | 0.000 | 0.283 | 1.813 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 96 | 63 | 413 | 86 | 107 | 53 | 231 |
N.S. |
1 | 1.00 | 3.10 | 2.03 | 13.32 | 2.77 | 3.45 | 1.71 | 7.45 |
time (sec) |
N/A | 0.050 | 0.133 | 13.366 | 0.233 | 0.290 | 0.100 | 0.263 | 1.922 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 42 | 67 | 95 | 151 | 99 | 92 | 113 |
N.S. |
1 | 1.00 | 1.17 | 1.86 | 2.64 | 4.19 | 2.75 | 2.56 | 3.14 |
time (sec) |
N/A | 0.057 | 0.066 | 9.066 | 0.222 | 0.287 | 0.112 | 0.263 | 1.621 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 67 | 37 | 109 | 38 | 46 | 29 | 80 |
N.S. |
1 | 1.00 | 2.91 | 1.61 | 4.74 | 1.65 | 2.00 | 1.26 | 3.48 |
time (sec) |
N/A | 0.047 | 0.090 | 5.965 | 0.234 | 0.327 | 0.072 | 0.275 | 1.403 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 20 | 31 | 42 | 55 | 32 | 53 | 29 |
N.S. |
1 | 1.00 | 0.77 | 1.19 | 1.62 | 2.12 | 1.23 | 2.04 | 1.12 |
time (sec) |
N/A | 0.036 | 0.017 | 4.032 | 0.232 | 0.289 | 0.066 | 0.271 | 0.177 |
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 | 19 | 19 | 17 | 21 | 28 | 17 | 19 | 23 | 24 |
N.S. |
1 | 1.00 | 0.89 | 1.11 | 1.47 | 0.89 | 1.00 | 1.21 | 1.26 |
time (sec) |
N/A | 0.021 | 0.010 | 4.119 | 0.220 | 0.275 | 0.090 | 0.278 | 1.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 41 | 23 | 27 | 37 | 22 | 24 | 28 |
N.S. |
1 | 1.00 | 3.42 | 1.92 | 2.25 | 3.08 | 1.83 | 2.00 | 2.33 |
time (sec) |
N/A | 0.028 | 0.076 | 6.122 | 0.225 | 0.276 | 0.071 | 0.264 | 0.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 24 | 67 | 31 | 32 | 23 | 25 |
N.S. |
1 | 1.00 | 1.00 | 1.60 | 4.47 | 2.07 | 2.13 | 1.53 | 1.67 |
time (sec) |
N/A | 0.039 | 0.010 | 9.270 | 0.219 | 0.297 | 0.065 | 0.277 | 1.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 111 | 46 | 61 | 90 | 61 | 44 | 74 |
N.S. |
1 | 1.00 | 4.27 | 1.77 | 2.35 | 3.46 | 2.35 | 1.69 | 2.85 |
time (sec) |
N/A | 0.053 | 0.053 | 13.286 | 0.219 | 0.293 | 0.100 | 0.263 | 0.330 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 33 | 45 | 205 | 63 | 70 | 51 | 44 |
N.S. |
1 | 1.00 | 1.43 | 1.96 | 8.91 | 2.74 | 3.04 | 2.22 | 1.91 |
time (sec) |
N/A | 0.052 | 0.010 | 17.705 | 0.201 | 0.263 | 0.091 | 0.279 | 1.344 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 175 | 65 | 91 | 144 | 100 | 62 | 124 |
N.S. |
1 | 1.00 | 4.86 | 1.81 | 2.53 | 4.00 | 2.78 | 1.72 | 3.44 |
time (sec) |
N/A | 0.065 | 0.080 | 25.379 | 0.198 | 0.269 | 0.127 | 0.282 | 1.692 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 112 | 69 | 573 | 104 | 128 | 65 | 395 |
N.S. |
1 | 1.00 | 2.38 | 1.47 | 12.19 | 2.21 | 2.72 | 1.38 | 8.40 |
time (sec) |
N/A | 0.080 | 0.165 | 28.339 | 0.206 | 0.271 | 0.134 | 0.270 | 4.900 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 52 | 76 | 115 | 197 | 129 | 102 | 209 |
N.S. |
1 | 1.00 | 0.79 | 1.15 | 1.74 | 2.98 | 1.95 | 1.55 | 3.17 |
time (sec) |
N/A | 0.044 | 0.105 | 20.248 | 0.196 | 0.277 | 0.131 | 0.263 | 2.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 84 | 43 | 197 | 56 | 66 | 41 | 139 |
N.S. |
1 | 1.00 | 2.27 | 1.16 | 5.32 | 1.51 | 1.78 | 1.11 | 3.76 |
time (sec) |
N/A | 0.074 | 0.144 | 13.904 | 0.218 | 0.262 | 0.095 | 0.276 | 0.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 29 | 36 | 61 | 94 | 58 | 66 | 99 |
N.S. |
1 | 1.00 | 0.81 | 1.00 | 1.69 | 2.61 | 1.61 | 1.83 | 2.75 |
time (sec) |
N/A | 0.024 | 0.028 | 9.282 | 0.192 | 0.267 | 0.099 | 0.261 | 1.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 31 | 48 | 54 | 36 | 33 | 49 |
N.S. |
1 | 1.00 | 1.00 | 1.24 | 1.92 | 2.16 | 1.44 | 1.32 | 1.96 |
time (sec) |
N/A | 0.025 | 0.022 | 8.642 | 0.220 | 0.271 | 0.088 | 0.266 | 0.312 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 66 | 35 | 53 | 78 | 49 | 48 | 60 |
N.S. |
1 | 1.00 | 2.54 | 1.35 | 2.04 | 3.00 | 1.88 | 1.85 | 2.31 |
time (sec) |
N/A | 0.045 | 0.173 | 14.276 | 0.224 | 0.310 | 0.102 | 0.273 | 1.483 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 45 | 63 | 70 | 53 | 54 | 56 |
N.S. |
1 | 1.00 | 1.00 | 1.55 | 2.17 | 2.41 | 1.83 | 1.86 | 1.93 |
time (sec) |
N/A | 0.032 | 0.020 | 21.470 | 0.216 | 0.286 | 0.109 | 0.271 | 0.271 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 107 | 56 | 67 | 100 | 66 | 50 | 111 |
N.S. |
1 | 1.00 | 3.82 | 2.00 | 2.39 | 3.57 | 2.36 | 1.79 | 3.96 |
time (sec) |
N/A | 0.062 | 0.092 | 31.665 | 0.220 | 0.280 | 0.122 | 0.266 | 0.223 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 41 | 171 | 59 | 65 | 38 | 40 |
N.S. |
1 | 1.00 | 1.00 | 1.52 | 6.33 | 2.19 | 2.41 | 1.41 | 1.48 |
time (sec) |
N/A | 0.027 | 0.011 | 43.296 | 0.211 | 0.277 | 0.102 | 0.277 | 1.344 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 175 | 74 | 103 | 160 | 114 | 74 | 246 |
N.S. |
1 | 1.00 | 3.65 | 1.54 | 2.15 | 3.33 | 2.38 | 1.54 | 5.12 |
time (sec) |
N/A | 0.062 | 0.107 | 61.777 | 0.219 | 0.280 | 0.156 | 0.274 | 1.509 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 124 | 124 | 108 | 171 | 241 | 1199 | 0 | 197 | 654 |
N.S. |
1 | 1.00 | 0.87 | 1.38 | 1.94 | 9.67 | 0.00 | 1.59 | 5.27 |
time (sec) |
N/A | 0.123 | 0.315 | 1.907 | 0.307 | 0.289 | 0.000 | 0.293 | 2.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 153 | 166 | 160 | 655 | 0 | 211 | 291 |
N.S. |
1 | 1.00 | 1.74 | 1.89 | 1.82 | 7.44 | 0.00 | 2.40 | 3.31 |
time (sec) |
N/A | 0.120 | 0.144 | 0.911 | 0.304 | 0.302 | 0.000 | 0.292 | 3.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 69 | 69 | 69 | 84 | 89 | 257 | 0 | 87 | 330 |
N.S. |
1 | 1.00 | 1.00 | 1.22 | 1.29 | 3.72 | 0.00 | 1.26 | 4.78 |
time (sec) |
N/A | 0.062 | 0.187 | 0.753 | 0.322 | 0.283 | 0.000 | 0.283 | 1.655 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 56 | 73 | 66 | 57 | 0 | 89 | 95 |
N.S. |
1 | 1.00 | 1.17 | 1.52 | 1.38 | 1.19 | 0.00 | 1.85 | 1.98 |
time (sec) |
N/A | 0.048 | 0.046 | 0.507 | 0.329 | 0.298 | 0.000 | 0.273 | 2.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 33 | 46 | 40 | 0 | 39 | 195 |
N.S. |
1 | 1.00 | 1.00 | 1.65 | 2.30 | 2.00 | 0.00 | 1.95 | 9.75 |
time (sec) |
N/A | 0.030 | 0.009 | 0.484 | 0.281 | 0.278 | 0.000 | 0.280 | 0.422 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 89 | 81 | 97 | 228 | 0 | 95 | 304 |
N.S. |
1 | 1.00 | 1.59 | 1.45 | 1.73 | 4.07 | 0.00 | 1.70 | 5.43 |
time (sec) |
N/A | 0.152 | 0.238 | 0.684 | 0.331 | 0.296 | 0.000 | 0.273 | 1.555 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 45 | 98 | 116 | 427 | 0 | 125 | 1163 |
N.S. |
1 | 1.00 | 0.87 | 1.88 | 2.23 | 8.21 | 0.00 | 2.40 | 22.37 |
time (sec) |
N/A | 0.061 | 0.046 | 0.885 | 0.252 | 0.285 | 0.000 | 0.274 | 1.975 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 108 | 108 | 197 | 169 | 212 | 1303 | 0 | 194 | 778 |
N.S. |
1 | 1.00 | 1.82 | 1.56 | 1.96 | 12.06 | 0.00 | 1.80 | 7.20 |
time (sec) |
N/A | 0.269 | 0.369 | 1.472 | 0.318 | 0.339 | 0.000 | 0.274 | 2.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 224 | 224 | 144 | 245 | 523 | 3534 | 0 | 292 | 543 |
N.S. |
1 | 1.00 | 0.64 | 1.09 | 2.33 | 15.78 | 0.00 | 1.30 | 2.42 |
time (sec) |
N/A | 0.305 | 0.306 | 2.697 | 0.351 | 0.321 | 0.000 | 0.306 | 2.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 135 | 135 | 150 | 237 | 375 | 2850 | 0 | 307 | 501 |
N.S. |
1 | 1.00 | 1.11 | 1.76 | 2.78 | 21.11 | 0.00 | 2.27 | 3.71 |
time (sec) |
N/A | 0.270 | 0.519 | 1.413 | 0.343 | 0.352 | 0.000 | 0.296 | 4.842 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 144 | 144 | 100 | 142 | 223 | 900 | 0 | 181 | 377 |
N.S. |
1 | 1.00 | 0.69 | 0.99 | 1.55 | 6.25 | 0.00 | 1.26 | 2.62 |
time (sec) |
N/A | 0.180 | 0.237 | 0.862 | 0.328 | 0.287 | 0.000 | 0.318 | 1.885 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 146 | 136 | 155 | 423 | 0 | 199 | 190 |
N.S. |
1 | 1.00 | 1.72 | 1.60 | 1.82 | 4.98 | 0.00 | 2.34 | 2.24 |
time (sec) |
N/A | 0.074 | 0.179 | 0.679 | 0.335 | 0.288 | 0.000 | 0.286 | 2.554 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 27 | 57 | 75 | 158 | 0 | 75 | 240 |
N.S. |
1 | 1.00 | 0.84 | 1.78 | 2.34 | 4.94 | 0.00 | 2.34 | 7.50 |
time (sec) |
N/A | 0.036 | 0.039 | 1.114 | 0.243 | 0.290 | 0.000 | 0.274 | 1.679 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 112 | 118 | 165 | 1257 | 0 | 148 | 897 |
N.S. |
1 | 1.00 | 1.40 | 1.48 | 2.06 | 15.71 | 0.00 | 1.85 | 11.21 |
time (sec) |
N/A | 0.272 | 0.447 | 2.055 | 0.326 | 0.316 | 0.000 | 0.283 | 2.583 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 73 | 142 | 202 | 1463 | 0 | 190 | 1375 |
N.S. |
1 | 1.00 | 0.96 | 1.87 | 2.66 | 19.25 | 0.00 | 2.50 | 18.09 |
time (sec) |
N/A | 0.076 | 0.151 | 3.468 | 0.222 | 0.303 | 0.000 | 0.288 | 2.381 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 159 | 159 | 235 | 221 | 339 | 3648 | 0 | 242 | 1450 |
N.S. |
1 | 1.00 | 1.48 | 1.39 | 2.13 | 22.94 | 0.00 | 1.52 | 9.12 |
time (sec) |
N/A | 0.449 | 0.637 | 4.995 | 0.294 | 0.352 | 0.000 | 0.292 | 2.284 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 21 | 0 | 356 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.57 | 0.00 | 9.62 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.045 | 0.017 | 1.857 | 0.000 | 0.451 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 17 | 0 | 370 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.71 | 0.00 | 15.42 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.039 | 0.011 | 0.914 | 0.000 | 0.333 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 59 | 49 | 68 | 170 | 517 | 87 | 198 |
N.S. |
1 | 1.00 | 1.16 | 0.96 | 1.33 | 3.33 | 10.14 | 1.71 | 3.88 |
time (sec) |
N/A | 0.091 | 0.078 | 1.651 | 0.293 | 0.300 | 15.127 | 0.274 | 3.516 |
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 | 25 | 48 | 23 | 19 | 36 | 20 | 22 | 24 |
N.S. |
1 | 1.00 | 1.92 | 0.92 | 0.76 | 1.44 | 0.80 | 0.88 | 0.96 |
time (sec) |
N/A | 0.056 | 0.131 | 1.126 | 0.203 | 0.270 | 0.082 | 0.269 | 0.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 81 | 24 | 20 | 35 | 20 | 21 | 23 |
N.S. |
1 | 1.00 | 3.00 | 0.89 | 0.74 | 1.30 | 0.74 | 0.78 | 0.85 |
time (sec) |
N/A | 0.061 | 0.383 | 0.809 | 0.205 | 0.263 | 0.081 | 0.259 | 0.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 149 | 117 | 125 | 172 | 0 | 123 | 914 |
N.S. |
1 | 1.00 | 1.67 | 1.31 | 1.40 | 1.93 | 0.00 | 1.38 | 10.27 |
time (sec) |
N/A | 0.127 | 0.649 | 0.581 | 0.327 | 1.187 | 0.000 | 0.287 | 9.686 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 65 | 73 | 106 | 183 | 0 | 102 | 164 |
N.S. |
1 | 1.00 | 1.08 | 1.22 | 1.77 | 3.05 | 0.00 | 1.70 | 2.73 |
time (sec) |
N/A | 0.106 | 1.399 | 0.885 | 0.329 | 0.293 | 0.000 | 0.304 | 12.324 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 89 | 89 | 93 | 102 | 125 | 172 | 0 | 123 | 864 |
N.S. |
1 | 1.00 | 1.04 | 1.15 | 1.40 | 1.93 | 0.00 | 1.38 | 9.71 |
time (sec) |
N/A | 0.180 | 0.271 | 1.880 | 0.324 | 1.889 | 0.000 | 0.282 | 11.666 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 58 | 58 | 77 | 58 | 141 | 172 | 0 | 90 | 539 |
N.S. |
1 | 1.00 | 1.33 | 1.00 | 2.43 | 2.97 | 0.00 | 1.55 | 9.29 |
time (sec) |
N/A | 0.101 | 1.127 | 0.934 | 0.331 | 0.497 | 0.000 | 0.296 | 2.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 85 | 111 | 176 | 249 | 1318 | 127 | 656 |
N.S. |
1 | 1.00 | 1.05 | 1.37 | 2.17 | 3.07 | 16.27 | 1.57 | 8.10 |
time (sec) |
N/A | 0.120 | 2.328 | 2.624 | 0.323 | 0.285 | 18.115 | 0.291 | 2.634 |
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 | 113 | 113 | 113 | 151 | 339 | 570 | 0 | 170 | 279 |
N.S. |
1 | 1.00 | 1.00 | 1.34 | 3.00 | 5.04 | 0.00 | 1.50 | 2.47 |
time (sec) |
N/A | 0.126 | 1.338 | 3.279 | 0.352 | 0.269 | 0.000 | 0.309 | 1.969 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 180 | 180 | 170 | 370 | 726 | 1880 | 0 | 405 | 0 |
N.S. |
1 | 1.00 | 0.94 | 2.06 | 4.03 | 10.44 | 0.00 | 2.25 | 0.00 |
time (sec) |
N/A | 0.197 | 1.542 | 15.393 | 0.335 | 0.297 | 0.000 | 0.327 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 250 | 250 | 235 | 699 | 1263 | 4350 | 0 | 685 | 0 |
N.S. |
1 | 1.00 | 0.94 | 2.80 | 5.05 | 17.40 | 0.00 | 2.74 | 0.00 |
time (sec) |
N/A | 0.306 | 1.832 | 75.691 | 0.339 | 0.397 | 0.000 | 0.347 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 439 | 439 | 598 | 919 | 0 | 1655 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.36 | 2.09 | 0.00 | 3.77 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.493 | 0.510 | 1.735 | 0.000 | 0.300 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 327 | 327 | 448 | 710 | 0 | 1247 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.37 | 2.17 | 0.00 | 3.81 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.387 | 0.343 | 0.133 | 0.000 | 0.302 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 215 | 215 | 294 | 505 | 0 | 837 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.37 | 2.35 | 0.00 | 3.89 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.224 | 0.247 | 0.112 | 0.000 | 0.322 | 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 | 47 | 47 | 41 | 47 | 42 | 67 | 0 | 42 | 0 |
N.S. |
1 | 1.00 | 0.87 | 1.00 | 0.89 | 1.43 | 0.00 | 0.89 | 0.00 |
time (sec) |
N/A | 0.312 | 0.097 | 3.306 | 0.285 | 0.254 | 0.000 | 0.279 | 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 | 58 | 58 | 55 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.078 | 0.057 | 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 | 58 | 58 | 57 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.054 | 0.031 | 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 | 26 | 26 | 26 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.029 | 0.023 | 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 | 34 | 34 | 36 | 32 | 35 | 34 | 48 | 34 | 35 |
N.S. |
1 | 1.00 | 1.06 | 0.94 | 1.03 | 1.00 | 1.41 | 1.00 | 1.03 |
time (sec) |
N/A | 0.028 | 12.930 | 0.880 | 0.329 | 0.272 | 10.068 | 0.431 | 1.398 |
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 | 36 | 36 | 38 | 32 | 187 | 34 | 51 | 34 | 35 |
N.S. |
1 | 1.00 | 1.06 | 0.89 | 5.19 | 0.94 | 1.42 | 0.94 | 0.97 |
time (sec) |
N/A | 0.055 | 44.088 | 0.520 | 0.346 | 0.258 | 34.708 | 0.600 | 1.524 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 54 | 54 | 41 | 42 | 52 | 44 | 0 | 47 | 43 |
N.S. |
1 | 1.00 | 0.76 | 0.78 | 0.96 | 0.81 | 0.00 | 0.87 | 0.80 |
time (sec) |
N/A | 0.009 | 0.045 | 0.920 | 0.243 | 0.261 | 0.000 | 0.269 | 1.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 88 | 88 | 55 | 58 | 67 | 91 | 0 | 169 | 53 |
N.S. |
1 | 1.00 | 0.62 | 0.66 | 0.76 | 1.03 | 0.00 | 1.92 | 0.60 |
time (sec) |
N/A | 0.015 | 0.067 | 2.711 | 0.234 | 0.278 | 0.000 | 0.283 | 1.371 |
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 | 149 | 149 | 120 | 166 | 114 | 200 | 0 | 665 | 93 |
N.S. |
1 | 1.00 | 0.81 | 1.11 | 0.77 | 1.34 | 0.00 | 4.46 | 0.62 |
time (sec) |
N/A | 0.029 | 0.337 | 5.521 | 0.256 | 0.271 | 0.000 | 0.302 | 1.408 |
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 | 191 | 191 | 167 | 132 | 129 | 294 | 0 | 777 | 102 |
N.S. |
1 | 1.00 | 0.87 | 0.69 | 0.68 | 1.54 | 0.00 | 4.07 | 0.53 |
time (sec) |
N/A | 0.037 | 0.307 | 14.180 | 0.232 | 0.263 | 0.000 | 0.322 | 1.449 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 73 | 74 | 54 | 0 | 64 | 98 | 0 | 235 | 56 |
N.S. |
1 | 1.01 | 0.74 | 0.00 | 0.88 | 1.34 | 0.00 | 3.22 | 0.77 |
time (sec) |
N/A | 0.020 | 0.093 | 0.000 | 0.214 | 0.265 | 0.000 | 0.294 | 1.448 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | F | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 120 | 122 | 89 | 0 | 87 | 248 | 0 | 758 | 74 |
N.S. |
1 | 1.02 | 0.74 | 0.00 | 0.72 | 2.07 | 0.00 | 6.32 | 0.62 |
time (sec) |
N/A | 0.033 | 0.198 | 0.000 | 0.203 | 0.264 | 0.000 | 0.293 | 1.502 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 203 | 203 | 292 | 0 | 138 | 585 | 0 | 3225 | 118 |
N.S. |
1 | 1.00 | 1.44 | 0.00 | 0.68 | 2.88 | 0.00 | 15.89 | 0.58 |
time (sec) |
N/A | 0.074 | 0.952 | 0.000 | 0.227 | 0.273 | 0.000 | 0.351 | 1.576 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | B | F | B | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 266 | 267 | 311 | 0 | 161 | 1125 | 0 | 6884 | 136 |
N.S. |
1 | 1.00 | 1.17 | 0.00 | 0.61 | 4.23 | 0.00 | 25.88 | 0.51 |
time (sec) |
N/A | 0.097 | 2.502 | 0.000 | 0.255 | 0.316 | 0.000 | 0.424 | 1.602 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 37 | 19 | 18 | 19 | 34 | 40 | 18 |
N.S. |
1 | 1.00 | 2.06 | 1.06 | 1.00 | 1.06 | 1.89 | 2.22 | 1.00 |
time (sec) |
N/A | 0.012 | 0.008 | 1.714 | 0.203 | 0.255 | 0.211 | 0.263 | 1.415 |
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 | 39 | 39 | 36 | 30 | 49 | 40 | 0 | 81 | 32 |
N.S. |
1 | 1.00 | 0.92 | 0.77 | 1.26 | 1.03 | 0.00 | 2.08 | 0.82 |
time (sec) |
N/A | 0.021 | 0.017 | 1.704 | 0.214 | 0.263 | 0.000 | 0.269 | 1.447 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 45 | 36 | 86 | 65 | 71 | 81 | 37 |
N.S. |
1 | 1.00 | 1.05 | 0.84 | 2.00 | 1.51 | 1.65 | 1.88 | 0.86 |
time (sec) |
N/A | 0.026 | 0.008 | 6.646 | 0.230 | 0.271 | 1.163 | 0.280 | 1.472 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 51 | 46 | 93 | 84 | 0 | 114 | 51 |
N.S. |
1 | 1.00 | 0.70 | 0.63 | 1.27 | 1.15 | 0.00 | 1.56 | 0.70 |
time (sec) |
N/A | 0.033 | 0.030 | 21.055 | 0.201 | 0.275 | 0.000 | 0.277 | 1.553 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 68 | 51 | 130 | 130 | 105 | 115 | 49 |
N.S. |
1 | 1.00 | 1.05 | 0.78 | 2.00 | 2.00 | 1.62 | 1.77 | 0.75 |
time (sec) |
N/A | 0.030 | 0.011 | 74.458 | 0.228 | 0.271 | 7.172 | 0.291 | 1.589 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 111 | 111 | 96 | 227 | 0 | 331 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.86 | 2.05 | 0.00 | 2.98 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.043 | 0.056 | 6.447 | 0.000 | 0.104 | 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 | 111 | 111 | 114 | 143 | 0 | 171 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.03 | 1.29 | 0.00 | 1.54 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.043 | 0.094 | 0.998 | 0.000 | 0.095 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 68 | 146 | 0 | 58 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.94 | 2.03 | 0.00 | 0.81 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.030 | 0.021 | 0.805 | 0.000 | 0.091 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 66 | 120 | 0 | 39 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.67 | 0.00 | 0.54 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.030 | 0.026 | 0.709 | 0.000 | 0.090 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | C | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 80 | 212 | 0 | 246 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.75 | 1.98 | 0.00 | 2.30 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.040 | 0.036 | 0.823 | 0.000 | 0.099 | 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 | 111 | 111 | 122 | 144 | 0 | 504 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.10 | 1.30 | 0.00 | 4.54 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.041 | 0.079 | 0.856 | 0.000 | 0.101 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 209 | 209 | 86 | 0 | 0 | 162 | 0 | 203 | 0 |
N.S. |
1 | 1.00 | 0.41 | 0.00 | 0.00 | 0.78 | 0.00 | 0.97 | 0.00 |
time (sec) |
N/A | 0.113 | 0.227 | 0.000 | 0.000 | 0.288 | 0.000 | 0.423 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F(-1) | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 74 | 0 | 0 | 117 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.72 | 0.00 | 0.00 | 1.14 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.064 | 0.189 | 0.000 | 0.000 | 0.268 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 61 | 0 | 0 | 68 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 1.42 | 0.00 | 0.00 | 1.58 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.038 | 0.097 | 0.000 | 0.000 | 0.263 | 0.000 | 0.543 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F(-1) | A | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 121 | 0 | 0 | 128 | 0 | 81 | 0 |
N.S. |
1 | 1.00 | 1.17 | 0.00 | 0.00 | 1.24 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.058 | 0.160 | 0.000 | 0.000 | 0.260 | 0.000 | 0.579 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 38 | 0 | 48 | 0 | 102 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 0.00 | 1.33 | 0.00 | 2.83 | 0.00 |
time (sec) |
N/A | 0.034 | 0.016 | 1.643 | 0.000 | 0.275 | 0.000 | 0.284 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 37 | 50 | 0 | 73 | 0 | 97 | 0 |
N.S. |
1 | 1.00 | 0.95 | 1.28 | 0.00 | 1.87 | 0.00 | 2.49 | 0.00 |
time (sec) |
N/A | 0.045 | 0.033 | 0.461 | 0.000 | 0.260 | 0.000 | 0.328 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 59 | 59 | 54 | 74 | 0 | 118 | 0 | 167 | 0 |
N.S. |
1 | 1.00 | 0.92 | 1.25 | 0.00 | 2.00 | 0.00 | 2.83 | 0.00 |
time (sec) |
N/A | 0.061 | 0.046 | 0.531 | 0.000 | 0.277 | 0.000 | 0.365 | 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 | 74 | 74 | 93 | 113 | 0 | 253 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.26 | 1.53 | 0.00 | 3.42 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.091 | 0.177 | 1.087 | 0.000 | 0.274 | 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 | 80 | 80 | 115 | 120 | 0 | 277 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.44 | 1.50 | 0.00 | 3.46 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.104 | 0.233 | 6.919 | 0.000 | 0.272 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 143 | 143 | 232 | 250 | 0 | 701 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.62 | 1.75 | 0.00 | 4.90 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.173 | 0.440 | 3.347 | 0.000 | 0.278 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 302 | 347 | 0 | 171 | 0 | 764 | 0 |
N.S. |
1 | 1.00 | 2.99 | 3.44 | 0.00 | 1.69 | 0.00 | 7.56 | 0.00 |
time (sec) |
N/A | 0.130 | 0.512 | 1.076 | 0.000 | 0.283 | 0.000 | 1.899 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | B | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 107 | 475 | 358 | 0 | 370 | 0 | 749 | 0 |
N.S. |
1 | 1.00 | 4.44 | 3.35 | 0.00 | 3.46 | 0.00 | 7.00 | 0.00 |
time (sec) |
N/A | 0.135 | 2.958 | 7.666 | 0.000 | 0.264 | 0.000 | 8.411 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 194 | 194 | 651 | 700 | 0 | 717 | 0 | 1383 | 0 |
N.S. |
1 | 1.00 | 3.36 | 3.61 | 0.00 | 3.70 | 0.00 | 7.13 | 0.00 |
time (sec) |
N/A | 0.252 | 5.816 | 1.886 | 0.000 | 0.282 | 0.000 | 9.575 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | A | F | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 363 | 463 | 0 | 202 | 0 | 1624 | 0 |
N.S. |
1 | 1.00 | 3.00 | 3.83 | 0.00 | 1.67 | 0.00 | 13.42 | 0.00 |
time (sec) |
N/A | 0.190 | 1.587 | 1.664 | 0.000 | 0.286 | 0.000 | 5.020 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 129 | 129 | 572 | 472 | 0 | 477 | 0 | 1596 | 0 |
N.S. |
1 | 1.00 | 4.43 | 3.66 | 0.00 | 3.70 | 0.00 | 12.37 | 0.00 |
time (sec) |
N/A | 0.197 | 3.562 | 9.178 | 0.000 | 0.277 | 0.000 | 22.527 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | F | B | F(-1) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 226 | 226 | 913 | 930 | 0 | 942 | 0 | 3021 | 0 |
N.S. |
1 | 1.00 | 4.04 | 4.12 | 0.00 | 4.17 | 0.00 | 13.37 | 0.00 |
time (sec) |
N/A | 0.334 | 6.484 | 2.496 | 0.000 | 0.285 | 0.000 | 27.948 | 0.000 |