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 | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 116 | 116 | 27 | 22 | 0 | 11 | 0 | 0 | 21 | 0 |
N.S. |
1 | 1.00 | 0.23 | 0.19 | 0.00 | 0.09 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.387 | 10.009 | 0.747 | 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 | A | F | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 19 | 0 | 68 | 0 | 31 | 25 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.00 | 2.83 | 0.00 | 1.29 | 1.04 | 0.00 |
time (sec) |
N/A | 0.265 | 0.024 | 0.158 | 0.000 | 0.114 | 0.000 | 0.112 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 312 | 310 | 27 | 22 | 0 | 14 | 0 | 0 | 23 | 0 |
N.S. |
1 | 0.99 | 0.09 | 0.07 | 0.00 | 0.04 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.739 | 10.012 | 0.964 | 0.000 | 0.105 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 281 | 271 | 27 | 22 | 0 | 37 | 0 | 0 | 21 | 0 |
N.S. |
1 | 0.96 | 0.10 | 0.08 | 0.00 | 0.13 | 0.00 | 0.00 | 0.07 | 0.00 |
time (sec) |
N/A | 0.594 | 10.012 | 0.456 | 0.000 | 0.104 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 67 | 59 | 48 | 0 | 169 | 0 | 114 | 64 | 0 |
N.S. |
1 | 0.89 | 0.79 | 0.64 | 0.00 | 2.25 | 0.00 | 1.52 | 0.85 | 0.00 |
time (sec) |
N/A | 0.333 | 1.538 | 0.214 | 0.000 | 0.264 | 0.000 | 0.197 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 44 | 52 | 40 | 0 | 153 | 0 | 69 | 49 | 0 |
N.S. |
1 | 0.88 | 1.04 | 0.80 | 0.00 | 3.06 | 0.00 | 1.38 | 0.98 | 0.00 |
time (sec) |
N/A | 0.288 | 0.282 | 0.185 | 0.000 | 0.198 | 0.000 | 0.178 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 34 | 17 | 0 | 98 | 0 | 59 | 36 | 0 |
N.S. |
1 | 1.00 | 1.42 | 0.71 | 0.00 | 4.08 | 0.00 | 2.46 | 1.50 | 0.00 |
time (sec) |
N/A | 0.254 | 0.336 | 0.158 | 0.000 | 0.177 | 0.000 | 0.136 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 18 | 41 | 17 | 0 | 28 | 17 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.78 | 1.78 | 0.74 | 0.00 | 1.22 | 0.74 | 0.74 |
time (sec) |
N/A | 0.225 | 0.268 | 0.160 | 0.114 | 0.076 | 0.000 | 0.156 | 0.143 | 22.353 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 52 | 30 | 25 | 50 | 25 | 0 | 0 | 24 | 29 |
N.S. |
1 | 1.06 | 0.61 | 0.51 | 1.02 | 0.51 | 0.00 | 0.00 | 0.49 | 0.59 |
time (sec) |
N/A | 0.255 | 1.292 | 0.168 | 0.113 | 0.101 | 0.000 | 0.000 | 0.150 | 22.295 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 36 | 0 | 0 | 0 | 0 | 71 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 1.92 | 0.00 |
time (sec) |
N/A | 0.259 | 0.039 | 0.260 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 62 | 40 | 35 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.29 | 0.83 | 0.73 | 0.00 | 0.00 | 0.00 | 0.00 | 0.50 | 0.00 |
time (sec) |
N/A | 0.275 | 0.045 | 0.243 | 0.000 | 0.000 | 0.000 | 0.000 | 0.155 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 66 | 44 | 37 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.27 | 0.85 | 0.71 | 0.00 | 0.00 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.274 | 0.046 | 0.255 | 0.000 | 0.000 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | F(-2) | F | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 80 | 33 | 30 | 18 | 0 | 0 | 0 | 16 | 43 |
N.S. |
1 | 2.35 | 0.97 | 0.88 | 0.53 | 0.00 | 0.00 | 0.00 | 0.47 | 1.26 |
time (sec) |
N/A | 0.331 | 0.086 | 0.221 | 0.102 | 0.000 | 0.000 | 0.000 | 0.151 | 22.610 |
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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 71 | 60 | 0 | 0 | 0 | 0 | 0 | 156 | 0 |
N.S. |
1 | 1.20 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.64 | 0.00 |
time (sec) |
N/A | 0.317 | 0.103 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 71 | 60 | 0 | 0 | 0 | 0 | 0 | 156 | 0 |
N.S. |
1 | 1.20 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.64 | 0.00 |
time (sec) |
N/A | 0.321 | 0.019 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 61 | 58 | 0 | 0 | 0 | 0 | 0 | 156 | 0 |
N.S. |
1 | 1.07 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.74 | 0.00 |
time (sec) |
N/A | 0.301 | 0.021 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 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 | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 61 | 58 | 0 | 0 | 0 | 0 | 0 | 156 | 0 |
N.S. |
1 | 1.07 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.74 | 0.00 |
time (sec) |
N/A | 0.308 | 0.021 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 26 | 23 | 18 | 26 | 29 | 0 | 29 | 19 | 0 |
N.S. |
1 | 0.70 | 0.62 | 0.49 | 0.70 | 0.78 | 0.00 | 0.78 | 0.51 | 0.00 |
time (sec) |
N/A | 0.247 | 0.070 | 0.479 | 0.110 | 0.111 | 0.000 | 0.108 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 26 | 23 | 18 | 26 | 29 | 0 | 29 | 19 | 0 |
N.S. |
1 | 0.70 | 0.62 | 0.49 | 0.70 | 0.78 | 0.00 | 0.78 | 0.51 | 0.00 |
time (sec) |
N/A | 0.250 | 0.002 | 0.372 | 0.111 | 0.119 | 0.000 | 0.143 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 71 | 37 | 34 | 30 | 40 | 41 | 0 | 42 | 30 | 0 |
N.S. |
1 | 0.52 | 0.48 | 0.42 | 0.56 | 0.58 | 0.00 | 0.59 | 0.42 | 0.00 |
time (sec) |
N/A | 0.276 | 0.067 | 0.447 | 0.148 | 0.135 | 0.000 | 0.118 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 42 | 37 | 42 | 256 | 0 | 48 | 39 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.76 | 0.86 | 5.22 | 0.00 | 0.98 | 0.80 | 0.00 |
time (sec) |
N/A | 0.279 | 0.081 | 0.247 | 0.106 | 0.108 | 0.000 | 0.112 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 42 | 37 | 42 | 256 | 0 | 48 | 39 | 0 |
N.S. |
1 | 1.00 | 0.86 | 0.76 | 0.86 | 5.22 | 0.00 | 0.98 | 0.80 | 0.00 |
time (sec) |
N/A | 0.279 | 0.003 | 0.231 | 0.111 | 0.120 | 0.000 | 0.115 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 37 | 30 | 26 | 32 | 126 | 0 | 43 | 22 | 0 |
N.S. |
1 | 0.84 | 0.68 | 0.59 | 0.73 | 2.86 | 0.00 | 0.98 | 0.50 | 0.00 |
time (sec) |
N/A | 0.259 | 0.035 | 0.433 | 0.117 | 0.129 | 0.000 | 0.116 | 0.141 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 134 | 103 | 132 | 105 | 66 | 484 | 46 | 90 | 345 |
N.S. |
1 | 1.21 | 0.93 | 1.19 | 0.95 | 0.59 | 4.36 | 0.41 | 0.81 | 3.11 |
time (sec) |
N/A | 0.376 | 0.491 | 0.200 | 0.106 | 0.101 | 43.551 | 0.116 | 0.155 | 28.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 105 | 95 | 111 | 83 | 58 | 393 | 40 | 71 | 269 |
N.S. |
1 | 1.21 | 1.09 | 1.28 | 0.95 | 0.67 | 4.52 | 0.46 | 0.82 | 3.09 |
time (sec) |
N/A | 0.356 | 0.375 | 0.174 | 0.107 | 0.098 | 10.354 | 0.118 | 0.166 | 25.821 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 76 | 87 | 90 | 61 | 50 | 269 | 34 | 52 | 191 |
N.S. |
1 | 1.21 | 1.38 | 1.43 | 0.97 | 0.79 | 4.27 | 0.54 | 0.83 | 3.03 |
time (sec) |
N/A | 0.306 | 0.278 | 0.235 | 0.107 | 0.106 | 5.148 | 0.127 | 0.141 | 24.240 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | C | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 43 | 75 | 70 | 41 | 44 | 133 | 28 | 36 | 118 |
N.S. |
1 | 1.16 | 2.03 | 1.89 | 1.11 | 1.19 | 3.59 | 0.76 | 0.97 | 3.19 |
time (sec) |
N/A | 0.272 | 0.204 | 0.223 | 0.104 | 0.079 | 2.774 | 0.124 | 0.158 | 23.313 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 43 | 68 | 38 | 41 | 48 | 71 | 51 | 46 | 47 |
N.S. |
1 | 1.48 | 2.34 | 1.31 | 1.41 | 1.66 | 2.45 | 1.76 | 1.59 | 1.62 |
time (sec) |
N/A | 0.270 | 0.155 | 0.169 | 0.108 | 0.109 | 3.452 | 0.122 | 0.247 | 22.667 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 53 | 29 | 25 | 42 | 27 | 107 | 88 | 46 | 24 |
N.S. |
1 | 1.18 | 0.64 | 0.56 | 0.93 | 0.60 | 2.38 | 1.96 | 1.02 | 0.53 |
time (sec) |
N/A | 0.247 | 0.117 | 0.231 | 0.109 | 0.090 | 2.784 | 0.124 | 0.249 | 22.536 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 82 | 37 | 33 | 62 | 35 | 189 | 130 | 65 | 32 |
N.S. |
1 | 1.12 | 0.51 | 0.45 | 0.85 | 0.48 | 2.59 | 1.78 | 0.89 | 0.44 |
time (sec) |
N/A | 0.275 | 0.144 | 0.216 | 0.103 | 0.104 | 3.834 | 0.121 | 0.218 | 22.669 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 97 | 111 | 45 | 41 | 84 | 43 | 274 | 175 | 84 | 40 |
N.S. |
1 | 1.14 | 0.46 | 0.42 | 0.87 | 0.44 | 2.82 | 1.80 | 0.87 | 0.41 |
time (sec) |
N/A | 0.299 | 0.213 | 0.179 | 0.104 | 0.091 | 5.223 | 0.123 | 0.239 | 22.641 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 140 | 53 | 49 | 106 | 51 | 359 | 217 | 103 | 48 |
N.S. |
1 | 1.16 | 0.44 | 0.40 | 0.88 | 0.42 | 2.97 | 1.79 | 0.85 | 0.40 |
time (sec) |
N/A | 0.320 | 0.152 | 0.181 | 0.105 | 0.115 | 8.692 | 0.126 | 0.220 | 22.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 114 | 114 | 106 | 191 | 0 | 274 | 0 | 0 | 41 | 0 |
N.S. |
1 | 1.00 | 0.93 | 1.68 | 0.00 | 2.40 | 0.00 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.369 | 4.235 | 0.792 | 0.000 | 0.167 | 0.000 | 0.000 | 0.929 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 24 | 40 | 25 | 0 | 16 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.14 | 1.90 | 1.19 | 0.00 | 0.76 | 0.00 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 0.236 | 0.844 | 0.210 | 0.000 | 0.114 | 0.000 | 0.000 | 0.279 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 24 | 73 | 33 | 0 | 16 | 0 | 0 | 22 | 0 |
N.S. |
1 | 1.14 | 3.48 | 1.57 | 0.00 | 0.76 | 0.00 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 0.302 | 0.792 | 0.266 | 0.000 | 0.114 | 0.000 | 0.000 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | B | F | A | F(-2) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 49 | 66 | 49 | 0 | 16 | 0 | 0 | 22 | 0 |
N.S. |
1 | 2.33 | 3.14 | 2.33 | 0.00 | 0.76 | 0.00 | 0.00 | 1.05 | 0.00 |
time (sec) |
N/A | 0.277 | 10.055 | 0.319 | 0.000 | 0.112 | 0.000 | 0.000 | 0.282 | 0.000 |