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 | B | B | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 62 | 79 | 383 | 1170 | 140 | 0 | 104 | 23 | 0 |
N.S. |
1 | 1.00 | 1.27 | 6.18 | 18.87 | 2.26 | 0.00 | 1.68 | 0.37 | 0.00 |
time (sec) |
N/A | 0.371 | 0.112 | 1.231 | 0.209 | 0.083 | 0.000 | 0.362 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 101 | 94 | 551 | 2642 | 155 | 0 | 131 | 23 | 0 |
N.S. |
1 | 0.99 | 0.92 | 5.40 | 25.90 | 1.52 | 0.00 | 1.28 | 0.23 | 0.00 |
time (sec) |
N/A | 0.501 | 0.202 | 1.259 | 2.998 | 0.093 | 0.000 | 0.323 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 142 | 109 | 717 | 5115 | 165 | 0 | 154 | 23 | 0 |
N.S. |
1 | 1.03 | 0.79 | 5.20 | 37.07 | 1.20 | 0.00 | 1.12 | 0.17 | 0.00 |
time (sec) |
N/A | 0.654 | 0.362 | 1.283 | 42.633 | 0.085 | 0.000 | 0.383 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 182 | 93 | 99 | 84 | 78 | 0 | 122 | 45 | 0 |
N.S. |
1 | 1.12 | 0.57 | 0.61 | 0.52 | 0.48 | 0.00 | 0.75 | 0.28 | 0.00 |
time (sec) |
N/A | 0.841 | 0.258 | 1.101 | 0.183 | 0.077 | 0.000 | 0.766 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 131 | 81 | 86 | 69 | 67 | 0 | 100 | 45 | 0 |
N.S. |
1 | 1.13 | 0.70 | 0.74 | 0.59 | 0.58 | 0.00 | 0.86 | 0.39 | 0.00 |
time (sec) |
N/A | 0.571 | 0.170 | 0.993 | 0.175 | 0.080 | 0.000 | 0.507 | 0.185 | 0.000 |
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 | 86 | 91 | 67 | 71 | 53 | 55 | 0 | 77 | 43 | 0 |
N.S. |
1 | 1.06 | 0.78 | 0.83 | 0.62 | 0.64 | 0.00 | 0.90 | 0.50 | 0.00 |
time (sec) |
N/A | 0.407 | 0.107 | 0.846 | 0.155 | 0.077 | 0.000 | 0.365 | 0.167 | 0.000 |
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 | 59 | 59 | 55 | 58 | 38 | 44 | 0 | 55 | 34 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.98 | 0.64 | 0.75 | 0.00 | 0.93 | 0.58 | 0.00 |
time (sec) |
N/A | 0.280 | 0.067 | 0.699 | 0.155 | 0.072 | 0.000 | 0.349 | 0.185 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 66 | 65 | 209 | 0 | 127 | 0 | 89 | 47 | 0 |
N.S. |
1 | 1.00 | 0.98 | 3.17 | 0.00 | 1.92 | 0.00 | 1.35 | 0.71 | 0.00 |
time (sec) |
N/A | 0.396 | 0.088 | 1.040 | 0.000 | 0.089 | 0.000 | 0.392 | 0.308 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 65 | 81 | 385 | 1314 | 146 | 0 | 107 | 51 | 0 |
N.S. |
1 | 1.00 | 1.25 | 5.92 | 20.22 | 2.25 | 0.00 | 1.65 | 0.78 | 0.00 |
time (sec) |
N/A | 0.369 | 0.128 | 1.118 | 0.195 | 0.090 | 0.000 | 0.382 | 0.310 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 104 | 97 | 551 | 3216 | 162 | 0 | 134 | 51 | 0 |
N.S. |
1 | 0.98 | 0.92 | 5.20 | 30.34 | 1.53 | 0.00 | 1.26 | 0.48 | 0.00 |
time (sec) |
N/A | 0.522 | 0.263 | 1.122 | 0.697 | 0.091 | 0.000 | 0.342 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 145 | 110 | 718 | 5542 | 173 | 0 | 158 | 51 | 0 |
N.S. |
1 | 1.01 | 0.76 | 4.99 | 38.49 | 1.20 | 0.00 | 1.10 | 0.35 | 0.00 |
time (sec) |
N/A | 0.677 | 0.382 | 1.145 | 149.803 | 0.087 | 0.000 | 0.364 | 0.203 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 203 | 227 | 107 | 112 | 111 | 101 | 0 | 156 | 69 | 0 |
N.S. |
1 | 1.12 | 0.53 | 0.55 | 0.55 | 0.50 | 0.00 | 0.77 | 0.34 | 0.00 |
time (sec) |
N/A | 1.062 | 0.509 | 6.525 | 0.173 | 0.075 | 0.000 | 1.824 | 0.198 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 146 | 165 | 95 | 99 | 94 | 88 | 0 | 132 | 69 | 0 |
N.S. |
1 | 1.13 | 0.65 | 0.68 | 0.64 | 0.60 | 0.00 | 0.90 | 0.47 | 0.00 |
time (sec) |
N/A | 0.700 | 0.331 | 2.365 | 0.168 | 0.087 | 0.000 | 0.878 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 125 | 84 | 86 | 77 | 75 | 0 | 108 | 67 | 0 |
N.S. |
1 | 1.08 | 0.72 | 0.74 | 0.66 | 0.65 | 0.00 | 0.93 | 0.58 | 0.00 |
time (sec) |
N/A | 0.493 | 0.231 | 1.095 | 0.169 | 0.073 | 0.000 | 0.512 | 0.174 | 0.000 |
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 | 89 | 93 | 71 | 73 | 60 | 62 | 0 | 84 | 58 | 0 |
N.S. |
1 | 1.04 | 0.80 | 0.82 | 0.67 | 0.70 | 0.00 | 0.94 | 0.65 | 0.00 |
time (sec) |
N/A | 0.360 | 0.110 | 0.773 | 0.151 | 0.074 | 0.000 | 0.406 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 101 | 89 | 246 | 0 | 147 | 0 | 120 | 77 | 0 |
N.S. |
1 | 1.03 | 0.91 | 2.51 | 0.00 | 1.50 | 0.00 | 1.22 | 0.79 | 0.00 |
time (sec) |
N/A | 0.555 | 0.440 | 1.721 | 0.000 | 0.090 | 0.000 | 0.438 | 0.281 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 99 | 217 | 432 | 10847 | 164 | 0 | 135 | 83 | 0 |
N.S. |
1 | 1.08 | 2.36 | 4.70 | 117.90 | 1.78 | 0.00 | 1.47 | 0.90 | 0.00 |
time (sec) |
N/A | 0.552 | 9.245 | 6.734 | 0.421 | 0.091 | 0.000 | 0.410 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 108 | 267 | 551 | 3667 | 170 | 0 | 140 | 83 | 0 |
N.S. |
1 | 1.02 | 2.52 | 5.20 | 34.59 | 1.60 | 0.00 | 1.32 | 0.78 | 0.00 |
time (sec) |
N/A | 0.578 | 7.360 | 30.141 | 2.883 | 0.096 | 0.000 | 0.437 | 0.227 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 148 | 284 | 717 | 6703 | 183 | 0 | 166 | 83 | 0 |
N.S. |
1 | 1.03 | 1.97 | 4.98 | 46.55 | 1.27 | 0.00 | 1.15 | 0.58 | 0.00 |
time (sec) |
N/A | 0.770 | 7.392 | 98.381 | 44.740 | 0.086 | 0.000 | 0.475 | 0.249 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 182 | 189 | 388 | 882 | 0 | 196 | 0 | 192 | 83 | 0 |
N.S. |
1 | 1.04 | 2.13 | 4.85 | 0.00 | 1.08 | 0.00 | 1.05 | 0.46 | 0.00 |
time (sec) |
N/A | 0.944 | 7.910 | 287.907 | 0.000 | 0.094 | 0.000 | 0.452 | 0.231 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 127 | 83 | 86 | 77 | 75 | 0 | 108 | 80 | 0 |
N.S. |
1 | 1.07 | 0.70 | 0.72 | 0.65 | 0.63 | 0.00 | 0.91 | 0.67 | 0.00 |
time (sec) |
N/A | 0.467 | 0.249 | 0.823 | 0.168 | 0.076 | 0.000 | 0.514 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 199 | 112 | 194 | 696204 | 153 | 0 | 141 | 36 | 0 |
N.S. |
1 | 1.14 | 0.64 | 1.11 | 4001.17 | 0.88 | 0.00 | 0.81 | 0.21 | 0.00 |
time (sec) |
N/A | 1.066 | 0.395 | 1.033 | 15.906 | 0.080 | 0.000 | 0.608 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 140 | 154 | 101 | 183 | 908518 | 143 | 0 | 139 | 36 | 0 |
N.S. |
1 | 1.10 | 0.72 | 1.31 | 6489.41 | 1.02 | 0.00 | 0.99 | 0.26 | 0.00 |
time (sec) |
N/A | 0.767 | 0.280 | 0.915 | 16.319 | 0.088 | 0.000 | 0.426 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 112 | 84 | 132 | 19437 | 131 | 0 | 103 | 36 | 97 |
N.S. |
1 | 1.08 | 0.81 | 1.27 | 186.89 | 1.26 | 0.00 | 0.99 | 0.35 | 0.93 |
time (sec) |
N/A | 0.466 | 0.158 | 0.869 | 0.414 | 0.084 | 0.000 | 0.367 | 0.177 | 42.408 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 53 | 120 | 18948 | 122 | 0 | 100 | 34 | 60 |
N.S. |
1 | 1.00 | 0.73 | 1.64 | 259.56 | 1.67 | 0.00 | 1.37 | 0.47 | 0.82 |
time (sec) |
N/A | 0.305 | 0.056 | 0.823 | 0.496 | 0.082 | 0.000 | 0.363 | 0.171 | 0.113 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 40 | 56 | 90 | 135 | 0 | 52 | 28 | 45 |
N.S. |
1 | 1.00 | 0.87 | 1.22 | 1.96 | 2.93 | 0.00 | 1.13 | 0.61 | 0.98 |
time (sec) |
N/A | 0.208 | 0.012 | 0.696 | 0.173 | 0.082 | 0.000 | 0.355 | 0.164 | 42.365 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 85 | 85 | 65 | 226 | 0 | 164 | 0 | 121 | 34 | 0 |
N.S. |
1 | 1.00 | 0.76 | 2.66 | 0.00 | 1.93 | 0.00 | 1.42 | 0.40 | 0.00 |
time (sec) |
N/A | 0.433 | 0.073 | 0.957 | 0.000 | 0.085 | 0.000 | 0.387 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | B | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 117 | 192 | 470 | 18435 | 236 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.08 | 1.78 | 4.35 | 170.69 | 2.19 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.635 | 1.491 | 1.072 | 0.347 | 0.093 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 159 | 360 | 677 | 0 | 251 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.08 | 2.45 | 4.61 | 0.00 | 1.71 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.917 | 2.181 | 1.067 | 0.000 | 0.091 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 206 | 385 | 883 | 0 | 263 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.14 | 2.13 | 4.88 | 0.00 | 1.45 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 1.199 | 2.375 | 1.093 | 0.000 | 0.106 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 199 | 118 | 265 | 0 | 184 | 0 | 167 | 46 | 0 |
N.S. |
1 | 1.09 | 0.64 | 1.45 | 0.00 | 1.01 | 0.00 | 0.91 | 0.25 | 0.00 |
time (sec) |
N/A | 1.070 | 0.433 | 1.018 | 0.000 | 0.086 | 0.000 | 1.183 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 154 | 110 | 234 | 0 | 174 | 0 | 101 | 46 | 0 |
N.S. |
1 | 1.06 | 0.76 | 1.61 | 0.00 | 1.20 | 0.00 | 0.70 | 0.32 | 0.00 |
time (sec) |
N/A | 0.804 | 0.307 | 0.901 | 0.000 | 0.081 | 0.000 | 0.715 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 109 | 100 | 173 | 0 | 164 | 0 | 79 | 46 | 0 |
N.S. |
1 | 1.04 | 0.95 | 1.65 | 0.00 | 1.56 | 0.00 | 0.75 | 0.44 | 0.00 |
time (sec) |
N/A | 0.479 | 0.212 | 0.884 | 0.000 | 0.085 | 0.000 | 0.540 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 54 | 140 | 46532 | 154 | 0 | 116 | 44 | 0 |
N.S. |
1 | 1.00 | 0.70 | 1.82 | 604.31 | 2.00 | 0.00 | 1.51 | 0.57 | 0.00 |
time (sec) |
N/A | 0.322 | 0.119 | 0.796 | 2.073 | 0.087 | 0.000 | 0.379 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 63 | 138 | 15721 | 153 | 0 | 112 | 38 | 0 |
N.S. |
1 | 1.00 | 0.82 | 1.79 | 204.17 | 1.99 | 0.00 | 1.45 | 0.49 | 0.00 |
time (sec) |
N/A | 0.288 | 0.077 | 0.725 | 0.804 | 0.081 | 0.000 | 0.343 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 120 | 227 | 290 | 0 | 254 | 0 | 137 | 44 | 0 |
N.S. |
1 | 1.05 | 1.99 | 2.54 | 0.00 | 2.23 | 0.00 | 1.20 | 0.39 | 0.00 |
time (sec) |
N/A | 0.654 | 2.144 | 0.974 | 0.000 | 0.098 | 0.000 | 0.404 | 0.202 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 152 | 103 | 567 | 139280 | 286 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.06 | 0.72 | 3.94 | 967.22 | 1.99 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.915 | 0.547 | 1.072 | 5.481 | 0.092 | 0.000 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | A | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 200 | 841 | 807 | 0 | 302 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.08 | 4.55 | 4.36 | 0.00 | 1.63 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.207 | 7.654 | 1.085 | 0.000 | 0.097 | 0.000 | 0.000 | 0.248 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 183 | 199 | 123 | 242 | 0 | 208 | 0 | 116 | 56 | 0 |
N.S. |
1 | 1.09 | 0.67 | 1.32 | 0.00 | 1.14 | 0.00 | 0.63 | 0.31 | 0.00 |
time (sec) |
N/A | 1.123 | 0.819 | 1.042 | 0.000 | 0.095 | 0.000 | 3.314 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 145 | 155 | 113 | 208 | 0 | 198 | 0 | 167 | 56 | 0 |
N.S. |
1 | 1.07 | 0.78 | 1.43 | 0.00 | 1.37 | 0.00 | 1.15 | 0.39 | 0.00 |
time (sec) |
N/A | 0.817 | 0.511 | 0.912 | 0.000 | 0.090 | 0.000 | 1.893 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 113 | 104 | 174 | 0 | 188 | 0 | 132 | 56 | 0 |
N.S. |
1 | 1.06 | 0.97 | 1.63 | 0.00 | 1.76 | 0.00 | 1.23 | 0.52 | 0.00 |
time (sec) |
N/A | 0.486 | 0.446 | 0.874 | 0.000 | 0.086 | 0.000 | 1.074 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 112 | 65 | 174 | 0 | 188 | 0 | 69 | 54 | 0 |
N.S. |
1 | 1.05 | 0.61 | 1.63 | 0.00 | 1.76 | 0.00 | 0.64 | 0.50 | 0.00 |
time (sec) |
N/A | 0.411 | 0.367 | 0.799 | 0.000 | 0.088 | 0.000 | 0.627 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 112 | 65 | 174 | 84332 | 188 | 0 | 129 | 48 | 0 |
N.S. |
1 | 1.05 | 0.61 | 1.63 | 788.15 | 1.76 | 0.00 | 1.21 | 0.45 | 0.00 |
time (sec) |
N/A | 0.380 | 0.165 | 0.715 | 15.754 | 0.083 | 0.000 | 0.405 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 156 | 603 | 325 | 0 | 298 | 0 | 0 | 54 | 0 |
N.S. |
1 | 1.08 | 4.19 | 2.26 | 0.00 | 2.07 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.904 | 7.584 | 0.954 | 0.000 | 0.098 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | B | F | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 174 | 190 | 731 | 601 | 0 | 330 | 0 | 0 | 56 | 0 |
N.S. |
1 | 1.09 | 4.20 | 3.45 | 0.00 | 1.90 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 1.169 | 7.734 | 1.061 | 0.000 | 0.097 | 0.000 | 0.000 | 0.216 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 117 | 490 | 270 | 0 | 148 | 0 | 0 | 39 | 87 |
N.S. |
1 | 1.05 | 4.41 | 2.43 | 0.00 | 1.33 | 0.00 | 0.00 | 0.35 | 0.78 |
time (sec) |
N/A | 0.500 | 6.477 | 11.502 | 0.000 | 0.092 | 0.000 | 0.000 | 0.180 | 42.071 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 89 | 232 | 219 | 0 | 137 | 0 | 0 | 37 | 80 |
N.S. |
1 | 1.02 | 2.67 | 2.52 | 0.00 | 1.57 | 0.00 | 0.00 | 0.43 | 0.92 |
time (sec) |
N/A | 0.384 | 5.806 | 7.106 | 0.000 | 0.090 | 0.000 | 0.000 | 0.196 | 41.749 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 62 | 222 | 225 | 0 | 125 | 0 | 0 | 28 | 53 |
N.S. |
1 | 1.02 | 3.64 | 3.69 | 0.00 | 2.05 | 0.00 | 0.00 | 0.46 | 0.87 |
time (sec) |
N/A | 0.359 | 5.097 | 4.551 | 0.000 | 0.086 | 0.000 | 0.000 | 0.166 | 0.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 155 | 150 | 0 | 107 | 0 | 0 | 30 | 27 |
N.S. |
1 | 1.00 | 4.43 | 4.29 | 0.00 | 3.06 | 0.00 | 0.00 | 0.86 | 0.77 |
time (sec) |
N/A | 0.278 | 2.126 | 1.947 | 0.000 | 0.088 | 0.000 | 0.000 | 0.178 | 41.784 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 58 | 209 | 148 | 0 | 156 | 0 | 0 | 39 | 60 |
N.S. |
1 | 1.02 | 3.67 | 2.60 | 0.00 | 2.74 | 0.00 | 0.00 | 0.68 | 1.05 |
time (sec) |
N/A | 0.365 | 5.322 | 2.015 | 0.000 | 0.084 | 0.000 | 0.000 | 0.186 | 41.253 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 85 | 444 | 368 | 0 | 175 | 0 | 0 | 39 | 87 |
N.S. |
1 | 1.02 | 5.35 | 4.43 | 0.00 | 2.11 | 0.00 | 0.00 | 0.47 | 1.05 |
time (sec) |
N/A | 0.397 | 6.381 | 3.057 | 0.000 | 0.091 | 0.000 | 0.000 | 0.162 | 41.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 113 | 477 | 384 | 0 | 188 | 0 | 0 | 39 | 87 |
N.S. |
1 | 1.02 | 4.30 | 3.46 | 0.00 | 1.69 | 0.00 | 0.00 | 0.35 | 0.78 |
time (sec) |
N/A | 0.490 | 6.461 | 4.307 | 0.000 | 0.087 | 0.000 | 0.000 | 0.177 | 40.973 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 532 | 260 | 0 | 175 | 0 | 0 | 61 | 136 |
N.S. |
1 | 1.00 | 3.62 | 1.77 | 0.00 | 1.19 | 0.00 | 0.00 | 0.41 | 0.93 |
time (sec) |
N/A | 0.368 | 6.629 | 18.408 | 0.000 | 0.094 | 0.000 | 0.000 | 0.187 | 40.908 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 500 | 272 | 0 | 162 | 0 | 0 | 59 | 129 |
N.S. |
1 | 1.00 | 4.13 | 2.25 | 0.00 | 1.34 | 0.00 | 0.00 | 0.49 | 1.07 |
time (sec) |
N/A | 0.343 | 6.574 | 11.497 | 0.000 | 0.091 | 0.000 | 0.000 | 0.173 | 40.880 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 95 | 235 | 250 | 0 | 149 | 0 | 0 | 50 | 104 |
N.S. |
1 | 1.00 | 2.47 | 2.63 | 0.00 | 1.57 | 0.00 | 0.00 | 0.53 | 1.09 |
time (sec) |
N/A | 0.310 | 6.292 | 7.547 | 0.000 | 0.090 | 0.000 | 0.000 | 0.180 | 40.966 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 67 | 67 | 224 | 228 | 0 | 134 | 0 | 0 | 50 | 59 |
N.S. |
1 | 1.00 | 3.34 | 3.40 | 0.00 | 2.00 | 0.00 | 0.00 | 0.75 | 0.88 |
time (sec) |
N/A | 0.286 | 5.881 | 3.229 | 0.000 | 0.095 | 0.000 | 0.000 | 0.183 | 40.869 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 112 | 185 | 0 | 97 | 0 | 0 | 52 | 82 |
N.S. |
1 | 1.00 | 2.55 | 4.20 | 0.00 | 2.20 | 0.00 | 0.00 | 1.18 | 1.86 |
time (sec) |
N/A | 0.275 | 0.429 | 3.177 | 0.000 | 0.107 | 0.000 | 0.000 | 0.178 | 40.904 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 111 | 371 | 0 | 187 | 0 | 0 | 61 | 109 |
N.S. |
1 | 1.00 | 1.22 | 4.08 | 0.00 | 2.05 | 0.00 | 0.00 | 0.67 | 1.20 |
time (sec) |
N/A | 0.311 | 0.350 | 3.247 | 0.000 | 0.110 | 0.000 | 0.000 | 0.172 | 41.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 114 | 386 | 0 | 202 | 0 | 0 | 61 | 114 |
N.S. |
1 | 1.00 | 0.94 | 3.19 | 0.00 | 1.67 | 0.00 | 0.00 | 0.50 | 0.94 |
time (sec) |
N/A | 0.335 | 0.463 | 4.957 | 0.000 | 0.097 | 0.000 | 0.000 | 0.169 | 41.253 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 532 | 260 | 0 | 175 | 0 | 0 | 79 | 206 |
N.S. |
1 | 1.00 | 3.62 | 1.77 | 0.00 | 1.19 | 0.00 | 0.00 | 0.54 | 1.40 |
time (sec) |
N/A | 0.385 | 7.302 | 17.186 | 0.000 | 0.098 | 0.000 | 0.000 | 0.214 | 41.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 500 | 272 | 0 | 162 | 0 | 0 | 70 | 143 |
N.S. |
1 | 1.00 | 4.13 | 2.25 | 0.00 | 1.34 | 0.00 | 0.00 | 0.58 | 1.18 |
time (sec) |
N/A | 0.348 | 7.280 | 11.487 | 0.000 | 0.091 | 0.000 | 0.000 | 0.173 | 40.986 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 468 | 250 | 0 | 148 | 0 | 0 | 70 | 104 |
N.S. |
1 | 1.00 | 5.14 | 2.75 | 0.00 | 1.63 | 0.00 | 0.00 | 0.77 | 1.14 |
time (sec) |
N/A | 0.322 | 7.307 | 6.566 | 0.000 | 0.089 | 0.000 | 0.000 | 0.175 | 41.003 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 146 | 172 | 0 | 180 | 0 | 0 | 70 | 104 |
N.S. |
1 | 1.00 | 1.60 | 1.89 | 0.00 | 1.98 | 0.00 | 0.00 | 0.77 | 1.14 |
time (sec) |
N/A | 0.330 | 0.587 | 5.835 | 0.000 | 0.093 | 0.000 | 0.000 | 0.178 | 41.119 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 91 | 139 | 371 | 0 | 187 | 0 | 0 | 72 | 126 |
N.S. |
1 | 1.00 | 1.53 | 4.08 | 0.00 | 2.05 | 0.00 | 0.00 | 0.79 | 1.38 |
time (sec) |
N/A | 0.321 | 0.507 | 5.352 | 0.000 | 0.105 | 0.000 | 0.000 | 0.167 | 41.512 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 138 | 386 | 0 | 200 | 0 | 0 | 81 | 154 |
N.S. |
1 | 1.00 | 1.18 | 3.30 | 0.00 | 1.71 | 0.00 | 0.00 | 0.69 | 1.32 |
time (sec) |
N/A | 0.357 | 0.693 | 6.128 | 0.000 | 0.085 | 0.000 | 0.000 | 0.178 | 41.571 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 140 | 439 | 0 | 215 | 0 | 0 | 81 | 145 |
N.S. |
1 | 1.00 | 0.95 | 2.99 | 0.00 | 1.46 | 0.00 | 0.00 | 0.55 | 0.99 |
time (sec) |
N/A | 0.383 | 0.994 | 8.188 | 0.000 | 0.095 | 0.000 | 0.000 | 0.184 | 41.689 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 173 | 271 | 273 | 0 | 188 | 0 | 0 | 99 | 221 |
N.S. |
1 | 1.00 | 1.57 | 1.58 | 0.00 | 1.09 | 0.00 | 0.00 | 0.57 | 1.28 |
time (sec) |
N/A | 0.448 | 4.865 | 24.638 | 0.000 | 0.106 | 0.000 | 0.000 | 0.182 | 41.221 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 532 | 260 | 0 | 175 | 0 | 0 | 90 | 223 |
N.S. |
1 | 1.00 | 3.62 | 1.77 | 0.00 | 1.19 | 0.00 | 0.00 | 0.61 | 1.52 |
time (sec) |
N/A | 0.395 | 7.087 | 17.726 | 0.000 | 0.129 | 0.000 | 0.000 | 0.189 | 40.945 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 500 | 272 | 0 | 162 | 0 | 0 | 90 | 146 |
N.S. |
1 | 1.00 | 4.13 | 2.25 | 0.00 | 1.34 | 0.00 | 0.00 | 0.74 | 1.21 |
time (sec) |
N/A | 0.368 | 7.474 | 17.240 | 0.000 | 0.098 | 0.000 | 0.000 | 0.207 | 40.858 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 119 | 157 | 194 | 0 | 194 | 0 | 0 | 90 | 149 |
N.S. |
1 | 1.00 | 1.32 | 1.63 | 0.00 | 1.63 | 0.00 | 0.00 | 0.76 | 1.25 |
time (sec) |
N/A | 0.361 | 1.506 | 17.354 | 0.000 | 0.096 | 0.000 | 0.000 | 0.230 | 40.980 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 98 | 186 | 292 | 0 | 125 | 0 | 0 | 90 | 145 |
N.S. |
1 | 1.00 | 1.90 | 2.98 | 0.00 | 1.28 | 0.00 | 0.00 | 0.92 | 1.48 |
time (sec) |
N/A | 0.347 | 1.130 | 15.980 | 0.000 | 0.098 | 0.000 | 0.000 | 0.263 | 41.081 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 121 | 169 | 386 | 0 | 202 | 0 | 0 | 92 | 202 |
N.S. |
1 | 1.00 | 1.40 | 3.19 | 0.00 | 1.67 | 0.00 | 0.00 | 0.76 | 1.67 |
time (sec) |
N/A | 0.379 | 1.118 | 15.950 | 0.000 | 0.099 | 0.000 | 0.000 | 0.271 | 41.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 147 | 147 | 171 | 439 | 0 | 215 | 0 | 0 | 101 | 199 |
N.S. |
1 | 1.00 | 1.16 | 2.99 | 0.00 | 1.46 | 0.00 | 0.00 | 0.69 | 1.35 |
time (sec) |
N/A | 0.403 | 1.690 | 14.230 | 0.000 | 0.095 | 0.000 | 0.000 | 0.169 | 41.623 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 128 | 132 | 315 | 229 | 0 | 208 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.03 | 2.46 | 1.79 | 0.00 | 1.62 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.575 | 3.005 | 5.150 | 0.000 | 0.115 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 104 | 289 | 215 | 0 | 198 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.04 | 2.89 | 2.15 | 0.00 | 1.98 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.542 | 2.228 | 4.319 | 0.000 | 0.090 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 76 | 264 | 199 | 0 | 186 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.06 | 3.67 | 2.76 | 0.00 | 2.58 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.436 | 3.590 | 2.639 | 0.000 | 0.080 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 75 | 256 | 198 | 0 | 184 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.07 | 3.66 | 2.83 | 0.00 | 2.63 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.426 | 1.655 | 1.974 | 0.000 | 0.084 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 76 | 257 | 200 | 0 | 184 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.09 | 3.67 | 2.86 | 0.00 | 2.63 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.422 | 1.758 | 1.020 | 0.000 | 0.079 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 96 | 100 | 297 | 253 | 0 | 236 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.04 | 3.09 | 2.64 | 0.00 | 2.46 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.546 | 2.901 | 1.950 | 0.000 | 0.087 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 128 | 332 | 413 | 0 | 258 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.03 | 2.68 | 3.33 | 0.00 | 2.08 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.574 | 4.723 | 2.888 | 0.000 | 0.098 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 160 | 174 | 148 | 283 | 0 | 288 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.09 | 0.92 | 1.77 | 0.00 | 1.80 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.848 | 1.504 | 7.415 | 0.000 | 0.099 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 147 | 136 | 270 | 0 | 278 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.07 | 0.99 | 1.96 | 0.00 | 2.01 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.827 | 0.987 | 6.162 | 0.000 | 0.119 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 118 | 128 | 257 | 0 | 268 | 0 | 0 | 42 | 0 |
N.S. |
1 | 1.05 | 1.14 | 2.29 | 0.00 | 2.39 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.670 | 0.789 | 5.387 | 0.000 | 0.091 | 0.000 | 0.000 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 119 | 114 | 257 | 0 | 268 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.09 | 1.05 | 2.36 | 0.00 | 2.46 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.637 | 0.631 | 2.751 | 0.000 | 0.095 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 71 | 188 | 0 | 150 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.00 | 1.25 | 3.30 | 0.00 | 2.63 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.288 | 0.444 | 2.845 | 0.000 | 0.091 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 109 | 118 | 304 | 257 | 0 | 268 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.08 | 2.79 | 2.36 | 0.00 | 2.46 | 0.00 | 0.00 | 0.38 | 0.00 |
time (sec) |
N/A | 0.658 | 3.317 | 1.228 | 0.000 | 0.101 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 142 | 334 | 405 | 0 | 318 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.04 | 2.46 | 2.98 | 0.00 | 2.34 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.782 | 3.205 | 2.813 | 0.000 | 0.097 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 171 | 364 | 413 | 0 | 338 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.06 | 2.25 | 2.55 | 0.00 | 2.09 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.816 | 7.450 | 3.722 | 0.000 | 0.093 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 226 | 175 | 296 | 0 | 364 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.09 | 0.85 | 1.43 | 0.00 | 1.76 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 1.152 | 3.359 | 11.908 | 0.000 | 0.116 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 198 | 166 | 283 | 0 | 354 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.09 | 0.92 | 1.56 | 0.00 | 1.96 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.066 | 2.159 | 11.450 | 0.000 | 0.105 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 170 | 157 | 270 | 0 | 344 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.10 | 1.01 | 1.74 | 0.00 | 2.22 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.927 | 2.122 | 10.383 | 0.000 | 0.126 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 170 | 146 | 270 | 0 | 344 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.10 | 0.94 | 1.74 | 0.00 | 2.22 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.910 | 1.655 | 10.889 | 0.000 | 0.101 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 170 | 146 | 270 | 0 | 344 | 0 | 0 | 50 | 0 |
N.S. |
1 | 1.10 | 0.94 | 1.74 | 0.00 | 2.22 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.915 | 1.744 | 4.368 | 0.000 | 0.090 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 170 | 139 | 270 | 0 | 344 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.10 | 0.90 | 1.74 | 0.00 | 2.22 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.893 | 3.627 | 4.504 | 0.000 | 0.096 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 155 | 170 | 304 | 268 | 0 | 344 | 0 | 0 | 51 | 0 |
N.S. |
1 | 1.10 | 1.96 | 1.73 | 0.00 | 2.22 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.940 | 7.522 | 1.654 | 0.000 | 0.099 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-2) | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 181 | 194 | 364 | 555 | 0 | 394 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.07 | 2.01 | 3.07 | 0.00 | 2.18 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 1.080 | 3.345 | 4.530 | 0.000 | 0.100 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F(-1) | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 207 | 222 | 394 | 453 | 0 | 414 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.07 | 1.90 | 2.19 | 0.00 | 2.00 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 1.124 | 4.025 | 5.014 | 0.000 | 0.128 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 154 | 158 | 105 | 263 | 1921 | 127 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.03 | 0.68 | 1.71 | 12.47 | 0.82 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.708 | 0.363 | 11.764 | 0.328 | 0.111 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 115 | 91 | 237 | 1059 | 117 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.99 | 0.78 | 2.04 | 9.13 | 1.01 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.517 | 0.221 | 11.531 | 0.267 | 0.086 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 77 | 211 | 791 | 105 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.00 | 1.07 | 2.93 | 10.99 | 1.46 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.363 | 0.102 | 11.132 | 0.234 | 0.088 | 0.000 | 0.000 | 0.180 | 0.000 |