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 | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 69 | 0 | 82 | 0 | 0 | 11 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.88 | 0.00 | 3.42 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.180 | 0.003 | 0.635 | 0.000 | 0.120 | 0.000 | 0.000 | 0.204 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | F(-2) | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 194 | 316 | 299 | 535 | 0 | 0 | 568 | 0 | 67 | 16 |
N.S. |
1 | 1.63 | 1.54 | 2.76 | 0.00 | 0.00 | 2.93 | 0.00 | 0.35 | 0.08 |
time (sec) |
N/A | 0.733 | 0.093 | 1.369 | 0.000 | 0.000 | 46.675 | 0.000 | 0.230 | 0.212 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 199 | 166 | 282 | 0 | 0 | 291 | 0 | 46 | 276 |
N.S. |
1 | 1.33 | 1.11 | 1.88 | 0.00 | 0.00 | 1.94 | 0.00 | 0.31 | 1.84 |
time (sec) |
N/A | 0.547 | 0.073 | 1.128 | 0.000 | 0.000 | 25.332 | 0.000 | 0.228 | 0.287 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 117 | 85 | 120 | 0 | 0 | 124 | 0 | 25 | 111 |
N.S. |
1 | 1.10 | 0.80 | 1.13 | 0.00 | 0.00 | 1.17 | 0.00 | 0.24 | 1.05 |
time (sec) |
N/A | 0.426 | 0.066 | 0.874 | 0.000 | 0.000 | 12.459 | 0.000 | 0.203 | 0.178 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 40 | 30 | 12 | 0 | 34 | 0 | 9 | 70 |
N.S. |
1 | 1.00 | 1.25 | 0.94 | 0.38 | 0.00 | 1.06 | 0.00 | 0.28 | 2.19 |
time (sec) |
N/A | 0.188 | 0.024 | 0.370 | 0.036 | 0.000 | 5.400 | 0.000 | 0.198 | 0.120 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A | B |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 17 | 15 | 17 | 0 | 12 | 17 | 17 | 16 |
N.S. |
1 | 1.00 | 1.13 | 1.00 | 1.13 | 0.00 | 0.80 | 1.13 | 1.13 | 1.07 |
time (sec) |
N/A | 0.198 | 0.201 | 0.023 | 0.069 | 0.000 | 21.278 | 0.109 | 0.255 | 0.080 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 82 | 83 | 78 | 93 | 0 | 0 | 0 | 0 | 28 | 16 |
N.S. |
1 | 1.01 | 0.95 | 1.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.34 | 0.20 |
time (sec) |
N/A | 0.563 | 0.103 | 1.917 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.146 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 156 | 124 | 185 | 0 | 0 | 0 | 0 | 39 | 16 |
N.S. |
1 | 1.14 | 0.91 | 1.35 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.12 |
time (sec) |
N/A | 0.684 | 0.484 | 2.481 | 0.000 | 0.000 | 0.000 | 0.000 | 0.203 | 0.166 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 273 | 180 | 304 | 0 | 0 | 0 | 0 | 50 | 16 |
N.S. |
1 | 1.51 | 0.99 | 1.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.09 |
time (sec) |
N/A | 0.873 | 0.465 | 3.492 | 0.000 | 0.000 | 0.000 | 0.000 | 0.241 | 0.193 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 124 | 71 | 164 | 159 | 156 | 223 | 163 | 164 | 163 |
N.S. |
1 | 1.11 | 0.63 | 1.46 | 1.42 | 1.39 | 1.99 | 1.46 | 1.46 | 1.46 |
time (sec) |
N/A | 0.422 | 0.226 | 0.507 | 0.060 | 0.093 | 0.092 | 0.109 | 0.214 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 95 | 56 | 104 | 110 | 101 | 146 | 103 | 104 | 103 |
N.S. |
1 | 1.09 | 0.64 | 1.20 | 1.26 | 1.16 | 1.68 | 1.18 | 1.20 | 1.18 |
time (sec) |
N/A | 0.341 | 0.152 | 0.467 | 0.047 | 0.101 | 0.077 | 0.115 | 0.196 | 0.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 66 | 41 | 58 | 69 | 57 | 82 | 57 | 58 | 57 |
N.S. |
1 | 1.06 | 0.66 | 0.94 | 1.11 | 0.92 | 1.32 | 0.92 | 0.94 | 0.92 |
time (sec) |
N/A | 0.281 | 0.115 | 0.464 | 0.048 | 0.082 | 0.074 | 0.114 | 0.224 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 24 | 24 | 36 | 23 | 34 | 23 | 26 | 23 |
N.S. |
1 | 1.00 | 0.65 | 0.65 | 0.97 | 0.62 | 0.92 | 0.62 | 0.70 | 0.62 |
time (sec) |
N/A | 0.205 | 0.077 | 0.356 | 0.028 | 0.096 | 0.051 | 0.111 | 0.240 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 15 | 14 | 14 | 12 | 14 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.93 | 0.93 | 0.80 | 0.93 | 0.93 | 0.93 |
time (sec) |
N/A | 0.151 | 0.002 | 0.108 | 0.037 | 0.090 | 0.034 | 0.114 | 0.206 | 0.060 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 29 | 40 | 28 | 31 | 0 | 29 | 26 | 0 |
N.S. |
1 | 1.00 | 1.04 | 1.43 | 1.00 | 1.11 | 0.00 | 1.04 | 0.93 | 0.00 |
time (sec) |
N/A | 0.184 | 0.060 | 0.643 | 0.077 | 0.090 | 0.000 | 0.110 | 0.210 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 54 | 69 | 35 | 63 | 0 | 307 | 42 | 0 |
N.S. |
1 | 1.00 | 1.02 | 1.30 | 0.66 | 1.19 | 0.00 | 5.79 | 0.79 | 0.00 |
time (sec) |
N/A | 0.304 | 0.087 | 0.681 | 0.072 | 0.088 | 0.000 | 0.123 | 0.225 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 86 | 72 | 106 | 35 | 107 | 0 | 169 | 58 | 0 |
N.S. |
1 | 1.02 | 0.86 | 1.26 | 0.42 | 1.27 | 0.00 | 2.01 | 0.69 | 0.00 |
time (sec) |
N/A | 0.422 | 0.095 | 0.705 | 0.091 | 0.097 | 0.000 | 0.112 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 119 | 88 | 137 | 35 | 165 | 0 | 278 | 74 | 0 |
N.S. |
1 | 1.07 | 0.79 | 1.23 | 0.32 | 1.49 | 0.00 | 2.50 | 0.67 | 0.00 |
time (sec) |
N/A | 0.567 | 0.104 | 0.697 | 0.090 | 0.094 | 0.000 | 0.113 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | F | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 314 | 223 | 240 | 0 | 279 | 374 | 0 | 248 | 248 |
N.S. |
1 | 3.20 | 2.28 | 2.45 | 0.00 | 2.85 | 3.82 | 0.00 | 2.53 | 2.53 |
time (sec) |
N/A | 1.155 | 0.088 | 0.608 | 0.000 | 0.089 | 0.118 | 0.000 | 0.228 | 0.144 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | B | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 256 | 160 | 136 | 0 | 180 | 216 | 0 | 138 | 149 |
N.S. |
1 | 2.67 | 1.67 | 1.42 | 0.00 | 1.88 | 2.25 | 0.00 | 1.44 | 1.55 |
time (sec) |
N/A | 0.923 | 0.064 | 0.602 | 0.000 | 0.087 | 0.085 | 0.000 | 0.228 | 0.123 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 93 | 198 | 99 | 54 | 0 | 100 | 92 | 0 | 57 | 70 |
N.S. |
1 | 2.13 | 1.06 | 0.58 | 0.00 | 1.08 | 0.99 | 0.00 | 0.61 | 0.75 |
time (sec) |
N/A | 0.579 | 0.064 | 0.440 | 0.000 | 0.093 | 0.060 | 0.000 | 0.201 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 53 | 21 | 27 | 42 | 29 | 0 | 22 | 20 |
N.S. |
1 | 1.00 | 1.83 | 0.72 | 0.93 | 1.45 | 1.00 | 0.00 | 0.76 | 0.69 |
time (sec) |
N/A | 0.191 | 0.018 | 0.168 | 0.057 | 0.089 | 0.048 | 0.000 | 0.231 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 81 | 81 | 0 | 107 | 0 | 0 | 0 | 0 | 99 | 0 |
N.S. |
1 | 1.00 | 0.00 | 1.32 | 0.00 | 0.00 | 0.00 | 0.00 | 1.22 | 0.00 |
time (sec) |
N/A | 0.459 | 0.000 | 0.709 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 79 | 87 | 174 | 0 | 106 | 0 | 0 | 770 | 0 |
N.S. |
1 | 1.08 | 1.19 | 2.38 | 0.00 | 1.45 | 0.00 | 0.00 | 10.55 | 0.00 |
time (sec) |
N/A | 0.360 | 0.056 | 0.722 | 0.000 | 0.096 | 0.000 | 0.000 | 0.212 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 126 | 94 | 314 | 0 | 179 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.29 | 0.96 | 3.20 | 0.00 | 1.83 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.438 | 0.106 | 0.710 | 0.000 | 0.102 | 0.000 | 0.000 | 0.228 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 193 | 117 | 412 | 0 | 276 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.97 | 1.19 | 4.20 | 0.00 | 2.82 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.535 | 0.162 | 0.764 | 0.000 | 0.124 | 0.000 | 0.000 | 0.207 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 259 | 191 | 510 | 0 | 384 | 0 | 0 | 0 | 0 |
N.S. |
1 | 2.64 | 1.95 | 5.20 | 0.00 | 3.92 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.647 | 0.169 | 0.802 | 0.000 | 0.152 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | F | B | B | F | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 529 | 361 | 421 | 0 | 401 | 741 | 0 | 462 | 411 |
N.S. |
1 | 3.78 | 2.58 | 3.01 | 0.00 | 2.86 | 5.29 | 0.00 | 3.30 | 2.94 |
time (sec) |
N/A | 1.168 | 0.146 | 0.773 | 0.000 | 0.096 | 0.199 | 0.000 | 0.209 | 0.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | B | A | F | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 436 | 252 | 252 | 0 | 265 | 447 | 0 | 265 | 239 |
N.S. |
1 | 3.18 | 1.84 | 1.84 | 0.00 | 1.93 | 3.26 | 0.00 | 1.93 | 1.74 |
time (sec) |
N/A | 0.947 | 0.103 | 0.714 | 0.000 | 0.089 | 0.153 | 0.000 | 0.234 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | F | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 349 | 146 | 111 | 0 | 149 | 202 | 0 | 114 | 121 |
N.S. |
1 | 4.15 | 1.74 | 1.32 | 0.00 | 1.77 | 2.40 | 0.00 | 1.36 | 1.44 |
time (sec) |
N/A | 0.809 | 0.075 | 0.552 | 0.000 | 0.087 | 0.101 | 0.000 | 0.227 | 0.087 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | A | F | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 81 | 39 | 27 | 64 | 65 | 0 | 40 | 43 |
N.S. |
1 | 1.00 | 2.79 | 1.34 | 0.93 | 2.21 | 2.24 | 0.00 | 1.38 | 1.48 |
time (sec) |
N/A | 0.185 | 0.021 | 0.357 | 0.052 | 0.099 | 0.071 | 0.000 | 0.256 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 179 | 0 | 239 | 0 | 0 | 0 | 0 | 215 | 0 |
N.S. |
1 | 1.10 | 0.00 | 1.48 | 0.00 | 0.00 | 0.00 | 0.00 | 1.33 | 0.00 |
time (sec) |
N/A | 0.906 | 0.000 | 0.839 | 0.000 | 0.000 | 0.000 | 0.000 | 0.214 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 122 | 88 | 335 | 0 | 164 | 0 | 0 | 1192 | 0 |
N.S. |
1 | 1.28 | 0.93 | 3.53 | 0.00 | 1.73 | 0.00 | 0.00 | 12.55 | 0.00 |
time (sec) |
N/A | 0.442 | 0.103 | 0.852 | 0.000 | 0.109 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 126 | 157 | 126 | 563 | 0 | 274 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.25 | 1.00 | 4.47 | 0.00 | 2.17 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.512 | 0.183 | 0.809 | 0.000 | 0.093 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 246 | 145 | 763 | 0 | 406 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.73 | 1.02 | 5.37 | 0.00 | 2.86 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.645 | 0.229 | 0.878 | 0.000 | 0.105 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 341 | 328 | 963 | 0 | 572 | 0 | 0 | 0 | 0 |
N.S. |
1 | 2.40 | 2.31 | 6.78 | 0.00 | 4.03 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.818 | 0.183 | 0.888 | 0.000 | 0.153 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 263 | 282 | 0 | 0 | 360 | 0 | 0 | 96 | 24 |
N.S. |
1 | 1.89 | 2.03 | 0.00 | 0.00 | 2.59 | 0.00 | 0.00 | 0.69 | 0.17 |
time (sec) |
N/A | 0.708 | 0.334 | 0.000 | 0.000 | 0.102 | 0.000 | 0.000 | 0.220 | 0.188 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 118 | 176 | 171 | 0 | 0 | 223 | 0 | 0 | 68 | 24 |
N.S. |
1 | 1.49 | 1.45 | 0.00 | 0.00 | 1.89 | 0.00 | 0.00 | 0.58 | 0.20 |
time (sec) |
N/A | 0.564 | 0.177 | 0.000 | 0.000 | 0.103 | 0.000 | 0.000 | 0.221 | 0.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 128 | 113 | 0 | 0 | 120 | 0 | 0 | 40 | 22 |
N.S. |
1 | 1.47 | 1.30 | 0.00 | 0.00 | 1.38 | 0.00 | 0.00 | 0.46 | 0.25 |
time (sec) |
N/A | 0.476 | 0.082 | 0.000 | 0.000 | 0.089 | 0.000 | 0.000 | 0.198 | 0.402 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 48 | 0 | 27 | 52 | 0 | 0 | 17 | 21 |
N.S. |
1 | 1.00 | 1.66 | 0.00 | 0.93 | 1.79 | 0.00 | 0.00 | 0.59 | 0.72 |
time (sec) |
N/A | 0.185 | 0.033 | 0.000 | 0.051 | 0.114 | 0.000 | 0.000 | 0.189 | 0.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | B |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 17 | 22 | 17 | 17 | 17 | 17 | 30 | 24 |
N.S. |
1 | 1.00 | 1.13 | 1.47 | 1.13 | 1.13 | 1.13 | 1.13 | 2.00 | 1.60 |
time (sec) |
N/A | 0.195 | 0.338 | 0.278 | 0.098 | 0.112 | 0.693 | 0.107 | 0.258 | 0.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 135 | 121 | 0 | 0 | 349 | 0 | 0 | 54 | 24 |
N.S. |
1 | 1.38 | 1.23 | 0.00 | 0.00 | 3.56 | 0.00 | 0.00 | 0.55 | 0.24 |
time (sec) |
N/A | 0.938 | 0.266 | 0.000 | 0.000 | 0.133 | 0.000 | 0.000 | 0.204 | 0.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 211 | 174 | 0 | 0 | 680 | 0 | 0 | 78 | 24 |
N.S. |
1 | 1.38 | 1.14 | 0.00 | 0.00 | 4.44 | 0.00 | 0.00 | 0.51 | 0.16 |
time (sec) |
N/A | 1.262 | 0.367 | 0.000 | 0.000 | 0.115 | 0.000 | 0.000 | 0.207 | 0.465 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | B | F | F | F | B |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 330 | 0 | 0 | 0 | 1218 | 0 | 0 | 102 | 24 |
N.S. |
1 | 1.68 | 0.00 | 0.00 | 0.00 | 6.18 | 0.00 | 0.00 | 0.52 | 0.12 |
time (sec) |
N/A | 1.531 | 0.000 | 0.000 | 0.000 | 0.144 | 0.000 | 0.000 | 0.210 | 0.581 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 274 | 398 | 0 | 0 | 506 | 0 | 0 | 140 | 24 |
N.S. |
1 | 1.89 | 2.74 | 0.00 | 0.00 | 3.49 | 0.00 | 0.00 | 0.97 | 0.17 |
time (sec) |
N/A | 0.821 | 0.348 | 0.000 | 0.000 | 0.117 | 0.000 | 0.000 | 0.221 | 1.444 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 226 | 229 | 0 | 0 | 326 | 0 | 0 | 101 | 24 |
N.S. |
1 | 2.02 | 2.04 | 0.00 | 0.00 | 2.91 | 0.00 | 0.00 | 0.90 | 0.21 |
time (sec) |
N/A | 0.645 | 0.238 | 0.000 | 0.000 | 0.100 | 0.000 | 0.000 | 0.197 | 1.390 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 195 | 142 | 0 | 0 | 178 | 0 | 0 | 62 | 22 |
N.S. |
1 | 2.32 | 1.69 | 0.00 | 0.00 | 2.12 | 0.00 | 0.00 | 0.74 | 0.26 |
time (sec) |
N/A | 0.595 | 0.145 | 0.000 | 0.000 | 0.103 | 0.000 | 0.000 | 0.200 | 2.356 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 77 | 0 | 27 | 83 | 0 | 0 | 28 | 29 |
N.S. |
1 | 1.00 | 2.66 | 0.00 | 0.93 | 2.86 | 0.00 | 0.00 | 0.97 | 1.00 |
time (sec) |
N/A | 0.192 | 0.040 | 0.000 | 0.061 | 0.091 | 0.000 | 0.000 | 0.251 | 1.322 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | B |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 17 | 22 | 17 | 17 | 19 | 17 | 54 | 24 |
N.S. |
1 | 1.00 | 1.13 | 1.47 | 1.13 | 1.13 | 1.27 | 1.13 | 3.60 | 1.60 |
time (sec) |
N/A | 0.200 | 0.666 | 0.326 | 0.086 | 0.085 | 1.526 | 0.109 | 0.209 | 3.721 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 120 | 224 | 198 | 0 | 0 | 821 | 0 | 0 | 95 | 24 |
N.S. |
1 | 1.87 | 1.65 | 0.00 | 0.00 | 6.84 | 0.00 | 0.00 | 0.79 | 0.20 |
time (sec) |
N/A | 1.181 | 0.277 | 0.000 | 0.000 | 0.113 | 0.000 | 0.000 | 0.197 | 5.709 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 179 | 306 | 309 | 0 | 0 | 1284 | 0 | 0 | 136 | 24 |
N.S. |
1 | 1.71 | 1.73 | 0.00 | 0.00 | 7.17 | 0.00 | 0.00 | 0.76 | 0.13 |
time (sec) |
N/A | 1.540 | 0.910 | 0.000 | 0.000 | 0.133 | 0.000 | 0.000 | 0.228 | 19.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | B | F | F | F | B |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 217 | 433 | 0 | 0 | 0 | 1987 | 0 | 0 | 177 | 24 |
N.S. |
1 | 2.00 | 0.00 | 0.00 | 0.00 | 9.16 | 0.00 | 0.00 | 0.82 | 0.11 |
time (sec) |
N/A | 1.420 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 | 0.000 | 0.182 | 61.743 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 355 | 482 | 0 | 0 | 662 | 0 | 0 | 184 | 24 |
N.S. |
1 | 2.55 | 3.47 | 0.00 | 0.00 | 4.76 | 0.00 | 0.00 | 1.32 | 0.17 |
time (sec) |
N/A | 0.857 | 0.322 | 0.000 | 0.000 | 0.094 | 0.000 | 0.000 | 0.193 | 0.226 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 330 | 351 | 0 | 0 | 424 | 0 | 0 | 134 | 24 |
N.S. |
1 | 3.03 | 3.22 | 0.00 | 0.00 | 3.89 | 0.00 | 0.00 | 1.23 | 0.22 |
time (sec) |
N/A | 0.818 | 0.235 | 0.000 | 0.000 | 0.107 | 0.000 | 0.000 | 0.227 | 0.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 284 | 270 | 0 | 0 | 235 | 0 | 0 | 84 | 22 |
N.S. |
1 | 3.38 | 3.21 | 0.00 | 0.00 | 2.80 | 0.00 | 0.00 | 1.00 | 0.26 |
time (sec) |
N/A | 0.713 | 0.126 | 0.000 | 0.000 | 0.147 | 0.000 | 0.000 | 0.231 | 0.472 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | A | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 89 | 0 | 27 | 113 | 0 | 0 | 39 | 29 |
N.S. |
1 | 1.00 | 3.07 | 0.00 | 0.93 | 3.90 | 0.00 | 0.00 | 1.34 | 1.00 |
time (sec) |
N/A | 0.186 | 0.031 | 0.000 | 0.052 | 0.086 | 0.000 | 0.000 | 0.198 | 0.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | B |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 17 | 22 | 17 | 17 | 19 | 17 | 78 | 24 |
N.S. |
1 | 1.00 | 1.13 | 1.47 | 1.13 | 1.13 | 1.27 | 1.13 | 5.20 | 1.60 |
time (sec) |
N/A | 0.194 | 0.262 | 0.313 | 0.103 | 0.113 | 2.004 | 0.105 | 0.214 | 0.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 349 | 273 | 0 | 0 | 1517 | 0 | 0 | 136 | 24 |
N.S. |
1 | 2.42 | 1.90 | 0.00 | 0.00 | 10.53 | 0.00 | 0.00 | 0.94 | 0.17 |
time (sec) |
N/A | 1.021 | 0.606 | 0.000 | 0.000 | 0.142 | 0.000 | 0.000 | 0.202 | 0.352 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | F | F | B | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 205 | 430 | 877 | 0 | 0 | 2285 | 0 | 0 | 194 | 24 |
N.S. |
1 | 2.10 | 4.28 | 0.00 | 0.00 | 11.15 | 0.00 | 0.00 | 0.95 | 0.12 |
time (sec) |
N/A | 1.171 | 6.908 | 0.000 | 0.000 | 0.206 | 0.000 | 0.000 | 0.247 | 0.422 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | F | F | F | B | F | F | F | B |
verified |
N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 573 | 0 | 0 | 0 | 3116 | 0 | 0 | 252 | 24 |
N.S. |
1 | 2.31 | 0.00 | 0.00 | 0.00 | 12.56 | 0.00 | 0.00 | 1.02 | 0.10 |
time (sec) |
N/A | 1.370 | 0.000 | 0.000 | 0.000 | 0.345 | 0.000 | 0.000 | 0.215 | 0.340 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 281 | 134 | 158 | 0 | 117 | 0 | 0 | 113 | 167 |
N.S. |
1 | 3.51 | 1.68 | 1.98 | 0.00 | 1.46 | 0.00 | 0.00 | 1.41 | 2.09 |
time (sec) |
N/A | 0.680 | 0.088 | 0.322 | 0.000 | 0.108 | 0.000 | 0.000 | 0.224 | 0.283 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 236 | 117 | 134 | 0 | 104 | 165 | 0 | 92 | 132 |
N.S. |
1 | 2.95 | 1.46 | 1.68 | 0.00 | 1.30 | 2.06 | 0.00 | 1.15 | 1.65 |
time (sec) |
N/A | 0.564 | 0.077 | 0.295 | 0.000 | 0.107 | 28.690 | 0.000 | 0.232 | 0.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 191 | 97 | 114 | 0 | 89 | 136 | 0 | 75 | 134 |
N.S. |
1 | 2.39 | 1.21 | 1.42 | 0.00 | 1.11 | 1.70 | 0.00 | 0.94 | 1.68 |
time (sec) |
N/A | 0.510 | 0.064 | 0.290 | 0.000 | 0.112 | 8.245 | 0.000 | 0.198 | 0.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 142 | 76 | 76 | 0 | 70 | 99 | 0 | 61 | 87 |
N.S. |
1 | 2.09 | 1.12 | 1.12 | 0.00 | 1.03 | 1.46 | 0.00 | 0.90 | 1.28 |
time (sec) |
N/A | 0.451 | 0.049 | 0.307 | 0.000 | 0.097 | 3.811 | 0.000 | 0.230 | 0.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 96 | 65 | 88 | 0 | 58 | 116 | 0 | 65 | 98 |
N.S. |
1 | 1.39 | 0.94 | 1.28 | 0.00 | 0.84 | 1.68 | 0.00 | 0.94 | 1.42 |
time (sec) |
N/A | 0.381 | 0.052 | 0.351 | 0.000 | 0.107 | 3.156 | 0.000 | 0.210 | 0.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 99 | 69 | 120 | 0 | 61 | 151 | 0 | 75 | 145 |
N.S. |
1 | 1.30 | 0.91 | 1.58 | 0.00 | 0.80 | 1.99 | 0.00 | 0.99 | 1.91 |
time (sec) |
N/A | 0.377 | 0.071 | 0.345 | 0.000 | 0.111 | 9.990 | 0.000 | 0.230 | 0.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 143 | 80 | 142 | 0 | 77 | 185 | 0 | 93 | 124 |
N.S. |
1 | 1.79 | 1.00 | 1.78 | 0.00 | 0.96 | 2.31 | 0.00 | 1.16 | 1.55 |
time (sec) |
N/A | 0.425 | 0.102 | 0.319 | 0.000 | 0.100 | 102.344 | 0.000 | 0.226 | 0.319 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 192 | 96 | 166 | 0 | 91 | 0 | 0 | 114 | 194 |
N.S. |
1 | 2.40 | 1.20 | 2.08 | 0.00 | 1.14 | 0.00 | 0.00 | 1.42 | 2.42 |
time (sec) |
N/A | 0.506 | 0.110 | 0.346 | 0.000 | 0.101 | 0.000 | 0.000 | 0.198 | 0.311 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | B |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 15 | 18 | 13 | 13 | 19 | 13 | 31 | 20 |
N.S. |
1 | 1.00 | 1.15 | 1.38 | 1.00 | 1.00 | 1.46 | 1.00 | 2.38 | 1.54 |
time (sec) |
N/A | 0.184 | 4.495 | 0.181 | 0.079 | 0.101 | 2.012 | 0.110 | 0.210 | 0.779 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | B |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 15 | 18 | 13 | 13 | 19 | 13 | 30 | 20 |
N.S. |
1 | 1.00 | 1.15 | 1.38 | 1.00 | 1.00 | 1.46 | 1.00 | 2.31 | 1.54 |
time (sec) |
N/A | 0.188 | 4.478 | 0.187 | 0.092 | 0.102 | 1.798 | 0.111 | 0.230 | 0.757 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | B |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 15 | 18 | 13 | 13 | 19 | 13 | 35 | 20 |
N.S. |
1 | 1.00 | 1.15 | 1.38 | 1.00 | 1.00 | 1.46 | 1.00 | 2.69 | 1.54 |
time (sec) |
N/A | 0.183 | 2.774 | 0.174 | 0.088 | 0.135 | 2.267 | 0.106 | 0.197 | 12.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | B |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 15 | 18 | 13 | 13 | 19 | 13 | 38 | 20 |
N.S. |
1 | 1.00 | 1.15 | 1.38 | 1.00 | 1.00 | 1.46 | 1.00 | 2.92 | 1.54 |
time (sec) |
N/A | 0.198 | 2.787 | 0.174 | 0.112 | 0.106 | 3.009 | 0.108 | 0.217 | 12.502 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 82 | 119 | 178 | 0 | 98 | 0 | 0 | 103 | 124 |
N.S. |
1 | 1.02 | 1.49 | 2.22 | 0.00 | 1.22 | 0.00 | 0.00 | 1.29 | 1.55 |
time (sec) |
N/A | 0.335 | 0.203 | 0.463 | 0.000 | 0.107 | 0.000 | 0.000 | 0.233 | 0.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 82 | 95 | 115 | 0 | 83 | 65 | 0 | 86 | 114 |
N.S. |
1 | 1.02 | 1.19 | 1.44 | 0.00 | 1.04 | 0.81 | 0.00 | 1.08 | 1.42 |
time (sec) |
N/A | 0.342 | 0.191 | 0.464 | 0.000 | 0.118 | 28.233 | 0.000 | 0.195 | 0.274 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 80 | 82 | 95 | 115 | 0 | 83 | 65 | 0 | 86 | 114 |
N.S. |
1 | 1.02 | 1.19 | 1.44 | 0.00 | 1.04 | 0.81 | 0.00 | 1.08 | 1.42 |
time (sec) |
N/A | 0.550 | 0.065 | 0.386 | 0.000 | 0.134 | 9.775 | 0.000 | 0.202 | 0.253 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 82 | 80 | 142 | 0 | 65 | 65 | 0 | 73 | 79 |
N.S. |
1 | 1.11 | 1.08 | 1.92 | 0.00 | 0.88 | 0.88 | 0.00 | 0.99 | 1.07 |
time (sec) |
N/A | 0.532 | 0.054 | 0.418 | 0.000 | 0.132 | 6.070 | 0.000 | 0.256 | 0.266 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 78 | 69 | 142 | 0 | 64 | 65 | 0 | 73 | 79 |
N.S. |
1 | 1.15 | 1.01 | 2.09 | 0.00 | 0.94 | 0.96 | 0.00 | 1.07 | 1.16 |
time (sec) |
N/A | 0.502 | 0.070 | 0.408 | 0.000 | 0.109 | 4.820 | 0.000 | 0.207 | 0.276 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 75 | 54 | 186 | 0 | 51 | 68 | 0 | 63 | 69 |
N.S. |
1 | 1.09 | 0.78 | 2.70 | 0.00 | 0.74 | 0.99 | 0.00 | 0.91 | 1.00 |
time (sec) |
N/A | 0.550 | 0.068 | 0.450 | 0.000 | 0.130 | 4.819 | 0.000 | 0.210 | 0.306 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 221 | 215 | 147 | 0 | 0 | 314 | 0 | 0 | 556 | 0 |
N.S. |
1 | 0.97 | 0.67 | 0.00 | 0.00 | 1.42 | 0.00 | 0.00 | 2.52 | 0.00 |
time (sec) |
N/A | 0.901 | 0.287 | 0.000 | 0.000 | 0.133 | 0.000 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 150 | 149 | 117 | 0 | 0 | 154 | 0 | 0 | 204 | 0 |
N.S. |
1 | 0.99 | 0.78 | 0.00 | 0.00 | 1.03 | 0.00 | 0.00 | 1.36 | 0.00 |
time (sec) |
N/A | 0.516 | 0.161 | 0.000 | 0.000 | 0.105 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 52 | 0 | 39 | 44 | 0 | 0 | 59 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.75 | 0.85 | 0.00 | 0.00 | 1.13 | 0.00 |
time (sec) |
N/A | 0.198 | 0.030 | 0.000 | 0.068 | 0.088 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | F(-1) | N/A | N/A | B |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 17 | 15 | 17 | 0 | 0 | 17 | 17 | 16 |
N.S. |
1 | 1.00 | 1.13 | 1.00 | 1.13 | 0.00 | 0.00 | 1.13 | 1.13 | 1.07 |
time (sec) |
N/A | 0.191 | 0.629 | 0.024 | 0.075 | 0.000 | 0.000 | 0.109 | 0.191 | 0.128 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | B |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 17 | 22 | 17 | 17 | 19 | 17 | 24 | 24 |
N.S. |
1 | 1.00 | 1.13 | 1.47 | 1.13 | 1.13 | 1.27 | 1.13 | 1.60 | 1.60 |
time (sec) |
N/A | 0.191 | 0.608 | 0.336 | 0.091 | 0.104 | 0.443 | 0.101 | 0.274 | 0.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | B |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 17 | 22 | 17 | 17 | 20 | 17 | 35 | 24 |
N.S. |
1 | 1.00 | 1.13 | 1.47 | 1.13 | 1.13 | 1.33 | 1.13 | 2.33 | 1.60 |
time (sec) |
N/A | 0.189 | 0.752 | 0.296 | 0.082 | 0.106 | 0.818 | 0.116 | 0.192 | 0.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | B |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 17 | 22 | 17 | 17 | 20 | 17 | 46 | 24 |
N.S. |
1 | 1.00 | 1.13 | 1.47 | 1.13 | 1.13 | 1.33 | 1.13 | 3.07 | 1.60 |
time (sec) |
N/A | 0.190 | 1.021 | 0.337 | 0.107 | 0.130 | 1.140 | 0.114 | 0.199 | 0.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 13 | 11 | 13 | 13 | 0 | 13 | 13 | 13 |
N.S. |
1 | 1.00 | 1.18 | 1.00 | 1.18 | 1.18 | 0.00 | 1.18 | 1.18 | 1.18 |
time (sec) |
N/A | 0.179 | 0.487 | 0.036 | 0.091 | 0.100 | 0.000 | 0.105 | 0.256 | 0.101 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 17 | 15 | 17 | 17 | 0 | 17 | 17 | 17 |
N.S. |
1 | 1.00 | 1.13 | 1.00 | 1.13 | 1.13 | 0.00 | 1.13 | 1.13 | 1.13 |
time (sec) |
N/A | 0.188 | 0.734 | 0.158 | 0.094 | 0.159 | 0.000 | 0.111 | 0.229 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 169 | 174 | 217 | 3717 | 0 | 1080 | 0 | 0 | 88 | 0 |
N.S. |
1 | 1.03 | 1.28 | 21.99 | 0.00 | 6.39 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.651 | 0.204 | 17.763 | 0.000 | 0.135 | 0.000 | 0.000 | 0.237 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 147 | 169 | 1929 | 0 | 618 | 0 | 0 | 67 | 0 |
N.S. |
1 | 1.02 | 1.17 | 13.40 | 0.00 | 4.29 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.593 | 0.126 | 5.845 | 0.000 | 0.143 | 0.000 | 0.000 | 0.232 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 120 | 119 | 875 | 0 | 310 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.04 | 1.03 | 7.61 | 0.00 | 2.70 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.527 | 0.097 | 1.774 | 0.000 | 0.102 | 0.000 | 0.000 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 93 | 65 | 315 | 0 | 127 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.06 | 0.74 | 3.58 | 0.00 | 1.44 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.452 | 0.100 | 0.741 | 0.000 | 0.099 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 36 | 88 | 29 | 47 | 0 | 0 | 9 | 0 |
N.S. |
1 | 1.00 | 1.16 | 2.84 | 0.94 | 1.52 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.189 | 0.023 | 0.206 | 0.073 | 0.095 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | 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 | TBD |
size | 15 | 15 | 17 | 15 | 17 | 17 | 12 | 17 | 17 | 17 |
N.S. |
1 | 1.00 | 1.13 | 1.00 | 1.13 | 1.13 | 0.80 | 1.13 | 1.13 | 1.13 |
time (sec) |
N/A | 0.199 | 0.272 | 0.157 | 0.088 | 0.099 | 51.539 | 0.110 | 0.227 | 0.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 17 | 15 | 17 | 28 | 0 | 17 | 28 | 17 |
N.S. |
1 | 1.00 | 1.13 | 1.00 | 1.13 | 1.87 | 0.00 | 1.13 | 1.87 | 1.13 |
time (sec) |
N/A | 0.202 | 0.613 | 0.193 | 0.093 | 0.095 | 0.000 | 0.125 | 0.223 | 0.308 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | F(-1) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 17 | 15 | 17 | 39 | 0 | 17 | 39 | 17 |
N.S. |
1 | 1.00 | 1.13 | 1.00 | 1.13 | 2.60 | 0.00 | 1.13 | 2.60 | 1.13 |
time (sec) |
N/A | 0.193 | 0.617 | 0.202 | 0.101 | 0.102 | 0.000 | 0.112 | 0.199 | 0.368 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 129 | 112 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.07 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 1.006 | 0.261 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.217 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 129 | 112 | 0 | 0 | 0 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.07 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.966 | 0.244 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.247 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 120 | 107 | 0 | 0 | 0 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.07 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.957 | 0.216 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.205 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 59 | 55 | 0 | 55 | 101 | 0 | 0 | 21 | 0 |
N.S. |
1 | 0.97 | 0.90 | 0.00 | 0.90 | 1.66 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.336 | 0.282 | 0.000 | 0.100 | 0.110 | 0.000 | 0.000 | 0.230 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 117 | 107 | 0 | 0 | 0 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.07 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.664 | 0.165 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.243 | 0.000 |