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 | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 18 | 0 | 22 | 37 | 0 | 22 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 1.22 | 2.06 | 0.00 | 1.22 | 0.89 |
time (sec) |
N/A | 0.234 | 10.043 | 0.554 | 0.000 | 0.071 | 0.339 | 0.000 | 0.249 | 17.888 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 49 | 0 | 16 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.45 | 0.00 | 0.80 | 0.00 | 0.00 | 1.50 | 0.00 |
time (sec) |
N/A | 0.259 | 10.032 | 0.582 | 0.000 | 0.068 | 0.000 | 0.000 | 0.242 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 51 | 84 | 0 | 44 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.21 | 2.00 | 0.00 | 1.05 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.321 | 10.071 | 0.621 | 0.000 | 0.069 | 0.000 | 0.000 | 0.267 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 55 | 80 | 0 | 41 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.20 | 1.74 | 0.00 | 0.89 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.337 | 10.086 | 0.614 | 0.000 | 0.083 | 0.000 | 0.000 | 0.250 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 48 | 49 | 84 | 0 | 44 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.09 | 1.11 | 1.91 | 0.00 | 1.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.361 | 10.208 | 0.602 | 0.000 | 0.071 | 0.000 | 0.000 | 0.241 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 54 | 50 | 0 | 16 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 3.00 | 2.78 | 0.00 | 0.89 | 0.00 | 0.00 | 1.78 | 0.00 |
time (sec) |
N/A | 0.258 | 10.043 | 0.566 | 0.000 | 0.073 | 0.000 | 0.000 | 0.262 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 52 | 84 | 0 | 44 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.16 | 1.87 | 0.00 | 0.98 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.323 | 10.052 | 0.673 | 0.000 | 0.076 | 0.000 | 0.000 | 0.238 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 44 | 43 | 84 | 0 | 35 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.10 | 1.08 | 2.10 | 0.00 | 0.88 | 0.00 | 0.00 | 0.80 | 0.00 |
time (sec) |
N/A | 0.397 | 10.066 | 0.612 | 0.000 | 0.074 | 0.000 | 0.000 | 0.299 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 65 | 51 | 0 | 9 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 6.50 | 5.10 | 0.00 | 0.90 | 0.00 | 0.00 | 3.20 | 0.00 |
time (sec) |
N/A | 0.265 | 10.121 | 0.559 | 0.000 | 0.075 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 51 | 84 | 0 | 44 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.16 | 1.91 | 0.00 | 1.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.347 | 10.065 | 0.618 | 0.000 | 0.075 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 50 | 84 | 0 | 42 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.11 | 1.87 | 0.00 | 0.93 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.322 | 10.064 | 0.627 | 0.000 | 0.090 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 49 | 84 | 0 | 42 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.11 | 1.91 | 0.00 | 0.95 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.308 | 10.052 | 0.612 | 0.000 | 0.075 | 0.000 | 0.000 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 47 | 0 | 16 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.00 | 2.35 | 0.00 | 0.80 | 0.00 | 0.00 | 1.50 | 0.00 |
time (sec) |
N/A | 0.251 | 10.045 | 0.569 | 0.000 | 0.077 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 18 | 0 | 16 | 37 | 0 | 22 | 16 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.00 | 0.89 | 2.06 | 0.00 | 1.22 | 0.89 |
time (sec) |
N/A | 0.234 | 10.044 | 0.543 | 0.000 | 0.084 | 0.346 | 0.000 | 0.172 | 17.264 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 65 | 43 | 0 | 9 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 5.42 | 3.58 | 0.00 | 0.75 | 0.00 | 0.00 | 2.50 | 0.00 |
time (sec) |
N/A | 0.245 | 10.030 | 0.567 | 0.000 | 0.102 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 51 | 84 | 0 | 44 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.21 | 2.00 | 0.00 | 1.05 | 0.00 | 0.00 | 0.76 | 0.00 |
time (sec) |
N/A | 0.317 | 10.053 | 0.625 | 0.000 | 0.093 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 43 | 43 | 52 | 84 | 0 | 44 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.21 | 1.95 | 0.00 | 1.02 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.292 | 10.076 | 0.628 | 0.000 | 0.078 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 44 | 44 | 51 | 84 | 0 | 44 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.16 | 1.91 | 0.00 | 1.00 | 0.00 | 0.00 | 0.73 | 0.00 |
time (sec) |
N/A | 0.335 | 10.069 | 0.594 | 0.000 | 0.075 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 54 | 50 | 0 | 16 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 3.00 | 2.78 | 0.00 | 0.89 | 0.00 | 0.00 | 1.78 | 0.00 |
time (sec) |
N/A | 0.253 | 10.033 | 0.553 | 0.000 | 0.080 | 0.000 | 0.000 | 0.169 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 42 | 45 | 84 | 0 | 35 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.11 | 1.18 | 2.21 | 0.00 | 0.92 | 0.00 | 0.00 | 0.84 | 0.00 |
time (sec) |
N/A | 0.347 | 10.078 | 0.603 | 0.000 | 0.076 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 52 | 84 | 0 | 44 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.16 | 1.87 | 0.00 | 0.98 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.309 | 10.055 | 0.620 | 0.000 | 0.085 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 18 | 43 | 0 | 9 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.50 | 3.58 | 0.00 | 0.75 | 0.00 | 0.00 | 2.50 | 0.00 |
time (sec) |
N/A | 0.242 | 10.032 | 0.540 | 0.000 | 0.071 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 67 | 54 | 53 | 0 | 16 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.24 | 1.00 | 0.98 | 0.00 | 0.30 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.278 | 10.041 | 0.597 | 0.000 | 0.077 | 0.000 | 0.000 | 0.161 | 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 | 100 | 141 | 81 | 84 | 0 | 44 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.41 | 0.81 | 0.84 | 0.00 | 0.44 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.392 | 10.073 | 0.562 | 0.000 | 0.073 | 0.000 | 0.000 | 0.167 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 146 | 83 | 84 | 0 | 41 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.49 | 0.85 | 0.86 | 0.00 | 0.42 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.392 | 10.083 | 0.577 | 0.000 | 0.072 | 0.000 | 0.000 | 0.174 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 141 | 83 | 84 | 0 | 44 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.44 | 0.85 | 0.86 | 0.00 | 0.45 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.371 | 10.063 | 0.579 | 0.000 | 0.074 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 63 | 48 | 43 | 0 | 16 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.17 | 0.89 | 0.80 | 0.00 | 0.30 | 0.00 | 0.00 | 0.48 | 0.00 |
time (sec) |
N/A | 0.288 | 10.039 | 0.546 | 0.000 | 0.066 | 0.000 | 0.000 | 0.161 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 115 | 40 | 40 | 0 | 22 | 34 | 0 | 20 | 31 |
N.S. |
1 | 2.88 | 1.00 | 1.00 | 0.00 | 0.55 | 0.85 | 0.00 | 0.50 | 0.78 |
time (sec) |
N/A | 0.321 | 10.049 | 0.540 | 0.000 | 0.075 | 0.350 | 0.000 | 0.170 | 0.090 |
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 | 50 | 65 | 60 | 53 | 0 | 9 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.30 | 1.20 | 1.06 | 0.00 | 0.18 | 0.00 | 0.00 | 0.60 | 0.00 |
time (sec) |
N/A | 0.286 | 10.033 | 0.552 | 0.000 | 0.072 | 0.000 | 0.000 | 0.163 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 148 | 81 | 84 | 0 | 42 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.51 | 0.83 | 0.86 | 0.00 | 0.43 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.395 | 10.073 | 0.564 | 0.000 | 0.077 | 0.000 | 0.000 | 0.177 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 153 | 81 | 84 | 0 | 41 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.56 | 0.83 | 0.86 | 0.00 | 0.42 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.402 | 10.079 | 0.568 | 0.000 | 0.080 | 0.000 | 0.000 | 0.165 | 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 | 98 | 148 | 81 | 84 | 0 | 44 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.51 | 0.83 | 0.86 | 0.00 | 0.45 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.401 | 10.073 | 0.554 | 0.000 | 0.079 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 63 | 65 | 53 | 0 | 17 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.29 | 1.33 | 1.08 | 0.00 | 0.35 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.284 | 10.033 | 0.544 | 0.000 | 0.070 | 0.000 | 0.000 | 0.169 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 148 | 80 | 84 | 0 | 44 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.48 | 0.80 | 0.84 | 0.00 | 0.44 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.378 | 10.061 | 0.616 | 0.000 | 0.076 | 0.000 | 0.000 | 0.166 | 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 | 94 | 148 | 77 | 84 | 0 | 40 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.57 | 0.82 | 0.89 | 0.00 | 0.43 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.402 | 10.088 | 0.564 | 0.000 | 0.091 | 0.000 | 0.000 | 0.162 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 54 | 67 | 54 | 53 | 0 | 16 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.24 | 1.00 | 0.98 | 0.00 | 0.30 | 0.00 | 0.00 | 0.56 | 0.00 |
time (sec) |
N/A | 0.295 | 10.033 | 0.538 | 0.000 | 0.080 | 0.000 | 0.000 | 0.170 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 148 | 83 | 84 | 0 | 44 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.41 | 0.79 | 0.80 | 0.00 | 0.42 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.402 | 10.090 | 0.575 | 0.000 | 0.067 | 0.000 | 0.000 | 0.165 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 146 | 80 | 84 | 0 | 44 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.49 | 0.82 | 0.86 | 0.00 | 0.45 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.398 | 10.072 | 0.600 | 0.000 | 0.075 | 0.000 | 0.000 | 0.167 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 143 | 83 | 84 | 0 | 44 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.46 | 0.85 | 0.86 | 0.00 | 0.45 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.383 | 10.062 | 0.562 | 0.000 | 0.077 | 0.000 | 0.000 | 0.164 | 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 | 48 | 63 | 63 | 51 | 0 | 9 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.31 | 1.31 | 1.06 | 0.00 | 0.19 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.285 | 10.033 | 0.554 | 0.000 | 0.074 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 112 | 40 | 40 | 0 | 16 | 34 | 0 | 20 | 31 |
N.S. |
1 | 2.80 | 1.00 | 1.00 | 0.00 | 0.40 | 0.85 | 0.00 | 0.50 | 0.78 |
time (sec) |
N/A | 0.333 | 10.049 | 0.546 | 0.000 | 0.080 | 0.351 | 0.000 | 0.173 | 0.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 56 | 65 | 51 | 45 | 0 | 16 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.16 | 0.91 | 0.80 | 0.00 | 0.29 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.288 | 10.027 | 0.556 | 0.000 | 0.086 | 0.000 | 0.000 | 0.175 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 150 | 81 | 84 | 0 | 42 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.53 | 0.83 | 0.86 | 0.00 | 0.43 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.396 | 10.064 | 0.581 | 0.000 | 0.077 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 153 | 78 | 84 | 0 | 42 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.56 | 0.80 | 0.86 | 0.00 | 0.43 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.404 | 10.064 | 0.575 | 0.000 | 0.078 | 0.000 | 0.000 | 0.170 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 155 | 83 | 84 | 0 | 44 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.50 | 0.81 | 0.82 | 0.00 | 0.43 | 0.00 | 0.00 | 0.29 | 0.00 |
time (sec) |
N/A | 0.398 | 10.079 | 0.566 | 0.000 | 0.068 | 0.000 | 0.000 | 0.172 | 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 | 49 | 63 | 65 | 53 | 0 | 17 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.29 | 1.33 | 1.08 | 0.00 | 0.35 | 0.00 | 0.00 | 0.61 | 0.00 |
time (sec) |
N/A | 0.290 | 10.035 | 0.547 | 0.000 | 0.070 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 155 | 75 | 84 | 0 | 38 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.65 | 0.80 | 0.89 | 0.00 | 0.40 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.411 | 10.072 | 0.557 | 0.000 | 0.076 | 0.000 | 0.000 | 0.172 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 98 | 153 | 80 | 84 | 0 | 44 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.56 | 0.82 | 0.86 | 0.00 | 0.45 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.394 | 10.068 | 0.572 | 0.000 | 0.070 | 0.000 | 0.000 | 0.174 | 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 | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 92 | 92 | 144 | 87 | 0 | 36 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.57 | 0.95 | 0.00 | 0.39 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.370 | 10.146 | 0.665 | 0.000 | 0.072 | 0.000 | 0.000 | 0.176 | 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 | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 90 | 147 | 87 | 0 | 36 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.63 | 0.97 | 0.00 | 0.40 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.330 | 10.102 | 0.554 | 0.000 | 0.072 | 0.000 | 0.000 | 0.165 | 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 | 48 | 52 | 58 | 44 | 0 | 11 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.08 | 1.21 | 0.92 | 0.00 | 0.23 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.272 | 0.018 | 0.507 | 0.000 | 0.078 | 0.000 | 0.000 | 0.167 | 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 | 47 | 58 | 58 | 48 | 0 | 16 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.23 | 1.23 | 1.02 | 0.00 | 0.34 | 0.00 | 0.00 | 0.64 | 0.00 |
time (sec) |
N/A | 0.277 | 10.031 | 0.450 | 0.000 | 0.082 | 0.000 | 0.000 | 0.172 | 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 | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 100 | 108 | 103 | 76 | 0 | 41 | 0 | 0 | 26 | 0 |
N.S. |
1 | 1.08 | 1.03 | 0.76 | 0.00 | 0.41 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.362 | 10.103 | 0.536 | 0.000 | 0.074 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 55 | 80 | 0 | 41 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.15 | 1.67 | 0.00 | 0.85 | 0.00 | 0.00 | 0.62 | 0.00 |
time (sec) |
N/A | 0.369 | 10.075 | 0.551 | 0.000 | 0.071 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 52 | 76 | 0 | 41 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.16 | 1.69 | 0.00 | 0.91 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.319 | 10.054 | 0.528 | 0.000 | 0.071 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 65 | 51 | 0 | 9 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 6.50 | 5.10 | 0.00 | 0.90 | 0.00 | 0.00 | 3.20 | 0.00 |
time (sec) |
N/A | 0.263 | 0.019 | 0.517 | 0.000 | 0.073 | 0.000 | 0.000 | 0.167 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 56 | 80 | 0 | 41 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.14 | 1.63 | 0.00 | 0.84 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.371 | 10.071 | 0.568 | 0.000 | 0.071 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 48 | 48 | 52 | 80 | 0 | 41 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.08 | 1.67 | 0.00 | 0.85 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.370 | 10.063 | 0.630 | 0.000 | 0.069 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 56 | 80 | 0 | 41 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.14 | 1.63 | 0.00 | 0.84 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.345 | 10.065 | 0.631 | 0.000 | 0.070 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 65 | 43 | 0 | 9 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 5.42 | 3.58 | 0.00 | 0.75 | 0.00 | 0.00 | 2.67 | 0.00 |
time (sec) |
N/A | 0.249 | 10.032 | 0.593 | 0.000 | 0.070 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 45 | 45 | 52 | 76 | 0 | 41 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.16 | 1.69 | 0.00 | 0.91 | 0.00 | 0.00 | 0.71 | 0.00 |
time (sec) |
N/A | 0.325 | 10.058 | 0.542 | 0.000 | 0.069 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 56 | 80 | 0 | 41 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.14 | 1.63 | 0.00 | 0.84 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.343 | 10.055 | 0.589 | 0.000 | 0.069 | 0.000 | 0.000 | 0.180 | 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 | 114 | 114 | 186 | 144 | 0 | 121 | 0 | 0 | 30 | 0 |
N.S. |
1 | 1.00 | 1.63 | 1.26 | 0.00 | 1.06 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.334 | 10.147 | 0.533 | 0.000 | 0.077 | 0.000 | 0.000 | 0.174 | 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 | 115 | 115 | 180 | 143 | 0 | 121 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.57 | 1.24 | 0.00 | 1.05 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.328 | 10.131 | 0.517 | 0.000 | 0.081 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 117 | 117 | 179 | 143 | 0 | 126 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.00 | 1.53 | 1.22 | 0.00 | 1.08 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.329 | 10.113 | 0.518 | 0.000 | 0.085 | 0.000 | 0.000 | 0.178 | 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 | 118 | 118 | 181 | 142 | 0 | 126 | 0 | 0 | 33 | 0 |
N.S. |
1 | 1.00 | 1.53 | 1.20 | 0.00 | 1.07 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.324 | 10.134 | 0.517 | 0.000 | 0.077 | 0.000 | 0.000 | 0.174 | 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 | 133 | 133 | 187 | 175 | 0 | 187 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 1.41 | 1.32 | 0.00 | 1.41 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.389 | 10.204 | 0.581 | 0.000 | 0.083 | 0.000 | 0.000 | 0.181 | 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 | 134 | 134 | 191 | 174 | 0 | 187 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.00 | 1.43 | 1.30 | 0.00 | 1.40 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.363 | 10.174 | 0.537 | 0.000 | 0.077 | 0.000 | 0.000 | 0.177 | 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 | 130 | 169 | 177 | 145 | 0 | 127 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.30 | 1.36 | 1.12 | 0.00 | 0.98 | 0.00 | 0.00 | 0.25 | 0.00 |
time (sec) |
N/A | 0.608 | 10.143 | 0.550 | 0.000 | 0.078 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 194 | 179 | 144 | 0 | 126 | 0 | 0 | 34 | 0 |
N.S. |
1 | 1.46 | 1.35 | 1.08 | 0.00 | 0.95 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.593 | 10.145 | 0.514 | 0.000 | 0.078 | 0.000 | 0.000 | 0.175 | 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 | 133 | 194 | 188 | 142 | 0 | 131 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.46 | 1.41 | 1.07 | 0.00 | 0.98 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.530 | 10.122 | 0.516 | 0.000 | 0.081 | 0.000 | 0.000 | 0.179 | 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 | 132 | 171 | 182 | 141 | 0 | 132 | 0 | 0 | 36 | 0 |
N.S. |
1 | 1.30 | 1.38 | 1.07 | 0.00 | 1.00 | 0.00 | 0.00 | 0.27 | 0.00 |
time (sec) |
N/A | 0.491 | 10.118 | 0.517 | 0.000 | 0.077 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 62 | 123 | 142 | 0 | 88 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.09 | 2.16 | 2.49 | 0.00 | 1.54 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.364 | 9.291 | 2.385 | 0.000 | 0.079 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 150 | 135 | 230 | 0 | 155 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.18 | 1.06 | 1.81 | 0.00 | 1.22 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.633 | 9.375 | 1.642 | 0.000 | 0.073 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 131 | 148 | 166 | 218 | 0 | 171 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.13 | 1.27 | 1.66 | 0.00 | 1.31 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.576 | 9.498 | 2.371 | 0.000 | 0.080 | 0.000 | 0.000 | 0.197 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 148 | 135 | 230 | 0 | 176 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.17 | 1.06 | 1.81 | 0.00 | 1.39 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.545 | 9.399 | 1.872 | 0.000 | 0.076 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 62 | 95 | 115 | 0 | 80 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.09 | 1.67 | 2.02 | 0.00 | 1.40 | 0.00 | 0.00 | 0.67 | 0.00 |
time (sec) |
N/A | 0.361 | 8.983 | 1.793 | 0.000 | 0.069 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 44 | 18 | 0 | 52 | 37 | 0 | 25 | 16 |
N.S. |
1 | 1.00 | 1.16 | 0.47 | 0.00 | 1.37 | 0.97 | 0.00 | 0.66 | 0.42 |
time (sec) |
N/A | 0.266 | 6.493 | 0.709 | 0.000 | 0.083 | 0.411 | 0.000 | 0.175 | 17.797 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 76 | 101 | 138 | 0 | 92 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.01 | 1.35 | 1.84 | 0.00 | 1.23 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.382 | 8.953 | 2.270 | 0.000 | 0.072 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 142 | 139 | 230 | 0 | 177 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.15 | 1.13 | 1.87 | 0.00 | 1.44 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.507 | 9.231 | 2.293 | 0.000 | 0.087 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 142 | 172 | 218 | 0 | 173 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.12 | 1.35 | 1.72 | 0.00 | 1.36 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.548 | 9.523 | 2.778 | 0.000 | 0.080 | 0.000 | 0.000 | 0.191 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 148 | 135 | 230 | 0 | 159 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.17 | 1.06 | 1.81 | 0.00 | 1.25 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.602 | 9.320 | 2.239 | 0.000 | 0.086 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 76 | 97 | 139 | 0 | 97 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.01 | 1.29 | 1.85 | 0.00 | 1.29 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.387 | 9.078 | 2.754 | 0.000 | 0.081 | 0.000 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 136 | 168 | 228 | 0 | 178 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.09 | 1.34 | 1.82 | 0.00 | 1.42 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.492 | 9.478 | 2.513 | 0.000 | 0.089 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 119 | 142 | 122 | 228 | 0 | 140 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.19 | 1.03 | 1.92 | 0.00 | 1.18 | 0.00 | 0.00 | 0.34 | 0.00 |
time (sec) |
N/A | 0.598 | 9.171 | 1.628 | 0.000 | 0.080 | 0.000 | 0.000 | 0.192 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 62 | 123 | 142 | 0 | 88 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.09 | 2.16 | 2.49 | 0.00 | 1.54 | 0.00 | 0.00 | 0.70 | 0.00 |
time (sec) |
N/A | 0.378 | 9.283 | 2.278 | 0.000 | 0.075 | 0.000 | 0.000 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 142 | 139 | 230 | 0 | 177 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.12 | 1.09 | 1.81 | 0.00 | 1.39 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.599 | 9.514 | 2.296 | 0.000 | 0.080 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 136 | 162 | 228 | 0 | 176 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.09 | 1.30 | 1.82 | 0.00 | 1.41 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.504 | 9.256 | 1.941 | 0.000 | 0.097 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 148 | 134 | 228 | 0 | 175 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.17 | 1.06 | 1.80 | 0.00 | 1.38 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.546 | 9.301 | 1.858 | 0.000 | 0.080 | 0.000 | 0.000 | 0.195 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 73 | 73 | 98 | 132 | 0 | 96 | 0 | 0 | 38 | 0 |
N.S. |
1 | 1.00 | 1.34 | 1.81 | 0.00 | 1.32 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.372 | 8.947 | 1.795 | 0.000 | 0.092 | 0.000 | 0.000 | 0.175 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | C | F | A | A | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 38 | 44 | 18 | 0 | 46 | 37 | 0 | 25 | 16 |
N.S. |
1 | 1.00 | 1.16 | 0.47 | 0.00 | 1.21 | 0.97 | 0.00 | 0.66 | 0.42 |
time (sec) |
N/A | 0.257 | 6.445 | 0.707 | 0.000 | 0.097 | 0.403 | 0.000 | 0.169 | 17.782 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 59 | 64 | 99 | 121 | 0 | 76 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.08 | 1.68 | 2.05 | 0.00 | 1.29 | 0.00 | 0.00 | 0.68 | 0.00 |
time (sec) |
N/A | 0.367 | 8.922 | 2.280 | 0.000 | 0.079 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 140 | 138 | 228 | 0 | 175 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.16 | 1.14 | 1.88 | 0.00 | 1.45 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.503 | 9.328 | 2.311 | 0.000 | 0.074 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 121 | 130 | 166 | 228 | 0 | 177 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.07 | 1.37 | 1.88 | 0.00 | 1.46 | 0.00 | 0.00 | 0.33 | 0.00 |
time (sec) |
N/A | 0.488 | 9.157 | 2.375 | 0.000 | 0.094 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 141 | 139 | 230 | 0 | 179 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.11 | 1.09 | 1.81 | 0.00 | 1.41 | 0.00 | 0.00 | 0.31 | 0.00 |
time (sec) |
N/A | 0.565 | 9.211 | 2.676 | 0.000 | 0.077 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 76 | 97 | 139 | 0 | 97 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.01 | 1.29 | 1.85 | 0.00 | 1.29 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.373 | 9.083 | 2.768 | 0.000 | 0.074 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | No | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 113 | 134 | 126 | 228 | 0 | 143 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.19 | 1.12 | 2.02 | 0.00 | 1.27 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.570 | 9.410 | 2.227 | 0.000 | 0.077 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 125 | 136 | 168 | 228 | 0 | 179 | 0 | 0 | 40 | 0 |
N.S. |
1 | 1.09 | 1.34 | 1.82 | 0.00 | 1.43 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.513 | 9.421 | 2.859 | 0.000 | 0.078 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 57 | 58 | 80 | 119 | 0 | 74 | 0 | 0 | 251 | 0 |
N.S. |
1 | 1.02 | 1.40 | 2.09 | 0.00 | 1.30 | 0.00 | 0.00 | 4.40 | 0.00 |
time (sec) |
N/A | 0.358 | 8.210 | 1.937 | 0.000 | 0.079 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | B | F | A | F | F | F | F(-1) |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 148 | 189 | 220 | 0 | 171 | 0 | 0 | 44 | 0 |
N.S. |
1 | 1.09 | 1.39 | 1.62 | 0.00 | 1.26 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.574 | 9.828 | 2.917 | 0.000 | 0.074 | 0.000 | 0.000 | 0.214 | 0.000 |