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 | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 36 | 35 | 33 | 0 | 35 | 49 | 32 | 25 | 0 |
N.S. |
1 | 0.69 | 0.67 | 0.63 | 0.00 | 0.67 | 0.94 | 0.62 | 0.48 | 0.00 |
time (sec) |
N/A | 0.260 | 0.053 | 0.154 | 0.000 | 0.098 | 0.960 | 0.141 | 0.142 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 46 | 37 | 32 | 49 | 42 | 49 | 35 | 29 | 0 |
N.S. |
1 | 0.70 | 0.56 | 0.48 | 0.74 | 0.64 | 0.74 | 0.53 | 0.44 | 0.00 |
time (sec) |
N/A | 0.279 | 0.057 | 0.216 | 0.026 | 0.106 | 0.333 | 0.118 | 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 | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 46 | 35 | 30 | 44 | 42 | 49 | 35 | 29 | 0 |
N.S. |
1 | 0.70 | 0.53 | 0.45 | 0.67 | 0.64 | 0.74 | 0.53 | 0.44 | 0.00 |
time (sec) |
N/A | 0.277 | 0.052 | 0.155 | 0.026 | 0.130 | 0.299 | 0.135 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 46 | 38 | 29 | 40 | 42 | 44 | 35 | 29 | 0 |
N.S. |
1 | 0.70 | 0.58 | 0.44 | 0.61 | 0.64 | 0.67 | 0.53 | 0.44 | 0.00 |
time (sec) |
N/A | 0.274 | 0.004 | 0.164 | 0.027 | 0.140 | 0.273 | 0.125 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 46 | 34 | 32 | 40 | 42 | 44 | 35 | 29 | 0 |
N.S. |
1 | 0.70 | 0.52 | 0.48 | 0.61 | 0.64 | 0.67 | 0.53 | 0.44 | 0.00 |
time (sec) |
N/A | 0.270 | 0.004 | 0.154 | 0.032 | 0.160 | 0.325 | 0.128 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 46 | 38 | 32 | 0 | 42 | 44 | 35 | 29 | 0 |
N.S. |
1 | 0.70 | 0.58 | 0.48 | 0.00 | 0.64 | 0.67 | 0.53 | 0.44 | 0.00 |
time (sec) |
N/A | 0.280 | 0.005 | 0.216 | 0.000 | 0.128 | 0.338 | 0.112 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 46 | 36 | 32 | 0 | 40 | 49 | 35 | 29 | 0 |
N.S. |
1 | 0.72 | 0.56 | 0.50 | 0.00 | 0.62 | 0.77 | 0.55 | 0.45 | 0.00 |
time (sec) |
N/A | 0.261 | 0.003 | 0.169 | 0.000 | 0.128 | 0.406 | 0.136 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | B | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 26 | 23 | 0 | 36 | 46 | 29 | 26 | 0 |
N.S. |
1 | 1.00 | 0.90 | 0.79 | 0.00 | 1.24 | 1.59 | 1.00 | 0.90 | 0.00 |
time (sec) |
N/A | 0.232 | 0.007 | 0.154 | 0.000 | 0.165 | 0.479 | 0.131 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 38 | 35 | 33 | 0 | 41 | 51 | 32 | 27 | 0 |
N.S. |
1 | 0.66 | 0.60 | 0.57 | 0.00 | 0.71 | 0.88 | 0.55 | 0.47 | 0.00 |
time (sec) |
N/A | 0.262 | 0.050 | 0.168 | 0.000 | 0.111 | 0.889 | 0.145 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 41 | 35 | 32 | 54 | 36 | 49 | 0 | 29 | 0 |
N.S. |
1 | 0.72 | 0.61 | 0.56 | 0.95 | 0.63 | 0.86 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.286 | 0.045 | 0.154 | 0.025 | 0.124 | 0.267 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 41 | 36 | 32 | 47 | 34 | 51 | 0 | 29 | 0 |
N.S. |
1 | 0.72 | 0.63 | 0.56 | 0.82 | 0.60 | 0.89 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.260 | 0.043 | 0.205 | 0.032 | 0.119 | 0.254 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 24 | 21 | 42 | 30 | 46 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 1.75 | 1.25 | 1.92 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.231 | 0.002 | 0.148 | 0.025 | 0.085 | 0.259 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 52 | 33 | 32 | 31 | 35 | 35 | 56 | 0 | 27 | 0 |
N.S. |
1 | 0.63 | 0.62 | 0.60 | 0.67 | 0.67 | 1.08 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.255 | 0.005 | 0.152 | 0.031 | 0.130 | 0.521 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 47 | 31 | 36 | 29 | 35 | 34 | 49 | 0 | 29 | 0 |
N.S. |
1 | 0.66 | 0.77 | 0.62 | 0.74 | 0.72 | 1.04 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.262 | 0.050 | 0.225 | 0.030 | 0.191 | 1.484 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 35 | 33 | 34 | 31 | 36 | 44 | 0 | 31 | 0 |
N.S. |
1 | 0.71 | 0.67 | 0.69 | 0.63 | 0.73 | 0.90 | 0.00 | 0.63 | 0.00 |
time (sec) |
N/A | 0.262 | 0.052 | 0.148 | 0.026 | 0.102 | 0.706 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 31 | 30 | 33 | 32 | 42 | 0 | 29 | 33 |
N.S. |
1 | 1.00 | 1.19 | 1.15 | 1.27 | 1.23 | 1.62 | 0.00 | 1.12 | 1.27 |
time (sec) |
N/A | 0.226 | 0.054 | 0.149 | 0.031 | 0.132 | 0.268 | 0.000 | 0.147 | 22.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 41 | 35 | 31 | 33 | 34 | 51 | 0 | 29 | 42 |
N.S. |
1 | 0.72 | 0.61 | 0.54 | 0.58 | 0.60 | 0.89 | 0.00 | 0.51 | 0.74 |
time (sec) |
N/A | 0.276 | 0.058 | 0.153 | 0.026 | 0.097 | 0.274 | 0.000 | 0.169 | 21.921 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | B | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 26 | 23 | 52 | 30 | 46 | 0 | 26 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.85 | 1.93 | 1.11 | 1.70 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.231 | 0.006 | 0.150 | 0.028 | 0.112 | 0.268 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 36 | 35 | 33 | 45 | 35 | 51 | 0 | 27 | 0 |
N.S. |
1 | 0.59 | 0.57 | 0.54 | 0.74 | 0.57 | 0.84 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.268 | 0.049 | 0.205 | 0.033 | 0.130 | 0.767 | 0.000 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 34 | 35 | 32 | 42 | 34 | 56 | 0 | 29 | 0 |
N.S. |
1 | 0.61 | 0.62 | 0.57 | 0.75 | 0.61 | 1.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.266 | 0.003 | 0.153 | 0.030 | 0.174 | 0.795 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 38 | 32 | 32 | 35 | 36 | 56 | 0 | 31 | 0 |
N.S. |
1 | 0.66 | 0.55 | 0.55 | 0.60 | 0.62 | 0.97 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.270 | 0.003 | 0.149 | 0.025 | 0.132 | 0.748 | 0.000 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 34 | 27 | 37 | 32 | 42 | 0 | 29 | 33 |
N.S. |
1 | 1.00 | 1.17 | 0.93 | 1.28 | 1.10 | 1.45 | 0.00 | 1.00 | 1.14 |
time (sec) |
N/A | 0.231 | 0.047 | 0.145 | 0.036 | 0.093 | 0.248 | 0.000 | 0.145 | 21.919 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 44 | 34 | 32 | 33 | 34 | 46 | 0 | 29 | 42 |
N.S. |
1 | 0.67 | 0.52 | 0.48 | 0.50 | 0.52 | 0.70 | 0.00 | 0.44 | 0.64 |
time (sec) |
N/A | 0.270 | 0.044 | 0.148 | 0.032 | 0.091 | 0.312 | 0.000 | 0.158 | 22.056 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 44 | 35 | 32 | 33 | 34 | 46 | 0 | 29 | 42 |
N.S. |
1 | 0.67 | 0.53 | 0.48 | 0.50 | 0.52 | 0.70 | 0.00 | 0.44 | 0.64 |
time (sec) |
N/A | 0.274 | 0.050 | 0.150 | 0.034 | 0.102 | 0.301 | 0.000 | 0.161 | 21.964 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 44 | 35 | 32 | 33 | 34 | 51 | 0 | 29 | 42 |
N.S. |
1 | 0.67 | 0.53 | 0.48 | 0.50 | 0.52 | 0.77 | 0.00 | 0.44 | 0.64 |
time (sec) |
N/A | 0.276 | 0.049 | 0.154 | 0.030 | 0.135 | 0.310 | 0.000 | 0.145 | 22.122 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 34 | 35 | 32 | 45 | 34 | 49 | 0 | 29 | 0 |
N.S. |
1 | 0.61 | 0.62 | 0.57 | 0.80 | 0.61 | 0.88 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.275 | 0.051 | 0.155 | 0.036 | 0.092 | 0.790 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 58 | 38 | 34 | 34 | 38 | 36 | 51 | 0 | 31 | 0 |
N.S. |
1 | 0.66 | 0.59 | 0.59 | 0.66 | 0.62 | 0.88 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.269 | 0.056 | 0.213 | 0.041 | 0.097 | 0.808 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 33 | 30 | 44 | 32 | 48 | 0 | 29 | 33 |
N.S. |
1 | 1.00 | 1.14 | 1.03 | 1.52 | 1.10 | 1.66 | 0.00 | 1.00 | 1.14 |
time (sec) |
N/A | 0.223 | 0.006 | 0.148 | 0.026 | 0.114 | 0.283 | 0.000 | 0.151 | 22.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 44 | 33 | 30 | 37 | 34 | 51 | 0 | 29 | 42 |
N.S. |
1 | 0.67 | 0.50 | 0.45 | 0.56 | 0.52 | 0.77 | 0.00 | 0.44 | 0.64 |
time (sec) |
N/A | 0.264 | 0.003 | 0.148 | 0.033 | 0.118 | 0.276 | 0.000 | 0.162 | 21.918 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 44 | 36 | 29 | 37 | 34 | 46 | 0 | 29 | 42 |
N.S. |
1 | 0.67 | 0.55 | 0.44 | 0.56 | 0.52 | 0.70 | 0.00 | 0.44 | 0.64 |
time (sec) |
N/A | 0.270 | 0.047 | 0.148 | 0.026 | 0.094 | 0.313 | 0.000 | 0.144 | 21.986 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 44 | 34 | 32 | 33 | 34 | 46 | 0 | 29 | 42 |
N.S. |
1 | 0.67 | 0.52 | 0.48 | 0.50 | 0.52 | 0.70 | 0.00 | 0.44 | 0.64 |
time (sec) |
N/A | 0.270 | 0.046 | 0.221 | 0.029 | 0.111 | 0.329 | 0.000 | 0.150 | 22.104 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 44 | 35 | 32 | 33 | 34 | 46 | 0 | 29 | 42 |
N.S. |
1 | 0.67 | 0.53 | 0.48 | 0.50 | 0.52 | 0.70 | 0.00 | 0.44 | 0.64 |
time (sec) |
N/A | 0.271 | 0.054 | 0.207 | 0.031 | 0.122 | 0.347 | 0.000 | 0.156 | 22.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 66 | 44 | 35 | 32 | 33 | 34 | 51 | 0 | 29 | 42 |
N.S. |
1 | 0.67 | 0.53 | 0.48 | 0.50 | 0.52 | 0.77 | 0.00 | 0.44 | 0.64 |
time (sec) |
N/A | 0.273 | 0.054 | 0.157 | 0.025 | 0.126 | 0.377 | 0.000 | 0.143 | 22.204 |
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 | 102 | 70 | 64 | 63 | 128 | 62 | 0 | 81 | 54 | 0 |
N.S. |
1 | 0.69 | 0.63 | 0.62 | 1.25 | 0.61 | 0.00 | 0.79 | 0.53 | 0.00 |
time (sec) |
N/A | 0.331 | 0.079 | 0.194 | 0.046 | 0.109 | 0.000 | 0.118 | 0.144 | 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 | 80 | 57 | 54 | 52 | 110 | 51 | 0 | 69 | 43 | 0 |
N.S. |
1 | 0.71 | 0.68 | 0.65 | 1.38 | 0.64 | 0.00 | 0.86 | 0.54 | 0.00 |
time (sec) |
N/A | 0.318 | 0.066 | 0.177 | 0.038 | 0.105 | 0.000 | 0.135 | 0.159 | 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 | 58 | 44 | 41 | 40 | 91 | 39 | 0 | 54 | 31 | 0 |
N.S. |
1 | 0.76 | 0.71 | 0.69 | 1.57 | 0.67 | 0.00 | 0.93 | 0.53 | 0.00 |
time (sec) |
N/A | 0.298 | 0.055 | 0.174 | 0.037 | 0.086 | 0.000 | 0.129 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 31 | 29 | 29 | 74 | 27 | 0 | 37 | 19 | 0 |
N.S. |
1 | 0.82 | 0.76 | 0.76 | 1.95 | 0.71 | 0.00 | 0.97 | 0.50 | 0.00 |
time (sec) |
N/A | 0.274 | 0.042 | 0.230 | 0.038 | 0.090 | 0.000 | 0.113 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 21 | 21 | 0 | 20 | 0 | 28 | 12 | 0 |
N.S. |
1 | 1.00 | 0.95 | 0.95 | 0.00 | 0.91 | 0.00 | 1.27 | 0.55 | 0.00 |
time (sec) |
N/A | 0.234 | 0.006 | 0.170 | 0.000 | 0.102 | 0.000 | 0.117 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 31 | 28 | 27 | 24 | 64 | 0 | 0 | 17 | 0 |
N.S. |
1 | 0.74 | 0.67 | 0.64 | 0.57 | 1.52 | 0.00 | 0.00 | 0.40 | 0.00 |
time (sec) |
N/A | 0.237 | 0.052 | 0.172 | 0.033 | 0.145 | 0.000 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 41 | 32 | 34 | 37 | 31 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.67 | 0.52 | 0.56 | 0.61 | 0.51 | 0.00 | 0.00 | 0.46 | 0.00 |
time (sec) |
N/A | 0.299 | 0.056 | 0.184 | 0.032 | 0.118 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 55 | 53 | 49 | 52 | 44 | 0 | 0 | 45 | 0 |
N.S. |
1 | 0.65 | 0.63 | 0.58 | 0.62 | 0.52 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.313 | 0.077 | 0.240 | 0.034 | 0.146 | 0.000 | 0.000 | 0.164 | 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 | 107 | 71 | 64 | 63 | 124 | 67 | 0 | 81 | 55 | 0 |
N.S. |
1 | 0.66 | 0.60 | 0.59 | 1.16 | 0.63 | 0.00 | 0.76 | 0.51 | 0.00 |
time (sec) |
N/A | 0.328 | 0.073 | 0.187 | 0.045 | 0.113 | 0.000 | 0.137 | 0.144 | 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 | 84 | 58 | 53 | 52 | 109 | 55 | 0 | 69 | 44 | 0 |
N.S. |
1 | 0.69 | 0.63 | 0.62 | 1.30 | 0.65 | 0.00 | 0.82 | 0.52 | 0.00 |
time (sec) |
N/A | 0.324 | 0.065 | 0.175 | 0.040 | 0.102 | 0.000 | 0.134 | 0.145 | 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 | 61 | 45 | 42 | 40 | 93 | 42 | 0 | 54 | 32 | 0 |
N.S. |
1 | 0.74 | 0.69 | 0.66 | 1.52 | 0.69 | 0.00 | 0.89 | 0.52 | 0.00 |
time (sec) |
N/A | 0.303 | 0.003 | 0.177 | 0.039 | 0.168 | 0.000 | 0.118 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | A | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 32 | 30 | 29 | 75 | 29 | 0 | 37 | 20 | 0 |
N.S. |
1 | 0.80 | 0.75 | 0.72 | 1.88 | 0.72 | 0.00 | 0.92 | 0.50 | 0.00 |
time (sec) |
N/A | 0.270 | 0.002 | 0.171 | 0.051 | 0.115 | 0.000 | 0.129 | 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 | 23 | 23 | 22 | 21 | 13 | 21 | 0 | 28 | 13 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.91 | 0.57 | 0.91 | 0.00 | 1.22 | 0.57 | 0.00 |
time (sec) |
N/A | 0.220 | 0.004 | 0.218 | 0.033 | 0.113 | 0.000 | 0.132 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 32 | 29 | 27 | 24 | 66 | 0 | 0 | 18 | 0 |
N.S. |
1 | 0.73 | 0.66 | 0.61 | 0.55 | 1.50 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.237 | 0.054 | 0.177 | 0.036 | 0.129 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 42 | 34 | 34 | 37 | 33 | 0 | 0 | 29 | 0 |
N.S. |
1 | 0.66 | 0.53 | 0.53 | 0.58 | 0.52 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.274 | 0.059 | 0.180 | 0.039 | 0.129 | 0.000 | 0.000 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 88 | 56 | 53 | 49 | 52 | 47 | 0 | 0 | 46 | 0 |
N.S. |
1 | 0.64 | 0.60 | 0.56 | 0.59 | 0.53 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.298 | 0.069 | 0.204 | 0.037 | 0.129 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 70 | 65 | 62 | 66 | 59 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.62 | 0.58 | 0.55 | 0.59 | 0.53 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.314 | 0.092 | 0.243 | 0.044 | 0.150 | 0.000 | 0.000 | 0.158 | 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 | 142 | 86 | 76 | 74 | 146 | 91 | 0 | 95 | 68 | 0 |
N.S. |
1 | 0.61 | 0.54 | 0.52 | 1.03 | 0.64 | 0.00 | 0.67 | 0.48 | 0.00 |
time (sec) |
N/A | 0.351 | 0.094 | 0.248 | 0.052 | 0.126 | 0.000 | 0.126 | 0.145 | 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 | 117 | 73 | 65 | 63 | 130 | 77 | 0 | 81 | 57 | 0 |
N.S. |
1 | 0.62 | 0.56 | 0.54 | 1.11 | 0.66 | 0.00 | 0.69 | 0.49 | 0.00 |
time (sec) |
N/A | 0.340 | 0.014 | 0.198 | 0.044 | 0.149 | 0.000 | 0.136 | 0.150 | 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 | 92 | 60 | 54 | 52 | 114 | 63 | 0 | 69 | 46 | 0 |
N.S. |
1 | 0.65 | 0.59 | 0.57 | 1.24 | 0.68 | 0.00 | 0.75 | 0.50 | 0.00 |
time (sec) |
N/A | 0.309 | 0.004 | 0.244 | 0.047 | 0.115 | 0.000 | 0.122 | 0.156 | 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 | 67 | 47 | 44 | 40 | 97 | 48 | 0 | 54 | 34 | 0 |
N.S. |
1 | 0.70 | 0.66 | 0.60 | 1.45 | 0.72 | 0.00 | 0.81 | 0.51 | 0.00 |
time (sec) |
N/A | 0.287 | 0.012 | 0.247 | 0.044 | 0.113 | 0.000 | 0.135 | 0.142 | 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 | 34 | 32 | 29 | 77 | 33 | 0 | 37 | 22 | 0 |
N.S. |
1 | 0.77 | 0.73 | 0.66 | 1.75 | 0.75 | 0.00 | 0.84 | 0.50 | 0.00 |
time (sec) |
N/A | 0.272 | 0.003 | 0.199 | 0.038 | 0.106 | 0.000 | 0.134 | 0.149 | 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 | 25 | 25 | 22 | 21 | 13 | 23 | 0 | 28 | 15 | 0 |
N.S. |
1 | 1.00 | 0.88 | 0.84 | 0.52 | 0.92 | 0.00 | 1.12 | 0.60 | 0.00 |
time (sec) |
N/A | 0.228 | 0.005 | 0.210 | 0.042 | 0.112 | 0.000 | 0.113 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 34 | 30 | 27 | 24 | 70 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.71 | 0.62 | 0.56 | 0.50 | 1.46 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.237 | 0.051 | 0.342 | 0.033 | 0.159 | 0.000 | 0.000 | 0.140 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 44 | 34 | 34 | 37 | 37 | 0 | 0 | 31 | 0 |
N.S. |
1 | 0.63 | 0.49 | 0.49 | 0.53 | 0.53 | 0.00 | 0.00 | 0.44 | 0.00 |
time (sec) |
N/A | 0.288 | 0.058 | 0.270 | 0.033 | 0.132 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 55 | 51 | 50 | 142 | 54 | 0 | 0 | 46 | 0 |
N.S. |
1 | 0.66 | 0.61 | 0.60 | 1.71 | 0.65 | 0.00 | 0.00 | 0.55 | 0.00 |
time (sec) |
N/A | 0.293 | 0.065 | 0.231 | 0.045 | 0.111 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 61 | 42 | 39 | 38 | 100 | 42 | 0 | 0 | 34 | 0 |
N.S. |
1 | 0.69 | 0.64 | 0.62 | 1.64 | 0.69 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.281 | 0.087 | 0.174 | 0.039 | 0.103 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 39 | 29 | 27 | 27 | 64 | 30 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.74 | 0.69 | 0.69 | 1.64 | 0.77 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.266 | 0.078 | 0.173 | 0.040 | 0.107 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 19 | 46 | 23 | 0 | 0 | 15 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 2.30 | 1.15 | 0.00 | 0.00 | 0.75 | 0.00 |
time (sec) |
N/A | 0.232 | 0.003 | 0.229 | 0.035 | 0.088 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 29 | 27 | 25 | 35 | 70 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.76 | 0.71 | 0.66 | 0.92 | 1.84 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.239 | 0.006 | 0.184 | 0.034 | 0.108 | 0.000 | 0.000 | 0.141 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 39 | 36 | 31 | 37 | 34 | 0 | 0 | 31 | 0 |
N.S. |
1 | 0.72 | 0.67 | 0.57 | 0.69 | 0.63 | 0.00 | 0.00 | 0.57 | 0.00 |
time (sec) |
N/A | 0.282 | 0.088 | 0.178 | 0.031 | 0.125 | 0.000 | 0.000 | 0.147 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 77 | 53 | 51 | 49 | 55 | 47 | 0 | 0 | 48 | 0 |
N.S. |
1 | 0.69 | 0.66 | 0.64 | 0.71 | 0.61 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.300 | 0.117 | 0.176 | 0.033 | 0.112 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 67 | 63 | 62 | 69 | 58 | 0 | 0 | 59 | 0 |
N.S. |
1 | 0.67 | 0.63 | 0.62 | 0.69 | 0.58 | 0.00 | 0.00 | 0.59 | 0.00 |
time (sec) |
N/A | 0.317 | 0.146 | 0.180 | 0.033 | 0.114 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 58 | 53 | 52 | 162 | 54 | 0 | 0 | 46 | 0 |
N.S. |
1 | 0.61 | 0.56 | 0.55 | 1.71 | 0.57 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.311 | 0.072 | 0.179 | 0.058 | 0.103 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 45 | 41 | 40 | 140 | 42 | 0 | 0 | 34 | 0 |
N.S. |
1 | 0.64 | 0.59 | 0.57 | 2.00 | 0.60 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.288 | 0.056 | 0.178 | 0.052 | 0.113 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 32 | 29 | 29 | 116 | 30 | 0 | 0 | 22 | 0 |
N.S. |
1 | 0.71 | 0.64 | 0.64 | 2.58 | 0.67 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.269 | 0.046 | 0.177 | 0.043 | 0.132 | 0.000 | 0.000 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 22 | 21 | 74 | 23 | 0 | 0 | 15 | 0 |
N.S. |
1 | 1.00 | 0.96 | 0.91 | 3.22 | 1.00 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.224 | 0.004 | 0.173 | 0.040 | 0.111 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 32 | 29 | 27 | 35 | 70 | 0 | 0 | 20 | 0 |
N.S. |
1 | 0.73 | 0.66 | 0.61 | 0.80 | 1.59 | 0.00 | 0.00 | 0.45 | 0.00 |
time (sec) |
N/A | 0.239 | 0.050 | 0.233 | 0.040 | 0.116 | 0.000 | 0.000 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 63 | 42 | 35 | 34 | 51 | 34 | 0 | 0 | 31 | 0 |
N.S. |
1 | 0.67 | 0.56 | 0.54 | 0.81 | 0.54 | 0.00 | 0.00 | 0.49 | 0.00 |
time (sec) |
N/A | 0.280 | 0.004 | 0.172 | 0.037 | 0.109 | 0.000 | 0.000 | 0.142 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 89 | 56 | 50 | 47 | 65 | 47 | 0 | 0 | 48 | 0 |
N.S. |
1 | 0.63 | 0.56 | 0.53 | 0.73 | 0.53 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.301 | 0.005 | 0.174 | 0.041 | 0.107 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 115 | 70 | 66 | 59 | 69 | 58 | 0 | 0 | 59 | 0 |
N.S. |
1 | 0.61 | 0.57 | 0.51 | 0.60 | 0.50 | 0.00 | 0.00 | 0.51 | 0.00 |
time (sec) |
N/A | 0.313 | 0.088 | 0.230 | 0.034 | 0.100 | 0.000 | 0.000 | 0.159 | 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 | 106 | 71 | 81 | 87 | 135 | 83 | 0 | 96 | 73 | 0 |
N.S. |
1 | 0.67 | 0.76 | 0.82 | 1.27 | 0.78 | 0.00 | 0.91 | 0.69 | 0.00 |
time (sec) |
N/A | 0.329 | 0.110 | 0.178 | 0.041 | 0.133 | 0.000 | 0.121 | 0.145 | 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 | 85 | 59 | 70 | 75 | 118 | 72 | 0 | 80 | 62 | 0 |
N.S. |
1 | 0.69 | 0.82 | 0.88 | 1.39 | 0.85 | 0.00 | 0.94 | 0.73 | 0.00 |
time (sec) |
N/A | 0.323 | 0.092 | 0.177 | 0.039 | 0.097 | 0.000 | 0.116 | 0.155 | 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 | 65 | 46 | 53 | 60 | 96 | 57 | 0 | 58 | 48 | 0 |
N.S. |
1 | 0.71 | 0.82 | 0.92 | 1.48 | 0.88 | 0.00 | 0.89 | 0.74 | 0.00 |
time (sec) |
N/A | 0.306 | 0.079 | 0.177 | 0.039 | 0.120 | 0.000 | 0.135 | 0.154 | 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 | 47 | 36 | 36 | 41 | 79 | 38 | 0 | 46 | 35 | 0 |
N.S. |
1 | 0.77 | 0.77 | 0.87 | 1.68 | 0.81 | 0.00 | 0.98 | 0.74 | 0.00 |
time (sec) |
N/A | 0.287 | 0.057 | 0.174 | 0.037 | 0.098 | 0.000 | 0.133 | 0.146 | 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 | 24 | 24 | 23 | 23 | 16 | 23 | 32 | 29 | 14 | 22 |
N.S. |
1 | 1.00 | 0.96 | 0.96 | 0.67 | 0.96 | 1.33 | 1.21 | 0.58 | 0.92 |
time (sec) |
N/A | 0.236 | 0.008 | 0.175 | 0.038 | 0.108 | 0.329 | 0.111 | 0.153 | 21.926 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 65 | 42 | 45 | 55 | 38 | 42 | 0 | 0 | 46 | 0 |
N.S. |
1 | 0.65 | 0.69 | 0.85 | 0.58 | 0.65 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.308 | 0.077 | 0.182 | 0.036 | 0.097 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 87 | 55 | 59 | 75 | 58 | 60 | 0 | 0 | 72 | 0 |
N.S. |
1 | 0.63 | 0.68 | 0.86 | 0.67 | 0.69 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.313 | 0.102 | 0.182 | 0.032 | 0.103 | 0.000 | 0.000 | 0.142 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 71 | 72 | 90 | 79 | 77 | 0 | 0 | 88 | 0 |
N.S. |
1 | 0.63 | 0.64 | 0.80 | 0.71 | 0.69 | 0.00 | 0.00 | 0.79 | 0.00 |
time (sec) |
N/A | 0.346 | 0.126 | 0.187 | 0.036 | 0.110 | 0.000 | 0.000 | 0.152 | 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 | 111 | 72 | 82 | 88 | 132 | 91 | 0 | 96 | 74 | 0 |
N.S. |
1 | 0.65 | 0.74 | 0.79 | 1.19 | 0.82 | 0.00 | 0.86 | 0.67 | 0.00 |
time (sec) |
N/A | 0.343 | 0.098 | 0.183 | 0.043 | 0.118 | 0.000 | 0.119 | 0.152 | 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 | 89 | 60 | 71 | 76 | 115 | 79 | 0 | 80 | 63 | 0 |
N.S. |
1 | 0.67 | 0.80 | 0.85 | 1.29 | 0.89 | 0.00 | 0.90 | 0.71 | 0.00 |
time (sec) |
N/A | 0.317 | 0.087 | 0.180 | 0.048 | 0.115 | 0.000 | 0.119 | 0.141 | 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 | 68 | 47 | 55 | 62 | 98 | 63 | 0 | 58 | 49 | 0 |
N.S. |
1 | 0.69 | 0.81 | 0.91 | 1.44 | 0.93 | 0.00 | 0.85 | 0.72 | 0.00 |
time (sec) |
N/A | 0.295 | 0.013 | 0.193 | 0.040 | 0.118 | 0.000 | 0.114 | 0.155 | 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 | 49 | 37 | 38 | 41 | 80 | 43 | 0 | 46 | 36 | 0 |
N.S. |
1 | 0.76 | 0.78 | 0.84 | 1.63 | 0.88 | 0.00 | 0.94 | 0.73 | 0.00 |
time (sec) |
N/A | 0.282 | 0.008 | 0.274 | 0.040 | 0.126 | 0.000 | 0.114 | 0.154 | 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 | 25 | 25 | 24 | 23 | 16 | 24 | 37 | 29 | 15 | 24 |
N.S. |
1 | 1.00 | 0.96 | 0.92 | 0.64 | 0.96 | 1.48 | 1.16 | 0.60 | 0.96 |
time (sec) |
N/A | 0.232 | 0.006 | 0.177 | 0.035 | 0.095 | 0.589 | 0.130 | 0.152 | 21.881 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 43 | 48 | 55 | 38 | 47 | 0 | 0 | 47 | 0 |
N.S. |
1 | 0.63 | 0.71 | 0.81 | 0.56 | 0.69 | 0.00 | 0.00 | 0.69 | 0.00 |
time (sec) |
N/A | 0.288 | 0.075 | 0.186 | 0.041 | 0.115 | 0.000 | 0.000 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 91 | 56 | 59 | 75 | 58 | 65 | 0 | 0 | 73 | 0 |
N.S. |
1 | 0.62 | 0.65 | 0.82 | 0.64 | 0.71 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.310 | 0.097 | 0.187 | 0.034 | 0.124 | 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 | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 72 | 72 | 93 | 79 | 82 | 0 | 0 | 89 | 0 |
N.S. |
1 | 0.62 | 0.62 | 0.79 | 0.68 | 0.70 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.327 | 0.104 | 0.195 | 0.035 | 0.129 | 0.000 | 0.000 | 0.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 107 | 69 | 80 | 81 | 168 | 85 | 0 | 0 | 76 | 0 |
N.S. |
1 | 0.64 | 0.75 | 0.76 | 1.57 | 0.79 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.324 | 0.098 | 0.183 | 0.044 | 0.102 | 0.000 | 0.000 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 57 | 69 | 69 | 129 | 74 | 0 | 0 | 65 | 0 |
N.S. |
1 | 0.66 | 0.80 | 0.80 | 1.50 | 0.86 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.309 | 0.093 | 0.181 | 0.055 | 0.107 | 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 | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 64 | 44 | 52 | 59 | 88 | 59 | 0 | 0 | 51 | 0 |
N.S. |
1 | 0.69 | 0.81 | 0.92 | 1.38 | 0.92 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.286 | 0.080 | 0.179 | 0.039 | 0.124 | 0.000 | 0.000 | 0.140 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 34 | 35 | 39 | 68 | 40 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.79 | 0.81 | 0.91 | 1.58 | 0.93 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.276 | 0.062 | 0.177 | 0.036 | 0.115 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F(-2) | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 21 | 21 | 25 | 42 | 0 | 17 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.95 | 1.14 | 1.91 | 0.00 | 0.77 | 1.14 |
time (sec) |
N/A | 0.229 | 0.005 | 0.230 | 0.038 | 0.114 | 0.488 | 0.000 | 0.154 | 22.358 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 40 | 44 | 53 | 61 | 44 | 0 | 0 | 49 | 0 |
N.S. |
1 | 0.68 | 0.75 | 0.90 | 1.03 | 0.75 | 0.00 | 0.00 | 0.83 | 0.00 |
time (sec) |
N/A | 0.283 | 0.012 | 0.227 | 0.040 | 0.114 | 0.000 | 0.000 | 0.140 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 53 | 50 | 69 | 57 | 62 | 0 | 0 | 75 | 0 |
N.S. |
1 | 0.68 | 0.64 | 0.88 | 0.73 | 0.79 | 0.00 | 0.00 | 0.96 | 0.00 |
time (sec) |
N/A | 0.308 | 0.112 | 0.181 | 0.037 | 0.105 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 69 | 71 | 86 | 76 | 79 | 0 | 0 | 91 | 0 |
N.S. |
1 | 0.67 | 0.69 | 0.83 | 0.74 | 0.77 | 0.00 | 0.00 | 0.88 | 0.00 |
time (sec) |
N/A | 0.322 | 0.119 | 0.188 | 0.033 | 0.122 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 47 | 54 | 62 | 149 | 63 | 0 | 0 | 51 | 0 |
N.S. |
1 | 0.64 | 0.74 | 0.85 | 2.04 | 0.86 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.297 | 0.084 | 0.212 | 0.055 | 0.124 | 0.000 | 0.000 | 0.142 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F | F(-2) | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 37 | 39 | 41 | 108 | 44 | 0 | 0 | 38 | 0 |
N.S. |
1 | 0.76 | 0.80 | 0.84 | 2.20 | 0.90 | 0.00 | 0.00 | 0.78 | 0.00 |
time (sec) |
N/A | 0.277 | 0.064 | 0.179 | 0.045 | 0.105 | 0.000 | 0.000 | 0.150 | 0.000 |