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 | A | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 154 | 62 | 94 | 117 | 145 | 0 | 111 | 102 | 228 |
N.S. |
1 | 1.83 | 0.74 | 1.12 | 1.39 | 1.73 | 0.00 | 1.32 | 1.21 | 2.71 |
time (sec) |
N/A | 0.605 | 0.203 | 0.127 | 0.113 | 0.080 | 0.000 | 0.134 | 0.163 | 0.707 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 31 | 266 | 0 | 137 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 1.00 | 8.58 | 0.00 | 4.42 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.183 | 0.037 | 0.350 | 0.000 | 0.081 | 0.000 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 29 | 98 | 0 | 137 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.00 | 0.94 | 3.16 | 0.00 | 4.42 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.182 | 0.029 | 0.454 | 0.000 | 0.086 | 0.000 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 50 | 41 | 171 | 0 | 151 | 0 | 0 | 10 | 0 |
N.S. |
1 | 1.11 | 0.91 | 3.80 | 0.00 | 3.36 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.243 | 0.032 | 2.845 | 0.000 | 0.084 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 43 | 396 | 0 | 76 | 0 | 0 | 23 | 0 |
N.S. |
1 | 1.00 | 0.91 | 8.43 | 0.00 | 1.62 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.273 | 0.063 | 6.173 | 0.000 | 0.083 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 69 | 50 | 174 | 0 | 181 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.13 | 0.82 | 2.85 | 0.00 | 2.97 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.411 | 0.083 | 3.810 | 0.000 | 0.091 | 0.000 | 0.000 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 68 | 56 | 1108 | 0 | 205 | 0 | 0 | 18 | 0 |
N.S. |
1 | 1.11 | 0.92 | 18.16 | 0.00 | 3.36 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.398 | 0.066 | 1.589 | 0.000 | 0.087 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 298 | 0 | 39 | 0 | 0 | 16 | 18 |
N.S. |
1 | 1.00 | 1.00 | 18.62 | 0.00 | 2.44 | 0.00 | 0.00 | 1.00 | 1.12 |
time (sec) |
N/A | 0.180 | 0.041 | 0.427 | 0.000 | 0.077 | 0.000 | 0.000 | 0.147 | 0.313 |
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 | 31 | 31 | 20 | 2946 | 0 | 32 | 0 | 0 | 18 | 20 |
N.S. |
1 | 1.00 | 0.65 | 95.03 | 0.00 | 1.03 | 0.00 | 0.00 | 0.58 | 0.65 |
time (sec) |
N/A | 0.249 | 0.040 | 5.905 | 0.000 | 0.078 | 0.000 | 0.000 | 0.150 | 0.222 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | B | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 31 | 24 | 121 | 0 | 43 | 0 | 0 | 18 | 29 |
N.S. |
1 | 1.07 | 0.83 | 4.17 | 0.00 | 1.48 | 0.00 | 0.00 | 0.62 | 1.00 |
time (sec) |
N/A | 0.298 | 0.032 | 0.384 | 0.000 | 0.080 | 0.000 | 0.000 | 0.154 | 0.247 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F(-1) | B | F(-1) | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 65 | 111 | 653 | 0 | 136 | 0 | 0 | 77 | 0 |
N.S. |
1 | 0.96 | 1.63 | 9.60 | 0.00 | 2.00 | 0.00 | 0.00 | 1.13 | 0.00 |
time (sec) |
N/A | 1.009 | 7.082 | 1.459 | 0.000 | 0.093 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | A | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 31 | 19 | 47 | 6 | 15 | 0 | 0 | 13 | 15 |
N.S. |
1 | 1.63 | 1.00 | 2.47 | 0.32 | 0.79 | 0.00 | 0.00 | 0.68 | 0.79 |
time (sec) |
N/A | 0.264 | 0.005 | 0.888 | 0.107 | 0.072 | 0.000 | 0.000 | 0.153 | 0.286 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 161 | 66 | 234 | 0 | 418 | 0 | 0 | 17 | 0 |
N.S. |
1 | 1.75 | 0.72 | 2.54 | 0.00 | 4.54 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.475 | 0.079 | 5.822 | 0.000 | 0.110 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 53 | 63 | 0 | 13 | 29 | 0 | 0 | 11 | 32 |
N.S. |
1 | 1.13 | 1.34 | 0.00 | 0.28 | 0.62 | 0.00 | 0.00 | 0.23 | 0.68 |
time (sec) |
N/A | 0.230 | 0.112 | 0.000 | 0.107 | 0.067 | 0.000 | 0.000 | 0.149 | 2.141 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 61 | 35 | 0 | 77 | 101 | 0 | 0 | 11 | 110 |
N.S. |
1 | 0.87 | 0.50 | 0.00 | 1.10 | 1.44 | 0.00 | 0.00 | 0.16 | 1.57 |
time (sec) |
N/A | 0.359 | 0.037 | 0.000 | 0.107 | 0.077 | 0.000 | 0.000 | 0.163 | 1.966 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F(-1) | F | F | F(-1) |
verified |
N/A | No | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 108 | 172 | 75 | 253 | 0 | 336 | 0 | 0 | 46 | 0 |
N.S. |
1 | 1.59 | 0.69 | 2.34 | 0.00 | 3.11 | 0.00 | 0.00 | 0.43 | 0.00 |
time (sec) |
N/A | 1.162 | 0.313 | 4.231 | 0.000 | 0.141 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | C | C | F | F(-2) | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 364 | 781 | 378 | 51988 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 2.15 | 1.04 | 142.82 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 3.262 | 16.340 | 87.517 | 0.000 | 0.000 | 0.000 | 0.000 | 0.251 | 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 | 125 | 151 | 58 | 0 | 60 | 56 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.21 | 0.46 | 0.00 | 0.48 | 0.45 | 0.00 | 0.00 | 0.22 | 0.00 |
time (sec) |
N/A | 0.993 | 0.595 | 0.000 | 0.148 | 0.083 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 83 | 61 | 56 | 55 | 108 | 0 | 55 | 70 | 43 |
N.S. |
1 | 1.14 | 0.84 | 0.77 | 0.75 | 1.48 | 0.00 | 0.75 | 0.96 | 0.59 |
time (sec) |
N/A | 0.238 | 0.102 | 1.261 | 0.101 | 0.098 | 0.000 | 0.128 | 0.162 | 0.073 |
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 | 69 | 79 | 48 | 103 | 53 | 88 | 0 | 41 | 68 | 0 |
N.S. |
1 | 1.14 | 0.70 | 1.49 | 0.77 | 1.28 | 0.00 | 0.59 | 0.99 | 0.00 |
time (sec) |
N/A | 0.246 | 0.048 | 2.582 | 0.101 | 0.085 | 0.000 | 0.129 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | C | F(-1) | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 63 | 61 | 82 | 36 | 123 | 0 | 41 | 49 | 0 |
N.S. |
1 | 1.09 | 1.05 | 1.41 | 0.62 | 2.12 | 0.00 | 0.71 | 0.84 | 0.00 |
time (sec) |
N/A | 0.239 | 0.050 | 0.394 | 0.100 | 0.073 | 0.000 | 0.128 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 60 | 37 | 51 | 43 | 51 | 0 | 30 | 64 | 28 |
N.S. |
1 | 1.09 | 0.67 | 0.93 | 0.78 | 0.93 | 0.00 | 0.55 | 1.16 | 0.51 |
time (sec) |
N/A | 0.232 | 0.080 | 0.516 | 0.022 | 0.094 | 0.000 | 0.131 | 0.168 | 0.366 |
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 | 39 | 39 | 39 | 83 | 716 | 100 | 0 | 38 | 34 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.13 | 18.36 | 2.56 | 0.00 | 0.97 | 0.87 | 0.00 |
time (sec) |
N/A | 0.236 | 0.068 | 0.410 | 0.163 | 0.095 | 0.000 | 0.138 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | B | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 53 | 63 | 53 | 69 | 131 | 0 | 40 | 74 | 0 |
N.S. |
1 | 1.10 | 1.31 | 1.10 | 1.44 | 2.73 | 0.00 | 0.83 | 1.54 | 0.00 |
time (sec) |
N/A | 0.257 | 0.283 | 0.464 | 0.111 | 0.092 | 0.000 | 0.134 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 53 | 28 | 46 | 192 | 42 | 0 | 33 | 44 | 28 |
N.S. |
1 | 1.08 | 0.57 | 0.94 | 3.92 | 0.86 | 0.00 | 0.67 | 0.90 | 0.57 |
time (sec) |
N/A | 0.310 | 0.059 | 0.347 | 0.046 | 0.086 | 0.000 | 0.122 | 0.158 | 0.338 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | C | A | F(-1) | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 111 | 119 | 295 | 124 | 115 | 127 | 0 | 0 | 115 | 0 |
N.S. |
1 | 1.07 | 2.66 | 1.12 | 1.04 | 1.14 | 0.00 | 0.00 | 1.04 | 0.00 |
time (sec) |
N/A | 0.723 | 4.627 | 2.120 | 0.109 | 0.623 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F(-1) | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 112 | 156 | 0 | 0 | 193 | 0 | 0 | 70 | 0 |
N.S. |
1 | 1.00 | 1.39 | 0.00 | 0.00 | 1.72 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.609 | 0.218 | 0.000 | 0.000 | 0.114 | 0.000 | 0.000 | 0.172 | 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 | 33 | 35 | 29 | 31 | 25 | 26 | 0 | 35 | 43 | 0 |
N.S. |
1 | 1.06 | 0.88 | 0.94 | 0.76 | 0.79 | 0.00 | 1.06 | 1.30 | 0.00 |
time (sec) |
N/A | 0.230 | 0.028 | 0.395 | 0.030 | 0.084 | 0.000 | 0.125 | 0.147 | 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 | 33 | 37 | 32 | 62 | 488 | 77 | 0 | 27 | 10 | 0 |
N.S. |
1 | 1.12 | 0.97 | 1.88 | 14.79 | 2.33 | 0.00 | 0.82 | 0.30 | 0.00 |
time (sec) |
N/A | 0.183 | 0.014 | 0.250 | 0.141 | 0.086 | 0.000 | 0.134 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 55 | 72 | 49 | 55 | 790 | 103 | 0 | 48 | 14 | 29 |
N.S. |
1 | 1.31 | 0.89 | 1.00 | 14.36 | 1.87 | 0.00 | 0.87 | 0.25 | 0.53 |
time (sec) |
N/A | 0.216 | 0.079 | 0.199 | 0.153 | 0.091 | 0.000 | 0.129 | 0.152 | 0.227 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | B | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 39 | 90 | 39 | 0 | 22 | 16 | 12 |
N.S. |
1 | 1.00 | 1.00 | 2.44 | 5.62 | 2.44 | 0.00 | 1.38 | 1.00 | 0.75 |
time (sec) |
N/A | 0.169 | 0.033 | 0.241 | 0.113 | 0.078 | 0.000 | 0.127 | 0.143 | 0.213 |
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 | 49 | 68 | 49 | 100 | 0 | 118 | 0 | 0 | 16 | 0 |
N.S. |
1 | 1.39 | 1.00 | 2.04 | 0.00 | 2.41 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.234 | 0.066 | 0.244 | 0.000 | 0.099 | 0.000 | 0.000 | 0.171 | 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 | 87 | 157 | 62 | 180 | 1359 | 163 | 0 | 55 | 51 | 0 |
N.S. |
1 | 1.80 | 0.71 | 2.07 | 15.62 | 1.87 | 0.00 | 0.63 | 0.59 | 0.00 |
time (sec) |
N/A | 0.549 | 0.252 | 1.283 | 0.230 | 0.102 | 0.000 | 0.138 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 71 | 115 | 200 | 0 | 130 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.04 | 1.69 | 2.94 | 0.00 | 1.91 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.234 | 0.149 | 7.185 | 0.000 | 0.087 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 79 | 89 | 0 | 115 | 0 | 0 | 28 | 0 |
N.S. |
1 | 1.00 | 1.98 | 2.22 | 0.00 | 2.88 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.192 | 0.085 | 2.064 | 0.000 | 0.084 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-1) | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 100 | 131 | 124 | 0 | 97 | 0 | 0 | 65 | 0 |
N.S. |
1 | 1.06 | 1.39 | 1.32 | 0.00 | 1.03 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.454 | 0.371 | 4.868 | 0.000 | 0.121 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 41 | 36 | 36 | 63 | 33 | 0 | 135 | 69 | 20 |
N.S. |
1 | 1.05 | 0.92 | 0.92 | 1.62 | 0.85 | 0.00 | 3.46 | 1.77 | 0.51 |
time (sec) |
N/A | 0.307 | 0.056 | 3.798 | 0.037 | 0.085 | 0.000 | 0.142 | 0.170 | 0.422 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 129 | 524 | 0 | 257 | 0 | 121 | 123 | 0 |
N.S. |
1 | 1.00 | 1.77 | 7.18 | 0.00 | 3.52 | 0.00 | 1.66 | 1.68 | 0.00 |
time (sec) |
N/A | 1.248 | 3.696 | 2.601 | 0.000 | 0.131 | 0.000 | 0.182 | 0.277 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 57 | 116 | 62 | 47 | 84 | 0 | 0 | 89 | 113 |
N.S. |
1 | 1.00 | 2.04 | 1.09 | 0.82 | 1.47 | 0.00 | 0.00 | 1.56 | 1.98 |
time (sec) |
N/A | 0.862 | 4.475 | 4.240 | 0.104 | 0.089 | 0.000 | 0.000 | 0.168 | 0.823 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 76 | 49 | 61 | 0 | 50 | 0 | 52 | 70 | 90 |
N.S. |
1 | 1.15 | 0.74 | 0.92 | 0.00 | 0.76 | 0.00 | 0.79 | 1.06 | 1.36 |
time (sec) |
N/A | 0.228 | 0.050 | 0.135 | 0.000 | 0.084 | 0.000 | 0.126 | 0.163 | 0.879 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 63 | 71 | 41 | 0 | 76 | 46 | 36 | 36 | 172 |
N.S. |
1 | 1.17 | 1.31 | 0.76 | 0.00 | 1.41 | 0.85 | 0.67 | 0.67 | 3.19 |
time (sec) |
N/A | 0.220 | 0.419 | 0.118 | 0.000 | 0.087 | 2.366 | 0.125 | 0.153 | 0.295 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 138 | 105 | 0 | 0 | 0 | 0 | 186 | 19 | 250 |
N.S. |
1 | 1.04 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 1.40 | 0.14 | 1.88 |
time (sec) |
N/A | 0.312 | 0.097 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.152 | 0.754 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | B | F | A | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 91 | 69 | 0 | 0 | 117 | 0 | 79 | 42 | 101 |
N.S. |
1 | 1.32 | 1.00 | 0.00 | 0.00 | 1.70 | 0.00 | 1.14 | 0.61 | 1.46 |
time (sec) |
N/A | 0.253 | 0.108 | 0.000 | 0.000 | 0.402 | 0.000 | 0.133 | 0.171 | 0.407 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | A | F(-1) | F | A | F | B |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 59 | 256 | 0 | 71 | 0 | 0 | 73 | 19 | 46 |
N.S. |
1 | 1.13 | 4.92 | 0.00 | 1.37 | 0.00 | 0.00 | 1.40 | 0.37 | 0.88 |
time (sec) |
N/A | 0.266 | 0.199 | 0.000 | 0.121 | 0.000 | 0.000 | 0.307 | 0.156 | 0.239 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | A | F(-1) | F | A | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 61 | 245 | 0 | 74 | 0 | 0 | 76 | 20 | 0 |
N.S. |
1 | 1.13 | 4.54 | 0.00 | 1.37 | 0.00 | 0.00 | 1.41 | 0.37 | 0.00 |
time (sec) |
N/A | 0.264 | 0.198 | 0.000 | 0.104 | 0.000 | 0.000 | 0.249 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F(-1) | F(-2) | F(-1) | F(-2) | F | F(-1) |
verified |
N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 200 | 785 | 0 | 0 | 0 | 0 | 0 | 315 | 0 |
N.S. |
1 | 1.50 | 5.90 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 2.37 | 0.00 |
time (sec) |
N/A | 4.300 | 18.102 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.046 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | B | F(-1) | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 138 | 169 | 499 | 0 | 271 | 0 | 193 | 55 | 0 |
N.S. |
1 | 1.38 | 1.69 | 4.99 | 0.00 | 2.71 | 0.00 | 1.93 | 0.55 | 0.00 |
time (sec) |
N/A | 1.131 | 4.822 | 3.970 | 0.000 | 0.101 | 0.000 | 0.222 | 0.186 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 114 | 47 | 127 | 136 | 185 | 0 | 0 | 53 | 0 |
N.S. |
1 | 1.02 | 0.42 | 1.13 | 1.21 | 1.65 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.324 | 0.039 | 0.638 | 0.109 | 0.083 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | B | F(-1) | F(-1) | B | B | F(-1) |
verified |
N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 159 | 154 | 0 | 145 | 0 | 0 | 146 | 19 | 0 |
N.S. |
1 | 1.67 | 1.62 | 0.00 | 1.53 | 0.00 | 0.00 | 1.54 | 0.20 | 0.00 |
time (sec) |
N/A | 0.346 | 0.097 | 0.000 | 0.107 | 0.000 | 0.000 | 0.169 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 53 | 30 | 0 | 37 | 46 | 0 | 37 | 42 | 0 |
N.S. |
1 | 1.08 | 0.61 | 0.00 | 0.76 | 0.94 | 0.00 | 0.76 | 0.86 | 0.00 |
time (sec) |
N/A | 0.281 | 0.356 | 0.000 | 0.032 | 0.117 | 0.000 | 0.122 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 26 | 86 | 35 | 0 | 25 | 39 | 43 |
N.S. |
1 | 1.00 | 1.00 | 1.30 | 4.30 | 1.75 | 0.00 | 1.25 | 1.95 | 2.15 |
time (sec) |
N/A | 0.414 | 0.263 | 0.308 | 0.093 | 0.076 | 0.000 | 0.139 | 0.157 | 0.196 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | B | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 35 | 97 | 0 | 0 | 93 | 0 | 40 | 39 | 0 |
N.S. |
1 | 1.30 | 3.59 | 0.00 | 0.00 | 3.44 | 0.00 | 1.48 | 1.44 | 0.00 |
time (sec) |
N/A | 1.017 | 0.431 | 0.000 | 0.000 | 0.807 | 0.000 | 0.140 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 126 | 89 | 0 | 100 | 461 | 0 | 0 | 160 | 0 |
N.S. |
1 | 1.25 | 0.88 | 0.00 | 0.99 | 4.56 | 0.00 | 0.00 | 1.58 | 0.00 |
time (sec) |
N/A | 1.332 | 0.265 | 0.000 | 0.126 | 35.596 | 0.000 | 0.000 | 0.226 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | A | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 37 | 20 | 0 | 0 | 26 | 0 | 25 | 15 | 0 |
N.S. |
1 | 1.48 | 0.80 | 0.00 | 0.00 | 1.04 | 0.00 | 1.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.230 | 0.080 | 0.000 | 0.000 | 0.077 | 0.000 | 0.116 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F(-1) | A | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 189 | 153 | 0 | 0 | 0 | 0 | 120 | 15 | 0 |
N.S. |
1 | 1.85 | 1.50 | 0.00 | 0.00 | 0.00 | 0.00 | 1.18 | 0.15 | 0.00 |
time (sec) |
N/A | 0.372 | 0.104 | 0.000 | 0.000 | 0.000 | 0.000 | 0.125 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | F | B | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 18 | 45 | 78 | 259 | 50 | 0 | 85 | 11 | 0 |
N.S. |
1 | 1.06 | 2.65 | 4.59 | 15.24 | 2.94 | 0.00 | 5.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.215 | 0.080 | 0.885 | 0.131 | 0.084 | 0.000 | 0.151 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | C | B | F | C | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 39 | 52 | 142 | 507 | 64 | 0 | 138 | 15 | 0 |
N.S. |
1 | 1.22 | 1.62 | 4.44 | 15.84 | 2.00 | 0.00 | 4.31 | 0.47 | 0.00 |
time (sec) |
N/A | 0.211 | 0.084 | 6.141 | 0.274 | 0.083 | 0.000 | 0.168 | 0.152 | 0.000 |
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 | 31 | 37 | 31 | 24 | 27 | 30 | 24 | 32 | 30 | 24 |
N.S. |
1 | 1.19 | 1.00 | 0.77 | 0.87 | 0.97 | 0.77 | 1.03 | 0.97 | 0.77 |
time (sec) |
N/A | 0.159 | 0.004 | 0.090 | 0.023 | 0.057 | 0.045 | 0.120 | 0.143 | 0.186 |
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 | 39 | 49 | 39 | 29 | 30 | 32 | 32 | 30 | 31 | 30 |
N.S. |
1 | 1.26 | 1.00 | 0.74 | 0.77 | 0.82 | 0.82 | 0.77 | 0.79 | 0.77 |
time (sec) |
N/A | 0.154 | 0.009 | 0.089 | 0.103 | 0.062 | 0.057 | 0.122 | 0.149 | 0.020 |
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 | 58 | 64 | 40 | 34 | 46 | 73 | 41 | 42 | 123 | 44 |
N.S. |
1 | 1.10 | 0.69 | 0.59 | 0.79 | 1.26 | 0.71 | 0.72 | 2.12 | 0.76 |
time (sec) |
N/A | 0.180 | 0.012 | 0.103 | 0.024 | 0.057 | 0.058 | 0.124 | 0.150 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 54 | 46 | 35 | 33 | 65 | 984 | 35 | 95 | 34 |
N.S. |
1 | 1.04 | 0.88 | 0.67 | 0.63 | 1.25 | 18.92 | 0.67 | 1.83 | 0.65 |
time (sec) |
N/A | 0.157 | 0.046 | 0.335 | 0.101 | 0.064 | 1.629 | 0.124 | 0.154 | 0.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 71 | 49 | 41 | 42 | 47 | 165 | 46 | 49 | 46 |
N.S. |
1 | 1.16 | 0.80 | 0.67 | 0.69 | 0.77 | 2.70 | 0.75 | 0.80 | 0.75 |
time (sec) |
N/A | 0.172 | 0.039 | 0.384 | 0.103 | 0.063 | 3.092 | 0.121 | 0.148 | 0.265 |
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 | 16 | 16 | 15 | 15 | 14 | 15 | 15 | 14 | 16 | 24 |
N.S. |
1 | 1.00 | 0.94 | 0.94 | 0.88 | 0.94 | 0.94 | 0.88 | 1.00 | 1.50 |
time (sec) |
N/A | 0.127 | 0.002 | 0.032 | 0.029 | 0.064 | 0.018 | 0.122 | 0.150 | 0.268 |
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 | 46 | 42 | 36 | 30 | 35 | 49 | 32 | 36 | 87 | 35 |
N.S. |
1 | 0.91 | 0.78 | 0.65 | 0.76 | 1.07 | 0.70 | 0.78 | 1.89 | 0.76 |
time (sec) |
N/A | 0.170 | 0.010 | 0.089 | 0.028 | 0.056 | 0.041 | 0.124 | 0.145 | 0.031 |
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 | 40 | 44 | 23 | 21 | 36 | 36 | 32 | 21 | 37 | 36 |
N.S. |
1 | 1.10 | 0.58 | 0.52 | 0.90 | 0.90 | 0.80 | 0.52 | 0.92 | 0.90 |
time (sec) |
N/A | 0.187 | 0.006 | 0.092 | 0.028 | 0.053 | 0.048 | 0.122 | 0.148 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 31 | 25 | 17 | 19 | 21 | 41 | 19 | 13 | 20 |
N.S. |
1 | 1.15 | 0.93 | 0.63 | 0.70 | 0.78 | 1.52 | 0.70 | 0.48 | 0.74 |
time (sec) |
N/A | 0.151 | 0.016 | 0.142 | 0.027 | 0.056 | 2.307 | 0.123 | 0.172 | 0.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 42 | 25 | 20 | 28 | 33 | 82 | 26 | 41 | 21 |
N.S. |
1 | 1.11 | 0.66 | 0.53 | 0.74 | 0.87 | 2.16 | 0.68 | 1.08 | 0.55 |
time (sec) |
N/A | 0.156 | 0.020 | 0.147 | 0.023 | 0.059 | 0.653 | 0.125 | 0.153 | 0.245 |
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 | 33 | 33 | 24 | 20 | 25 | 34 | 61 | 19 | 58 | 99 |
N.S. |
1 | 1.00 | 0.73 | 0.61 | 0.76 | 1.03 | 1.85 | 0.58 | 1.76 | 3.00 |
time (sec) |
N/A | 0.138 | 0.031 | 0.104 | 0.023 | 0.061 | 0.755 | 0.130 | 0.142 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 26 | 23 | 51 | 61 | 0 | 21 | 81 | 22 |
N.S. |
1 | 1.00 | 0.60 | 0.53 | 1.19 | 1.42 | 0.00 | 0.49 | 1.88 | 0.51 |
time (sec) |
N/A | 0.150 | 0.151 | 0.197 | 0.024 | 0.076 | 0.000 | 0.125 | 0.144 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 52 | 28 | 23 | 35 | 40 | 153 | 62 | 51 | 24 |
N.S. |
1 | 1.11 | 0.60 | 0.49 | 0.74 | 0.85 | 3.26 | 1.32 | 1.09 | 0.51 |
time (sec) |
N/A | 0.148 | 0.035 | 0.135 | 0.103 | 0.061 | 1.046 | 0.137 | 0.149 | 0.262 |
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 | 28 | 28 | 19 | 16 | 16 | 15 | 24 | 16 | 15 | 17 |
N.S. |
1 | 1.00 | 0.68 | 0.57 | 0.57 | 0.54 | 0.86 | 0.57 | 0.54 | 0.61 |
time (sec) |
N/A | 0.140 | 0.014 | 0.074 | 0.023 | 0.055 | 0.619 | 0.117 | 0.150 | 0.023 |
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 | 52 | 58 | 49 | 47 | 53 | 74 | 49 | 58 | 93 | 51 |
N.S. |
1 | 1.12 | 0.94 | 0.90 | 1.02 | 1.42 | 0.94 | 1.12 | 1.79 | 0.98 |
time (sec) |
N/A | 0.173 | 0.018 | 0.117 | 0.028 | 0.057 | 0.063 | 0.114 | 0.155 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 22 | 0 | 21 | 0 | 0 | 39 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.00 | 0.84 | 0.00 | 0.00 | 1.56 | 0.60 |
time (sec) |
N/A | 0.180 | 6.703 | 0.098 | 0.000 | 0.222 | 0.000 | 0.000 | 0.768 | 0.259 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-1) | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 35 | 28 | 79 | 69 | 0 | 98 | 50 | 0 |
N.S. |
1 | 1.00 | 0.70 | 0.56 | 1.58 | 1.38 | 0.00 | 1.96 | 1.00 | 0.00 |
time (sec) |
N/A | 0.151 | 0.191 | 0.326 | 0.103 | 0.075 | 0.000 | 0.177 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 40 | 22 | 21 | 46 | 49 | 29 | 30 | 54 |
N.S. |
1 | 1.00 | 1.67 | 0.92 | 0.88 | 1.92 | 2.04 | 1.21 | 1.25 | 2.25 |
time (sec) |
N/A | 0.137 | 0.055 | 0.251 | 0.105 | 0.062 | 0.172 | 0.138 | 0.143 | 0.171 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 40 | 46 | 32 | 45 | 45 | 32 | 77 | 38 | 33 |
N.S. |
1 | 1.00 | 1.15 | 0.80 | 1.12 | 1.12 | 0.80 | 1.92 | 0.95 | 0.82 |
time (sec) |
N/A | 0.148 | 0.053 | 0.543 | 0.105 | 0.065 | 0.316 | 0.127 | 0.156 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 54 | 28 | 25 | 37 | 44 | 291 | 35 | 39 | 179 |
N.S. |
1 | 1.10 | 0.57 | 0.51 | 0.76 | 0.90 | 5.94 | 0.71 | 0.80 | 3.65 |
time (sec) |
N/A | 0.144 | 0.167 | 0.108 | 0.030 | 0.064 | 2.799 | 0.133 | 0.157 | 0.165 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 31 | 28 | 59 | 47 | 0 | 35 | 38 | 29 |
N.S. |
1 | 1.00 | 0.66 | 0.60 | 1.26 | 1.00 | 0.00 | 0.74 | 0.81 | 0.62 |
time (sec) |
N/A | 0.152 | 0.138 | 0.263 | 0.027 | 0.063 | 0.000 | 0.130 | 0.154 | 0.162 |
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 | 36 | 36 | 36 | 33 | 32 | 32 | 34 | 32 | 33 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.89 | 0.89 | 0.94 | 0.89 | 0.92 | 0.89 |
time (sec) |
N/A | 0.165 | 0.002 | 0.171 | 0.025 | 0.053 | 0.020 | 0.124 | 0.157 | 0.019 |
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 | 39 | 39 | 39 | 29 | 29 | 29 | 34 | 29 | 28 | 29 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.74 | 0.74 | 0.87 | 0.74 | 0.72 | 0.74 |
time (sec) |
N/A | 0.161 | 0.001 | 0.154 | 0.029 | 0.055 | 0.024 | 0.117 | 0.147 | 0.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 33 | 30 | 59 | 73 | 0 | 27 | 113 | 29 |
N.S. |
1 | 1.00 | 0.70 | 0.64 | 1.26 | 1.55 | 0.00 | 0.57 | 2.40 | 0.62 |
time (sec) |
N/A | 0.157 | 0.195 | 0.286 | 0.023 | 0.063 | 0.000 | 0.130 | 0.155 | 0.215 |
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 | 45 | 45 | 33 | 30 | 76 | 73 | 0 | 41 | 91 | 29 |
N.S. |
1 | 1.00 | 0.73 | 0.67 | 1.69 | 1.62 | 0.00 | 0.91 | 2.02 | 0.64 |
time (sec) |
N/A | 0.180 | 0.311 | 0.246 | 0.028 | 0.064 | 0.000 | 0.142 | 0.156 | 0.099 |
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 | 83 | 113 | 67 | 56 | 55 | 57 | 112 | 55 | 64 | 69 |
N.S. |
1 | 1.36 | 0.81 | 0.67 | 0.66 | 0.69 | 1.35 | 0.66 | 0.77 | 0.83 |
time (sec) |
N/A | 0.640 | 0.040 | 1.366 | 0.032 | 0.069 | 0.302 | 0.119 | 0.151 | 0.227 |
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 | 73 | 92 | 51 | 50 | 49 | 52 | 92 | 49 | 59 | 59 |
N.S. |
1 | 1.26 | 0.70 | 0.68 | 0.67 | 0.71 | 1.26 | 0.67 | 0.81 | 0.81 |
time (sec) |
N/A | 0.646 | 0.068 | 0.754 | 0.028 | 0.068 | 0.226 | 0.117 | 0.155 | 0.192 |
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 | 105 | 181 | 70 | 67 | 66 | 72 | 192 | 66 | 83 | 88 |
N.S. |
1 | 1.72 | 0.67 | 0.64 | 0.63 | 0.69 | 1.83 | 0.63 | 0.79 | 0.84 |
time (sec) |
N/A | 0.804 | 0.062 | 2.042 | 0.033 | 0.069 | 0.443 | 0.117 | 0.148 | 0.235 |
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 | 44 | 48 | 39 | 32 | 35 | 36 | 53 | 35 | 34 | 40 |
N.S. |
1 | 1.09 | 0.89 | 0.73 | 0.80 | 0.82 | 1.20 | 0.80 | 0.77 | 0.91 |
time (sec) |
N/A | 0.311 | 0.080 | 0.655 | 0.026 | 0.067 | 0.149 | 0.116 | 0.155 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F(-2) | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 56 | 0 | 45 | 507 | 206 | 58 | 56 |
N.S. |
1 | 1.00 | 1.00 | 1.70 | 0.00 | 1.36 | 15.36 | 6.24 | 1.76 | 1.70 |
time (sec) |
N/A | 0.308 | 0.025 | 0.490 | 0.000 | 0.075 | 0.559 | 0.144 | 0.156 | 0.372 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 104 | 70 | 619 | 47 | 551 | 341 | 82 | 35 |
N.S. |
1 | 1.00 | 3.47 | 2.33 | 20.63 | 1.57 | 18.37 | 11.37 | 2.73 | 1.17 |
time (sec) |
N/A | 0.200 | 0.088 | 0.384 | 0.114 | 0.073 | 0.505 | 0.274 | 0.152 | 0.559 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 13 | 132 | 15 | 128 | 53 | 14 | 16 |
N.S. |
1 | 1.00 | 1.00 | 0.81 | 8.25 | 0.94 | 8.00 | 3.31 | 0.88 | 1.00 |
time (sec) |
N/A | 0.201 | 0.014 | 0.263 | 0.032 | 0.062 | 0.343 | 0.128 | 0.163 | 0.216 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 62 | 74 | 57 | 57 | 66 | 113 | 0 | 0 | 12 | 0 |
N.S. |
1 | 1.19 | 0.92 | 0.92 | 1.06 | 1.82 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.408 | 0.017 | 0.363 | 0.128 | 0.083 | 0.000 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 66 | 54 | 59 | 210 | 138 | 0 | 0 | 143 | 0 |
N.S. |
1 | 1.12 | 0.92 | 1.00 | 3.56 | 2.34 | 0.00 | 0.00 | 2.42 | 0.00 |
time (sec) |
N/A | 0.359 | 0.011 | 0.201 | 0.124 | 0.083 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | B | A | F | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 14 | 44 | 78 | 13 | 0 | 10 | 58 | 0 |
N.S. |
1 | 1.00 | 1.17 | 3.67 | 6.50 | 1.08 | 0.00 | 0.83 | 4.83 | 0.00 |
time (sec) |
N/A | 0.242 | 0.225 | 3.575 | 0.123 | 0.069 | 0.000 | 0.131 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 19 | 20 | 69 | 19 | 66 | 39 | 19 | 0 |
N.S. |
1 | 1.00 | 0.95 | 1.00 | 3.45 | 0.95 | 3.30 | 1.95 | 0.95 | 0.00 |
time (sec) |
N/A | 0.230 | 0.293 | 0.951 | 0.030 | 0.066 | 0.572 | 0.124 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 23 | 0 | 22 | 42 | 325 | 22 | 22 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 0.00 | 1.00 | 1.91 | 14.77 | 1.00 | 1.00 |
time (sec) |
N/A | 0.174 | 0.019 | 0.111 | 0.000 | 0.060 | 0.301 | 0.127 | 0.149 | 0.187 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F(-2) | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 41 | 46 | 42 | 0 | 52 | 0 | 436 | 55 | 34 |
N.S. |
1 | 1.21 | 1.35 | 1.24 | 0.00 | 1.53 | 0.00 | 12.82 | 1.62 | 1.00 |
time (sec) |
N/A | 0.386 | 0.051 | 0.200 | 0.000 | 0.065 | 0.000 | 0.189 | 0.155 | 0.248 |
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 | 9 | 9 | 9 | 8 | 7 | 11 | 7 | 7 | 13 | 4 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.78 | 1.22 | 0.78 | 0.78 | 1.44 | 0.44 |
time (sec) |
N/A | 0.141 | 0.007 | 0.046 | 0.028 | 0.057 | 0.032 | 0.123 | 0.148 | 0.027 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 25 | 22 | 17 | 16 | 21 | 17 | 24 | 24 | 8 |
N.S. |
1 | 1.14 | 1.00 | 0.77 | 0.73 | 0.95 | 0.77 | 1.09 | 1.09 | 0.36 |
time (sec) |
N/A | 0.179 | 0.010 | 0.069 | 0.029 | 0.060 | 0.040 | 0.119 | 0.152 | 0.030 |
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 | 31 | 31 | 30 | 24 | 23 | 24 | 24 | 25 | 30 | 23 |
N.S. |
1 | 1.00 | 0.97 | 0.77 | 0.74 | 0.77 | 0.77 | 0.81 | 0.97 | 0.74 |
time (sec) |
N/A | 0.179 | 0.027 | 0.135 | 0.029 | 0.062 | 0.047 | 0.121 | 0.158 | 0.177 |
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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 38 | 37 | 29 | 28 | 31 | 31 | 36 | 38 | 28 |
N.S. |
1 | 1.06 | 1.03 | 0.81 | 0.78 | 0.86 | 0.86 | 1.00 | 1.06 | 0.78 |
time (sec) |
N/A | 0.189 | 0.040 | 0.185 | 0.027 | 0.064 | 0.054 | 0.115 | 0.154 | 0.173 |
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 | 48 | 52 | 45 | 0 | 0 | 0 | 0 | 0 | 60 | 0 |
N.S. |
1 | 1.08 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.25 | 0.00 |
time (sec) |
N/A | 0.202 | 0.055 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.154 | 0.000 |