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 | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 57 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.78 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.505 | 0.476 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 63 | 0 | 0 | 0 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.511 | 0.448 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 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 | 76 | 76 | 104 | 0 | 0 | 0 | 0 | 0 | 31 | 0 |
N.S. |
1 | 1.00 | 1.37 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.613 | 33.014 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.208 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 75 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.531 | 10.601 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.206 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 76 | 76 | 72 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.541 | 10.668 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 78 | 73 | 0 | 0 | 0 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.00 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.557 | 10.773 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.259 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 117 | 67 | 153 | 0 | 95 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.17 | 0.67 | 1.53 | 0.00 | 0.95 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.841 | 0.424 | 1.003 | 0.000 | 0.116 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 81 | 62 | 248 | 0 | 93 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.08 | 0.83 | 3.31 | 0.00 | 1.24 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.646 | 0.290 | 0.950 | 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 | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 81 | 55 | 141 | 0 | 82 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.12 | 0.76 | 1.96 | 0.00 | 1.14 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.608 | 0.290 | 0.776 | 0.000 | 0.116 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 43 | 237 | 0 | 59 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.00 | 0.98 | 5.39 | 0.00 | 1.34 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 0.430 | 0.079 | 0.891 | 0.000 | 0.112 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 42 | 120 | 0 | 55 | 0 | 0 | 12 | 63 |
N.S. |
1 | 1.00 | 0.98 | 2.79 | 0.00 | 1.28 | 0.00 | 0.00 | 0.28 | 1.47 |
time (sec) |
N/A | 0.379 | 0.071 | 0.648 | 0.000 | 0.121 | 0.000 | 0.000 | 0.204 | 25.560 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 75 | 57 | 155 | 0 | 80 | 0 | 0 | 19 | 0 |
N.S. |
1 | 1.10 | 0.84 | 2.28 | 0.00 | 1.18 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.583 | 0.177 | 0.719 | 0.000 | 0.123 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 79 | 55 | 135 | 0 | 96 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.07 | 0.74 | 1.82 | 0.00 | 1.30 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.577 | 0.231 | 0.751 | 0.000 | 0.095 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 109 | 68 | 246 | 0 | 128 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.09 | 0.68 | 2.46 | 0.00 | 1.28 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.766 | 0.269 | 0.841 | 0.000 | 0.109 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 117 | 68 | 154 | 0 | 99 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.14 | 0.66 | 1.50 | 0.00 | 0.96 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.812 | 0.366 | 1.006 | 0.000 | 0.095 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 81 | 62 | 249 | 0 | 98 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.05 | 0.81 | 3.23 | 0.00 | 1.27 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.608 | 0.424 | 0.956 | 0.000 | 0.090 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 81 | 56 | 141 | 0 | 85 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.08 | 0.75 | 1.88 | 0.00 | 1.13 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.613 | 0.178 | 0.800 | 0.000 | 0.094 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 45 | 238 | 0 | 61 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 0.98 | 5.17 | 0.00 | 1.33 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.441 | 0.018 | 0.809 | 0.000 | 0.096 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 43 | 121 | 0 | 57 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 0.98 | 2.75 | 0.00 | 1.30 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.418 | 0.010 | 0.674 | 0.000 | 0.118 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 71 | 54 | 156 | 0 | 83 | 0 | 0 | 20 | 0 |
N.S. |
1 | 1.00 | 0.76 | 2.20 | 0.00 | 1.17 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.518 | 0.012 | 0.726 | 0.000 | 0.114 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 79 | 58 | 136 | 0 | 99 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.10 | 0.81 | 1.89 | 0.00 | 1.38 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.571 | 0.222 | 0.770 | 0.000 | 0.081 | 0.000 | 0.000 | 0.194 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 109 | 68 | 247 | 0 | 138 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.06 | 0.66 | 2.40 | 0.00 | 1.34 | 0.00 | 0.00 | 0.21 | 0.00 |
time (sec) |
N/A | 0.758 | 0.419 | 0.817 | 0.000 | 0.088 | 0.000 | 0.000 | 0.245 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 117 | 70 | 155 | 0 | 98 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.15 | 0.69 | 1.52 | 0.00 | 0.96 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.790 | 0.292 | 1.032 | 0.000 | 0.123 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 81 | 57 | 254 | 0 | 96 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.12 | 0.79 | 3.53 | 0.00 | 1.33 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.602 | 0.218 | 0.918 | 0.000 | 0.110 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 79 | 64 | 139 | 0 | 85 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.07 | 0.86 | 1.88 | 0.00 | 1.15 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.583 | 0.103 | 0.757 | 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 | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 42 | 243 | 0 | 62 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.98 | 5.65 | 0.00 | 1.44 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.371 | 0.023 | 0.793 | 0.000 | 0.086 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 45 | 125 | 0 | 58 | 0 | 0 | 15 | 0 |
N.S. |
1 | 1.00 | 0.98 | 2.72 | 0.00 | 1.26 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.411 | 0.010 | 0.727 | 0.000 | 0.101 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 75 | 52 | 161 | 0 | 83 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.07 | 0.74 | 2.30 | 0.00 | 1.19 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.581 | 0.271 | 0.729 | 0.000 | 0.089 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 79 | 60 | 145 | 0 | 99 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.03 | 0.78 | 1.88 | 0.00 | 1.29 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.572 | 0.169 | 0.751 | 0.000 | 0.092 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 117 | 70 | 158 | 0 | 98 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.14 | 0.68 | 1.53 | 0.00 | 0.95 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.789 | 0.195 | 1.023 | 0.000 | 0.088 | 0.000 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 79 | 60 | 257 | 0 | 96 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.07 | 0.81 | 3.47 | 0.00 | 1.30 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.593 | 0.131 | 0.926 | 0.000 | 0.112 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 77 | 63 | 142 | 0 | 85 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.82 | 1.84 | 0.00 | 1.10 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.542 | 0.012 | 0.759 | 0.000 | 0.111 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 45 | 246 | 0 | 62 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.98 | 5.35 | 0.00 | 1.35 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.420 | 0.020 | 0.779 | 0.000 | 0.078 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 45 | 128 | 0 | 58 | 0 | 0 | 15 | 0 |
N.S. |
1 | 1.00 | 0.98 | 2.78 | 0.00 | 1.26 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.426 | 0.011 | 0.747 | 0.000 | 0.090 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 75 | 55 | 167 | 0 | 83 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.03 | 0.75 | 2.29 | 0.00 | 1.14 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.573 | 0.228 | 0.749 | 0.000 | 0.124 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 79 | 60 | 148 | 0 | 99 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.03 | 0.78 | 1.92 | 0.00 | 1.29 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.583 | 0.228 | 0.753 | 0.000 | 0.092 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | C | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 109 | 73 | 272 | 0 | 134 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.04 | 0.70 | 2.59 | 0.00 | 1.28 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.797 | 0.340 | 0.844 | 0.000 | 0.090 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 87 | 102 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 1.17 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.500 | 12.037 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.167 | 0.000 |