Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S. means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table fit the page, the name Mathematica was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 34 | 28 | 25 | 36 | 75 | 33 | 35 |
N.S. |
1 | 1.00 | 0.94 | 0.78 | 0.69 | 1.00 | 2.08 | 0.92 | 0.97 |
time (sec) |
N/A | 0.054 | 0.043 | 0.420 | 0.217 | 0.242 | 0.148 | 0.271 | 21.216 |
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 | 24 | 24 | 26 | 20 | 20 | 27 | 27 | 25 | 32 |
N.S. |
1 | 1.00 | 1.08 | 0.83 | 0.83 | 1.12 | 1.12 | 1.04 | 1.33 |
time (sec) |
N/A | 0.055 | 0.041 | 0.434 | 0.214 | 0.258 | 0.100 | 0.274 | 22.554 |
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 | 25 | 20 | 21 | 19 | 37 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.84 | 0.76 | 1.48 | 0.76 | 0.76 |
time (sec) |
N/A | 0.036 | 0.008 | 0.185 | 0.207 | 0.236 | 0.079 | 0.273 | 21.222 |
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 | 10 | 10 | 10 | 11 | 10 | 10 | 8 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 1.10 | 1.00 | 1.00 | 0.80 | 1.00 | 1.00 |
time (sec) |
N/A | 0.009 | 0.049 | 0.155 | 0.213 | 0.253 | 0.028 | 0.272 | 20.984 |
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 | 9 | 9 | 14 | 10 | 9 | 11 | 8 | 24 | 54 |
N.S. |
1 | 1.00 | 1.56 | 1.11 | 1.00 | 1.22 | 0.89 | 2.67 | 6.00 |
time (sec) |
N/A | 0.027 | 0.018 | 0.359 | 0.203 | 0.263 | 0.514 | 0.278 | 21.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 25 | 17 | 24 | 33 | 24 | 33 | 24 |
N.S. |
1 | 1.00 | 2.08 | 1.42 | 2.00 | 2.75 | 2.00 | 2.75 | 2.00 |
time (sec) |
N/A | 0.041 | 0.045 | 0.409 | 0.207 | 0.246 | 0.951 | 0.276 | 20.675 |
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 | 15 | 19 | 17 | 13 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 1.00 | 1.27 | 1.13 | 0.87 | 0.93 |
time (sec) |
N/A | 0.051 | 0.049 | 0.569 | 0.222 | 0.236 | 1.840 | 0.272 | 20.816 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | B | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 94 | 97 | 209 | 93 | 0 | 148 | 3512 |
N.S. |
1 | 1.00 | 1.03 | 1.07 | 2.30 | 1.02 | 0.00 | 1.63 | 38.59 |
time (sec) |
N/A | 0.135 | 0.346 | 0.551 | 0.291 | 0.253 | 0.000 | 0.289 | 29.176 |
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 | 68 | 68 | 62 | 84 | 106 | 144 | 706 | 94 | 94 |
N.S. |
1 | 1.00 | 0.91 | 1.24 | 1.56 | 2.12 | 10.38 | 1.38 | 1.38 |
time (sec) |
N/A | 0.106 | 0.250 | 0.369 | 0.309 | 0.271 | 76.317 | 0.306 | 20.937 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | B | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 47 | 46 | 88 | 46 | 165 | 55 | 970 |
N.S. |
1 | 1.00 | 1.34 | 1.31 | 2.51 | 1.31 | 4.71 | 1.57 | 27.71 |
time (sec) |
N/A | 0.069 | 0.173 | 0.280 | 0.294 | 0.243 | 0.321 | 0.273 | 23.048 |
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 | 36 | 36 | 38 | 35 | 61 | 96 | 112 | 61 | 31 |
N.S. |
1 | 1.00 | 1.06 | 0.97 | 1.69 | 2.67 | 3.11 | 1.69 | 0.86 |
time (sec) |
N/A | 0.023 | 0.065 | 0.297 | 0.300 | 0.260 | 1.567 | 0.307 | 21.374 |
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 | 23 | 23 | 20 | 21 | 48 | 44 | 0 | 22 | 32 |
N.S. |
1 | 1.00 | 0.87 | 0.91 | 2.09 | 1.91 | 0.00 | 0.96 | 1.39 |
time (sec) |
N/A | 0.078 | 0.369 | 0.442 | 0.217 | 0.255 | 0.000 | 0.293 | 21.418 |
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 | 55 | 55 | 67 | 81 | 107 | 133 | 0 | 108 | 170 |
N.S. |
1 | 1.00 | 1.22 | 1.47 | 1.95 | 2.42 | 0.00 | 1.96 | 3.09 |
time (sec) |
N/A | 0.076 | 0.341 | 0.435 | 0.297 | 0.277 | 0.000 | 0.322 | 22.965 |
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 | 55 | 55 | 48 | 53 | 119 | 117 | 0 | 78 | 91 |
N.S. |
1 | 1.00 | 0.87 | 0.96 | 2.16 | 2.13 | 0.00 | 1.42 | 1.65 |
time (sec) |
N/A | 0.149 | 1.297 | 0.559 | 0.196 | 0.267 | 0.000 | 0.277 | 21.322 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 107 | 283 | 107 | 140 | 253 | 240 | 0 | 186 | 224 |
N.S. |
1 | 2.64 | 1.00 | 1.31 | 2.36 | 2.24 | 0.00 | 1.74 | 2.09 |
time (sec) |
N/A | 1.532 | 0.599 | 0.612 | 0.311 | 0.267 | 0.000 | 0.307 | 21.871 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 64 | 64 | 121 | 81 | 117 | 132 | 0 | 139 | 626 |
N.S. |
1 | 1.00 | 1.89 | 1.27 | 1.83 | 2.06 | 0.00 | 2.17 | 9.78 |
time (sec) |
N/A | 0.137 | 0.420 | 0.541 | 0.295 | 0.263 | 0.000 | 0.277 | 27.715 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | F(-2) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 62 | 97 | 128 | 164 | 0 | 103 | 86 |
N.S. |
1 | 1.00 | 1.03 | 1.62 | 2.13 | 2.73 | 0.00 | 1.72 | 1.43 |
time (sec) |
N/A | 0.054 | 0.265 | 0.388 | 0.309 | 0.256 | 0.000 | 0.298 | 21.686 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 14 | 14 | 39 | 605 | 13 | 29 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.82 | 2.29 | 35.59 | 0.76 | 1.71 |
time (sec) |
N/A | 0.014 | 0.034 | 0.367 | 0.199 | 0.241 | 157.808 | 0.267 | 21.078 |
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 | 63 | 63 | 72 | 85 | 128 | 220 | 0 | 109 | 492 |
N.S. |
1 | 1.00 | 1.14 | 1.35 | 2.03 | 3.49 | 0.00 | 1.73 | 7.81 |
time (sec) |
N/A | 0.067 | 0.612 | 0.563 | 0.300 | 0.289 | 0.000 | 0.306 | 21.951 |
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 | 49 | 49 | 76 | 56 | 62 | 134 | 0 | 63 | 114 |
N.S. |
1 | 1.00 | 1.55 | 1.14 | 1.27 | 2.73 | 0.00 | 1.29 | 2.33 |
time (sec) |
N/A | 0.088 | 2.433 | 0.642 | 0.217 | 0.274 | 0.000 | 0.277 | 21.710 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 118 | 118 | 270 | 158 | 242 | 345 | 0 | 215 | 511 |
N.S. |
1 | 1.00 | 2.29 | 1.34 | 2.05 | 2.92 | 0.00 | 1.82 | 4.33 |
time (sec) |
N/A | 0.217 | 2.421 | 0.714 | 0.311 | 0.322 | 0.000 | 0.313 | 22.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | B | B | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 114 | 134 | 359 | 282 | 0 | 242 | 5324 |
N.S. |
1 | 1.00 | 1.16 | 1.37 | 3.66 | 2.88 | 0.00 | 2.47 | 54.33 |
time (sec) |
N/A | 0.228 | 1.054 | 0.750 | 0.292 | 0.270 | 0.000 | 0.282 | 30.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 92 | 300 | 92 | 212 | 299 | 282 | 0 | 197 | 263 |
N.S. |
1 | 3.26 | 1.00 | 2.30 | 3.25 | 3.07 | 0.00 | 2.14 | 2.86 |
time (sec) |
N/A | 0.826 | 0.606 | 0.602 | 0.307 | 0.253 | 0.000 | 0.307 | 21.145 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 19 | 47 | 29 | 84 | 116 | 0 | 20 | 48 |
N.S. |
1 | 1.27 | 3.13 | 1.93 | 5.60 | 7.73 | 0.00 | 1.33 | 3.20 |
time (sec) |
N/A | 0.028 | 0.169 | 0.444 | 0.244 | 0.270 | 0.000 | 0.282 | 21.077 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | B | B | B | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 101 | 157 | 250 | 225 | 0 | 166 | 216 |
N.S. |
1 | 1.00 | 1.38 | 2.15 | 3.42 | 3.08 | 0.00 | 2.27 | 2.96 |
time (sec) |
N/A | 0.039 | 0.205 | 0.530 | 0.334 | 0.260 | 0.000 | 0.299 | 21.692 |
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 | 59 | 59 | 96 | 73 | 172 | 220 | 0 | 77 | 131 |
N.S. |
1 | 1.00 | 1.63 | 1.24 | 2.92 | 3.73 | 0.00 | 1.31 | 2.22 |
time (sec) |
N/A | 0.092 | 0.653 | 0.698 | 0.233 | 0.266 | 0.000 | 0.285 | 21.556 |
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 | 184 | 184 | 193 | 163 | 276 | 463 | 0 | 212 | 813 |
N.S. |
1 | 1.00 | 1.05 | 0.89 | 1.50 | 2.52 | 0.00 | 1.15 | 4.42 |
time (sec) |
N/A | 0.252 | 1.288 | 0.759 | 0.305 | 0.340 | 0.000 | 0.331 | 21.745 |
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 | 117 | 117 | 208 | 128 | 308 | 385 | 0 | 146 | 253 |
N.S. |
1 | 1.00 | 1.78 | 1.09 | 2.63 | 3.29 | 0.00 | 1.25 | 2.16 |
time (sec) |
N/A | 0.161 | 2.024 | 0.905 | 0.268 | 0.279 | 0.000 | 0.298 | 21.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 367 | 0 | 0 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 5.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.072 | 5.003 | 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 | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 57 | 62 | 62 | 62 | 175 | 95 | 149 |
N.S. |
1 | 1.00 | 0.66 | 0.71 | 0.71 | 0.71 | 2.01 | 1.09 | 1.71 |
time (sec) |
N/A | 0.115 | 0.138 | 0.732 | 0.206 | 0.258 | 0.357 | 0.309 | 24.580 |
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 | 60 | 60 | 60 | 46 | 49 | 51 | 87 | 85 | 67 |
N.S. |
1 | 1.00 | 1.00 | 0.77 | 0.82 | 0.85 | 1.45 | 1.42 | 1.12 |
time (sec) |
N/A | 0.079 | 0.010 | 0.688 | 0.211 | 0.256 | 0.225 | 0.288 | 22.662 |
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 | 65 | 65 | 62 | 52 | 48 | 51 | 128 | 65 | 107 |
N.S. |
1 | 1.00 | 0.95 | 0.80 | 0.74 | 0.78 | 1.97 | 1.00 | 1.65 |
time (sec) |
N/A | 0.092 | 0.108 | 0.649 | 0.201 | 0.269 | 0.184 | 0.285 | 24.891 |
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 | 44 | 44 | 44 | 36 | 35 | 38 | 63 | 55 | 47 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.80 | 0.86 | 1.43 | 1.25 | 1.07 |
time (sec) |
N/A | 0.068 | 0.012 | 0.611 | 0.199 | 0.248 | 0.114 | 0.284 | 21.311 |
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 | 43 | 43 | 46 | 36 | 37 | 35 | 73 | 35 | 35 |
N.S. |
1 | 1.00 | 1.07 | 0.84 | 0.86 | 0.81 | 1.70 | 0.81 | 0.81 |
time (sec) |
N/A | 0.048 | 0.056 | 0.398 | 0.207 | 0.264 | 0.096 | 0.273 | 21.439 |
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 | 24 | 24 | 46 | 23 | 24 | 23 | 31 | 24 | 38 |
N.S. |
1 | 1.00 | 1.92 | 0.96 | 1.00 | 0.96 | 1.29 | 1.00 | 1.58 |
time (sec) |
N/A | 0.016 | 0.008 | 0.239 | 0.203 | 0.256 | 0.081 | 0.261 | 20.792 |
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 | 17 | 17 | 17 | 23 | 30 | 21 | 0 | 27 | 70 |
N.S. |
1 | 1.00 | 1.00 | 1.35 | 1.76 | 1.24 | 0.00 | 1.59 | 4.12 |
time (sec) |
N/A | 0.029 | 0.019 | 0.664 | 0.198 | 0.255 | 0.000 | 0.272 | 20.922 |
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 | 24 | 24 | 24 | 32 | 40 | 54 | 0 | 54 | 38 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.67 | 2.25 | 0.00 | 2.25 | 1.58 |
time (sec) |
N/A | 0.051 | 0.016 | 0.595 | 0.240 | 0.263 | 0.000 | 0.291 | 21.124 |
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 | 28 | 28 | 28 | 25 | 30 | 30 | 0 | 25 | 23 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 1.07 | 1.07 | 0.00 | 0.89 | 0.82 |
time (sec) |
N/A | 0.063 | 0.016 | 0.828 | 0.214 | 0.237 | 0.000 | 0.295 | 20.954 |
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 | 52 | 52 | 52 | 50 | 61 | 74 | 0 | 99 | 105 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 1.17 | 1.42 | 0.00 | 1.90 | 2.02 |
time (sec) |
N/A | 0.078 | 0.011 | 0.855 | 0.216 | 0.267 | 0.000 | 0.300 | 22.908 |
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 | 44 | 44 | 41 | 38 | 41 | 45 | 0 | 48 | 40 |
N.S. |
1 | 1.00 | 0.93 | 0.86 | 0.93 | 1.02 | 0.00 | 1.09 | 0.91 |
time (sec) |
N/A | 0.072 | 0.104 | 0.874 | 0.215 | 0.249 | 0.000 | 0.311 | 21.957 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 74 | 63 | 86 | 88 | 0 | 141 | 175 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 1.16 | 1.19 | 0.00 | 1.91 | 2.36 |
time (sec) |
N/A | 0.093 | 0.013 | 0.987 | 0.210 | 0.276 | 0.000 | 0.321 | 26.168 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 53 | 48 | 53 | 57 | 0 | 70 | 65 |
N.S. |
1 | 1.00 | 0.88 | 0.80 | 0.88 | 0.95 | 0.00 | 1.17 | 1.08 |
time (sec) |
N/A | 0.083 | 0.174 | 1.026 | 0.246 | 0.244 | 0.000 | 0.329 | 21.170 |
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 | 137 | 137 | 92 | 99 | 98 | 94 | 187 | 155 | 176 |
N.S. |
1 | 1.00 | 0.67 | 0.72 | 0.72 | 0.69 | 1.36 | 1.13 | 1.28 |
time (sec) |
N/A | 0.169 | 0.329 | 1.096 | 0.221 | 0.254 | 0.496 | 0.345 | 21.809 |
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 | 174 | 174 | 147 | 118 | 102 | 95 | 340 | 132 | 156 |
N.S. |
1 | 1.00 | 0.84 | 0.68 | 0.59 | 0.55 | 1.95 | 0.76 | 0.90 |
time (sec) |
N/A | 0.227 | 0.862 | 1.023 | 0.210 | 0.258 | 0.368 | 0.355 | 21.947 |
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 | 103 | 103 | 69 | 79 | 77 | 74 | 138 | 114 | 115 |
N.S. |
1 | 1.00 | 0.67 | 0.77 | 0.75 | 0.72 | 1.34 | 1.11 | 1.12 |
time (sec) |
N/A | 0.158 | 0.179 | 0.967 | 0.224 | 0.253 | 0.240 | 0.327 | 21.691 |
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 | 126 | 126 | 98 | 84 | 75 | 75 | 238 | 85 | 89 |
N.S. |
1 | 1.00 | 0.78 | 0.67 | 0.60 | 0.60 | 1.89 | 0.67 | 0.71 |
time (sec) |
N/A | 0.165 | 0.957 | 0.704 | 0.229 | 0.255 | 0.195 | 0.309 | 20.895 |
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 | 67 | 67 | 67 | 52 | 52 | 53 | 85 | 73 | 77 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 0.78 | 0.79 | 1.27 | 1.09 | 1.15 |
time (sec) |
N/A | 0.111 | 0.050 | 0.642 | 0.235 | 0.240 | 0.120 | 0.310 | 21.750 |
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 | 55 | 55 | 52 | 57 | 68 | 52 | 128 | 50 | 63 |
N.S. |
1 | 1.00 | 0.95 | 1.04 | 1.24 | 0.95 | 2.33 | 0.91 | 1.15 |
time (sec) |
N/A | 0.021 | 0.075 | 0.471 | 0.250 | 0.256 | 0.095 | 0.293 | 21.161 |
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 | 55 | 55 | 84 | 53 | 60 | 62 | 0 | 89 | 66 |
N.S. |
1 | 1.00 | 1.53 | 0.96 | 1.09 | 1.13 | 0.00 | 1.62 | 1.20 |
time (sec) |
N/A | 0.085 | 0.119 | 0.717 | 0.231 | 0.259 | 0.000 | 0.311 | 21.410 |
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 | 39 | 39 | 69 | 44 | 49 | 60 | 0 | 44 | 118 |
N.S. |
1 | 1.00 | 1.77 | 1.13 | 1.26 | 1.54 | 0.00 | 1.13 | 3.03 |
time (sec) |
N/A | 0.069 | 0.115 | 0.779 | 0.478 | 0.254 | 0.000 | 0.302 | 23.216 |
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 | 67 | 67 | 67 | 83 | 89 | 96 | 0 | 122 | 106 |
N.S. |
1 | 1.00 | 1.00 | 1.24 | 1.33 | 1.43 | 0.00 | 1.82 | 1.58 |
time (sec) |
N/A | 0.106 | 0.015 | 0.773 | 0.237 | 0.250 | 0.000 | 0.317 | 22.225 |
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 | 30 | 30 | 46 | 48 | 45 | 55 | 0 | 41 | 68 |
N.S. |
1 | 1.00 | 1.53 | 1.60 | 1.50 | 1.83 | 0.00 | 1.37 | 2.27 |
time (sec) |
N/A | 0.056 | 0.022 | 0.986 | 0.213 | 0.246 | 0.000 | 0.310 | 21.592 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 120 | 120 | 118 | 129 | 120 | 0 | 249 | 216 |
N.S. |
1 | 1.00 | 1.00 | 0.98 | 1.08 | 1.00 | 0.00 | 2.08 | 1.80 |
time (sec) |
N/A | 0.183 | 0.019 | 1.149 | 0.239 | 0.264 | 0.000 | 0.329 | 24.788 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 54 | 82 | 70 | 79 | 0 | 80 | 98 |
N.S. |
1 | 1.00 | 0.64 | 0.96 | 0.82 | 0.93 | 0.00 | 0.94 | 1.15 |
time (sec) |
N/A | 0.090 | 0.190 | 1.144 | 0.227 | 0.241 | 0.000 | 0.323 | 22.483 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 168 | 168 | 168 | 149 | 180 | 142 | 0 | 343 | 328 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 1.07 | 0.85 | 0.00 | 2.04 | 1.95 |
time (sec) |
N/A | 0.217 | 0.018 | 1.335 | 0.233 | 0.262 | 0.000 | 0.343 | 25.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 125 | 125 | 104 | 110 | 91 | 100 | 0 | 118 | 130 |
N.S. |
1 | 1.00 | 0.83 | 0.88 | 0.73 | 0.80 | 0.00 | 0.94 | 1.04 |
time (sec) |
N/A | 0.124 | 0.717 | 1.243 | 0.245 | 0.246 | 0.000 | 0.344 | 22.703 |
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 | 265 | 265 | 235 | 175 | 163 | 150 | 532 | 218 | 523 |
N.S. |
1 | 1.00 | 0.89 | 0.66 | 0.62 | 0.57 | 2.01 | 0.82 | 1.97 |
time (sec) |
N/A | 0.304 | 1.351 | 1.411 | 0.254 | 0.267 | 0.781 | 0.417 | 24.216 |
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 | 175 | 175 | 141 | 131 | 126 | 123 | 233 | 197 | 214 |
N.S. |
1 | 1.00 | 0.81 | 0.75 | 0.72 | 0.70 | 1.33 | 1.13 | 1.22 |
time (sec) |
N/A | 0.208 | 3.162 | 1.197 | 0.228 | 0.257 | 0.594 | 0.410 | 24.043 |
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 | 216 | 216 | 171 | 154 | 131 | 128 | 400 | 157 | 407 |
N.S. |
1 | 1.00 | 0.79 | 0.71 | 0.61 | 0.59 | 1.85 | 0.73 | 1.88 |
time (sec) |
N/A | 0.253 | 1.895 | 1.097 | 0.208 | 0.257 | 0.404 | 0.381 | 24.120 |
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 | 140 | 140 | 121 | 111 | 107 | 102 | 182 | 145 | 147 |
N.S. |
1 | 1.00 | 0.86 | 0.79 | 0.76 | 0.73 | 1.30 | 1.04 | 1.05 |
time (sec) |
N/A | 0.191 | 1.223 | 1.108 | 0.242 | 0.246 | 0.283 | 0.373 | 22.843 |
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 | 78 | 78 | 94 | 109 | 91 | 100 | 272 | 104 | 281 |
N.S. |
1 | 1.00 | 1.21 | 1.40 | 1.17 | 1.28 | 3.49 | 1.33 | 3.60 |
time (sec) |
N/A | 0.075 | 1.009 | 0.743 | 0.230 | 0.269 | 0.210 | 0.340 | 23.855 |
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 | 58 | 58 | 81 | 75 | 84 | 77 | 117 | 91 | 104 |
N.S. |
1 | 1.00 | 1.40 | 1.29 | 1.45 | 1.33 | 2.02 | 1.57 | 1.79 |
time (sec) |
N/A | 0.027 | 0.322 | 0.955 | 0.234 | 0.250 | 0.133 | 0.297 | 22.400 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 401 | 98 | 91 | 79 | 0 | 93 | 156 |
N.S. |
1 | 1.00 | 4.41 | 1.08 | 1.00 | 0.87 | 0.00 | 1.02 | 1.71 |
time (sec) |
N/A | 0.146 | 0.633 | 0.974 | 0.259 | 0.253 | 0.000 | 0.349 | 23.259 |
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 | 86 | 86 | 131 | 96 | 84 | 109 | 0 | 150 | 116 |
N.S. |
1 | 1.00 | 1.52 | 1.12 | 0.98 | 1.27 | 0.00 | 1.74 | 1.35 |
time (sec) |
N/A | 0.129 | 1.103 | 0.978 | 0.217 | 0.264 | 0.000 | 0.347 | 22.859 |
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 | 72 | 72 | 79 | 70 | 85 | 88 | 0 | 71 | 183 |
N.S. |
1 | 1.00 | 1.10 | 0.97 | 1.18 | 1.22 | 0.00 | 0.99 | 2.54 |
time (sec) |
N/A | 0.114 | 0.244 | 1.075 | 0.313 | 0.262 | 0.000 | 0.355 | 23.584 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 293 | 116 | 118 | 123 | 0 | 171 | 160 |
N.S. |
1 | 1.00 | 2.84 | 1.13 | 1.15 | 1.19 | 0.00 | 1.66 | 1.55 |
time (sec) |
N/A | 0.150 | 1.686 | 1.180 | 0.233 | 0.274 | 0.000 | 0.378 | 25.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 57 | 72 | 87 | 78 | 0 | 57 | 88 |
N.S. |
1 | 1.00 | 1.90 | 2.40 | 2.90 | 2.60 | 0.00 | 1.90 | 2.93 |
time (sec) |
N/A | 0.056 | 0.179 | 1.207 | 0.229 | 0.236 | 0.000 | 0.368 | 22.631 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 158 | 158 | 464 | 154 | 157 | 147 | 0 | 333 | 293 |
N.S. |
1 | 1.00 | 2.94 | 0.97 | 0.99 | 0.93 | 0.00 | 2.11 | 1.85 |
time (sec) |
N/A | 0.211 | 1.315 | 1.625 | 0.228 | 0.266 | 0.000 | 0.384 | 26.530 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 120 | 120 | 54 | 119 | 122 | 105 | 0 | 112 | 123 |
N.S. |
1 | 1.00 | 0.45 | 0.99 | 1.02 | 0.88 | 0.00 | 0.93 | 1.02 |
time (sec) |
N/A | 0.126 | 0.374 | 1.289 | 0.240 | 0.253 | 0.000 | 0.390 | 22.478 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 210 | 210 | 637 | 186 | 208 | 170 | 0 | 465 | 423 |
N.S. |
1 | 1.00 | 3.03 | 0.89 | 0.99 | 0.81 | 0.00 | 2.21 | 2.01 |
time (sec) |
N/A | 0.284 | 2.007 | 1.794 | 0.218 | 0.268 | 0.000 | 0.411 | 26.803 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 174 | 174 | 115 | 147 | 154 | 128 | 0 | 166 | 156 |
N.S. |
1 | 1.00 | 0.66 | 0.84 | 0.89 | 0.74 | 0.00 | 0.95 | 0.90 |
time (sec) |
N/A | 0.184 | 0.592 | 1.510 | 0.229 | 0.245 | 0.000 | 0.402 | 23.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 259 | 259 | 810 | 214 | 248 | 192 | 0 | 597 | 547 |
N.S. |
1 | 1.00 | 3.13 | 0.83 | 0.96 | 0.74 | 0.00 | 2.31 | 2.11 |
time (sec) |
N/A | 0.316 | 5.455 | 2.144 | 0.241 | 0.289 | 0.000 | 0.422 | 26.784 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 213 | 213 | 177 | 175 | 184 | 150 | 0 | 220 | 189 |
N.S. |
1 | 1.00 | 0.83 | 0.82 | 0.86 | 0.70 | 0.00 | 1.03 | 0.89 |
time (sec) |
N/A | 0.204 | 2.170 | 1.851 | 0.263 | 0.280 | 0.000 | 0.421 | 23.921 |
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 | 279 | 279 | 370 | 193 | 186 | 177 | 367 | 269 | 334 |
N.S. |
1 | 1.00 | 1.33 | 0.69 | 0.67 | 0.63 | 1.32 | 0.96 | 1.20 |
time (sec) |
N/A | 0.292 | 6.165 | 1.730 | 0.239 | 0.260 | 1.067 | 0.529 | 24.666 |
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 | 381 | 381 | 222 | 241 | 199 | 184 | 760 | 245 | 343 |
N.S. |
1 | 1.00 | 0.58 | 0.63 | 0.52 | 0.48 | 1.99 | 0.64 | 0.90 |
time (sec) |
N/A | 0.444 | 3.118 | 1.616 | 0.228 | 0.263 | 0.808 | 0.489 | 23.874 |
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 | 220 | 220 | 165 | 163 | 154 | 149 | 286 | 229 | 291 |
N.S. |
1 | 1.00 | 0.75 | 0.74 | 0.70 | 0.68 | 1.30 | 1.04 | 1.32 |
time (sec) |
N/A | 0.264 | 2.947 | 1.468 | 0.222 | 0.254 | 0.539 | 0.445 | 23.255 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 301 | 301 | 178 | 187 | 170 | 151 | 563 | 187 | 471 |
N.S. |
1 | 1.00 | 0.59 | 0.62 | 0.56 | 0.50 | 1.87 | 0.62 | 1.56 |
time (sec) |
N/A | 0.345 | 1.866 | 1.175 | 0.233 | 0.254 | 0.419 | 0.427 | 24.589 |
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 | 165 | 165 | 128 | 131 | 123 | 123 | 206 | 165 | 204 |
N.S. |
1 | 1.00 | 0.78 | 0.79 | 0.75 | 0.75 | 1.25 | 1.00 | 1.24 |
time (sec) |
N/A | 0.208 | 1.458 | 1.066 | 0.252 | 0.252 | 0.263 | 0.400 | 22.837 |
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 | 108 | 108 | 107 | 135 | 136 | 121 | 381 | 122 | 320 |
N.S. |
1 | 1.00 | 0.99 | 1.25 | 1.26 | 1.12 | 3.53 | 1.13 | 2.96 |
time (sec) |
N/A | 0.048 | 1.110 | 1.049 | 0.232 | 0.253 | 0.209 | 0.311 | 24.138 |
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 | 150 | 150 | 181 | 116 | 126 | 121 | 0 | 217 | 190 |
N.S. |
1 | 1.00 | 1.21 | 0.77 | 0.84 | 0.81 | 0.00 | 1.45 | 1.27 |
time (sec) |
N/A | 0.183 | 2.421 | 1.311 | 0.234 | 0.270 | 0.000 | 0.385 | 26.105 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 477 | 155 | 135 | 136 | 0 | 128 | 255 |
N.S. |
1 | 1.00 | 4.01 | 1.30 | 1.13 | 1.14 | 0.00 | 1.08 | 2.14 |
time (sec) |
N/A | 0.201 | 6.352 | 1.305 | 0.311 | 0.269 | 0.000 | 0.389 | 22.908 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 151 | 151 | 268 | 157 | 142 | 153 | 0 | 206 | 221 |
N.S. |
1 | 1.00 | 1.77 | 1.04 | 0.94 | 1.01 | 0.00 | 1.36 | 1.46 |
time (sec) |
N/A | 0.179 | 3.549 | 1.330 | 0.238 | 0.268 | 0.000 | 0.410 | 24.833 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 105 | 101 | 116 | 119 | 0 | 104 | 546 |
N.S. |
1 | 1.00 | 1.02 | 0.98 | 1.13 | 1.16 | 0.00 | 1.01 | 5.30 |
time (sec) |
N/A | 0.181 | 0.389 | 1.269 | 0.330 | 0.265 | 0.000 | 0.415 | 23.648 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 168 | 168 | 936 | 198 | 192 | 163 | 0 | 325 | 278 |
N.S. |
1 | 1.00 | 5.57 | 1.18 | 1.14 | 0.97 | 0.00 | 1.93 | 1.65 |
time (sec) |
N/A | 0.214 | 7.520 | 1.573 | 0.237 | 0.252 | 0.000 | 0.450 | 25.486 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 73 | 96 | 103 | 109 | 0 | 73 | 139 |
N.S. |
1 | 1.00 | 2.43 | 3.20 | 3.43 | 3.63 | 0.00 | 2.43 | 4.63 |
time (sec) |
N/A | 0.052 | 0.351 | 1.306 | 0.244 | 0.248 | 0.000 | 0.436 | 22.349 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 258 | 258 | 1342 | 255 | 251 | 187 | 0 | 536 | 419 |
N.S. |
1 | 1.00 | 5.20 | 0.99 | 0.97 | 0.72 | 0.00 | 2.08 | 1.62 |
time (sec) |
N/A | 0.335 | 7.849 | 1.859 | 0.220 | 0.275 | 0.000 | 0.452 | 26.550 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 143 | 143 | 54 | 166 | 151 | 142 | 0 | 144 | 186 |
N.S. |
1 | 1.00 | 0.38 | 1.16 | 1.06 | 0.99 | 0.00 | 1.01 | 1.30 |
time (sec) |
N/A | 0.142 | 0.621 | 1.642 | 0.243 | 0.239 | 0.000 | 0.453 | 24.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 330 | 330 | 1732 | 304 | 322 | 214 | 0 | 706 | 566 |
N.S. |
1 | 1.00 | 5.25 | 0.92 | 0.98 | 0.65 | 0.00 | 2.14 | 1.72 |
time (sec) |
N/A | 0.377 | 7.976 | 1.951 | 0.244 | 0.273 | 0.000 | 0.473 | 26.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 201 | 201 | 115 | 213 | 193 | 167 | 0 | 214 | 447 |
N.S. |
1 | 1.00 | 0.57 | 1.06 | 0.96 | 0.83 | 0.00 | 1.06 | 2.22 |
time (sec) |
N/A | 0.194 | 0.897 | 1.902 | 0.228 | 0.252 | 0.000 | 0.477 | 26.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 408 | 408 | 242 | 350 | 382 | 251 | 0 | 880 | 703 |
N.S. |
1 | 1.00 | 0.59 | 0.86 | 0.94 | 0.62 | 0.00 | 2.16 | 1.72 |
time (sec) |
N/A | 0.461 | 3.158 | 2.509 | 0.232 | 0.278 | 0.000 | 0.501 | 27.359 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 254 | 254 | 175 | 259 | 233 | 194 | 0 | 284 | 560 |
N.S. |
1 | 1.00 | 0.69 | 1.02 | 0.92 | 0.76 | 0.00 | 1.12 | 2.20 |
time (sec) |
N/A | 0.266 | 1.844 | 2.357 | 0.244 | 0.273 | 0.000 | 0.481 | 26.398 |
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 | 515 | 515 | 307 | 325 | 290 | 250 | 1037 | 342 | 801 |
N.S. |
1 | 1.00 | 0.60 | 0.63 | 0.56 | 0.49 | 2.01 | 0.66 | 1.56 |
time (sec) |
N/A | 0.625 | 7.337 | 2.049 | 0.229 | 0.288 | 1.508 | 0.492 | 24.163 |
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 | 337 | 337 | 542 | 236 | 224 | 217 | 440 | 313 | 495 |
N.S. |
1 | 1.00 | 1.61 | 0.70 | 0.66 | 0.64 | 1.31 | 0.93 | 1.47 |
time (sec) |
N/A | 0.387 | 6.210 | 1.869 | 0.221 | 0.271 | 1.033 | 0.532 | 26.800 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 426 | 426 | 259 | 279 | 228 | 220 | 826 | 278 | 650 |
N.S. |
1 | 1.00 | 0.61 | 0.65 | 0.54 | 0.52 | 1.94 | 0.65 | 1.53 |
time (sec) |
N/A | 0.510 | 3.568 | 1.740 | 0.251 | 0.264 | 0.769 | 0.581 | 26.059 |
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 | 275 | 275 | 450 | 206 | 194 | 186 | 357 | 259 | 372 |
N.S. |
1 | 1.00 | 1.64 | 0.75 | 0.71 | 0.68 | 1.30 | 0.94 | 1.35 |
time (sec) |
N/A | 0.351 | 6.210 | 1.517 | 0.230 | 0.267 | 0.545 | 0.537 | 27.647 |
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 | 126 | 126 | 188 | 221 | 187 | 182 | 609 | 211 | 472 |
N.S. |
1 | 1.00 | 1.49 | 1.75 | 1.48 | 1.44 | 4.83 | 1.67 | 3.75 |
time (sec) |
N/A | 0.113 | 3.821 | 1.197 | 0.245 | 0.261 | 0.420 | 0.489 | 24.994 |
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 | 94 | 94 | 156 | 167 | 172 | 155 | 267 | 187 | 248 |
N.S. |
1 | 1.00 | 1.66 | 1.78 | 1.83 | 1.65 | 2.84 | 1.99 | 2.64 |
time (sec) |
N/A | 0.059 | 1.737 | 1.449 | 0.234 | 0.249 | 0.288 | 0.364 | 23.199 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 170 | 170 | 711 | 192 | 170 | 160 | 0 | 199 | 297 |
N.S. |
1 | 1.00 | 4.18 | 1.13 | 1.00 | 0.94 | 0.00 | 1.17 | 1.75 |
time (sec) |
N/A | 0.242 | 6.512 | 1.554 | 0.215 | 0.263 | 0.000 | 0.508 | 24.929 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 205 | 205 | 632 | 169 | 162 | 177 | 0 | 283 | 277 |
N.S. |
1 | 1.00 | 3.08 | 0.82 | 0.79 | 0.86 | 0.00 | 1.38 | 1.35 |
time (sec) |
N/A | 0.262 | 8.365 | 1.820 | 0.240 | 0.264 | 0.000 | 0.512 | 26.784 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 169 | 169 | 571 | 209 | 179 | 177 | 0 | 173 | 354 |
N.S. |
1 | 1.00 | 3.38 | 1.24 | 1.06 | 1.05 | 0.00 | 1.02 | 2.09 |
time (sec) |
N/A | 0.268 | 6.356 | 1.582 | 0.305 | 0.264 | 0.000 | 0.527 | 25.009 |