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 | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 14 | 13 | 13 | 12 | 13 | 15 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.88 | 0.76 |
time (sec) |
N/A | 0.233 | 0.002 | 0.184 | 0.032 | 0.073 | 0.017 | 0.126 | 0.209 | 0.026 |
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 | 17 | 17 | 14 | 14 | 13 | 12 | 13 | 14 | 13 |
N.S. |
1 | 1.06 | 1.06 | 0.88 | 0.88 | 0.81 | 0.75 | 0.81 | 0.88 | 0.81 |
time (sec) |
N/A | 0.241 | 0.002 | 0.178 | 0.025 | 0.083 | 0.017 | 0.118 | 0.202 | 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 | 13 | 13 | 13 | 12 | 14 | 11 | 10 | 14 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 1.08 | 0.85 | 0.77 | 1.08 | 0.85 | 0.85 |
time (sec) |
N/A | 0.238 | 0.004 | 0.075 | 0.029 | 0.070 | 0.036 | 0.124 | 0.216 | 0.024 |
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 | 13 | 13 | 13 | 12 | 14 | 17 | 10 | 20 | 17 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 1.08 | 1.31 | 0.77 | 1.54 | 1.31 | 0.85 |
time (sec) |
N/A | 0.247 | 0.003 | 0.059 | 0.034 | 0.063 | 0.056 | 0.119 | 0.197 | 0.146 |
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 | 17 | 17 | 17 | 14 | 13 | 13 | 14 | 13 | 15 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.82 | 0.76 | 0.88 | 0.76 |
time (sec) |
N/A | 0.251 | 0.002 | 0.064 | 0.026 | 0.063 | 0.072 | 0.123 | 0.188 | 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 | 17 | 17 | 17 | 14 | 15 | 15 | 15 | 15 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.245 | 0.002 | 0.075 | 0.043 | 0.066 | 0.094 | 0.114 | 0.178 | 0.032 |
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 | 17 | 17 | 17 | 14 | 13 | 13 | 12 | 13 | 15 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.88 | 0.76 |
time (sec) |
N/A | 0.249 | 0.002 | 0.208 | 0.027 | 0.064 | 0.021 | 0.120 | 0.223 | 0.022 |
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 | 17 | 17 | 17 | 14 | 13 | 13 | 12 | 13 | 15 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.88 | 0.76 |
time (sec) |
N/A | 0.253 | 0.002 | 0.204 | 0.027 | 0.072 | 0.021 | 0.120 | 0.224 | 0.024 |
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 | 17 | 17 | 17 | 14 | 13 | 13 | 12 | 13 | 15 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.88 | 0.76 |
time (sec) |
N/A | 0.250 | 0.002 | 0.078 | 0.027 | 0.064 | 0.024 | 0.124 | 0.207 | 0.022 |
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 | 17 | 17 | 17 | 14 | 13 | 13 | 12 | 13 | 14 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.71 | 0.76 | 0.82 | 0.76 |
time (sec) |
N/A | 0.247 | 0.002 | 0.070 | 0.030 | 0.069 | 0.021 | 0.116 | 0.210 | 0.022 |
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 | 12 | 12 | 12 | 11 | 10 | 10 | 8 | 10 | 12 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 0.83 | 0.67 | 0.83 | 1.00 | 0.83 |
time (sec) |
N/A | 0.235 | 0.000 | 0.046 | 0.025 | 0.071 | 0.027 | 0.125 | 0.229 | 0.018 |
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 | 15 | 15 | 15 | 14 | 13 | 14 | 8 | 13 | 14 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.93 | 0.53 | 0.87 | 0.93 | 0.87 |
time (sec) |
N/A | 0.245 | 0.002 | 0.075 | 0.041 | 0.072 | 0.038 | 0.116 | 0.196 | 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 | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 14 | 13 | 14 | 12 | 13 | 14 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.82 | 0.71 | 0.76 | 0.82 | 0.76 |
time (sec) |
N/A | 0.249 | 0.001 | 0.070 | 0.025 | 0.074 | 0.040 | 0.120 | 0.222 | 0.025 |
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 | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 11 | 10 | 15 | 8 | 10 | 15 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.83 | 1.25 | 0.67 | 0.83 | 1.25 | 0.83 |
time (sec) |
N/A | 0.247 | 0.001 | 0.070 | 0.026 | 0.070 | 0.046 | 0.125 | 0.208 | 0.024 |
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 | 15 | 15 | 15 | 14 | 13 | 13 | 14 | 13 | 15 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 0.93 | 0.87 | 1.00 | 0.87 |
time (sec) |
N/A | 0.247 | 0.002 | 0.059 | 0.025 | 0.072 | 0.065 | 0.122 | 0.250 | 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 | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 14 | 13 | 13 | 14 | 13 | 15 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 0.76 | 0.82 | 0.76 | 0.88 | 0.76 |
time (sec) |
N/A | 0.255 | 0.003 | 0.059 | 0.026 | 0.067 | 0.065 | 0.123 | 0.205 | 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 | 17 | 17 | 17 | 14 | 15 | 15 | 15 | 15 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.272 | 0.002 | 0.062 | 0.030 | 0.066 | 0.087 | 0.121 | 0.191 | 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 | 17 | 17 | 17 | 14 | 15 | 15 | 15 | 15 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 | 0.88 |
time (sec) |
N/A | 0.253 | 0.003 | 0.062 | 0.034 | 0.068 | 0.098 | 0.126 | 0.194 | 0.029 |
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 | 30 | 34 | 30 | 25 | 24 | 24 | 24 | 24 | 26 | 24 |
N.S. |
1 | 1.13 | 1.00 | 0.83 | 0.80 | 0.80 | 0.80 | 0.80 | 0.87 | 0.80 |
time (sec) |
N/A | 0.277 | 0.001 | 0.484 | 0.030 | 0.071 | 0.019 | 0.126 | 0.212 | 0.040 |
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 | 16 | 16 | 30 | 15 | 14 | 24 | 24 | 14 | 25 | 24 |
N.S. |
1 | 1.00 | 1.88 | 0.94 | 0.88 | 1.50 | 1.50 | 0.88 | 1.56 | 1.50 |
time (sec) |
N/A | 0.231 | 0.001 | 0.473 | 0.026 | 0.073 | 0.020 | 0.123 | 0.238 | 0.036 |
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 | 26 | 30 | 26 | 23 | 25 | 22 | 22 | 25 | 22 | 22 |
N.S. |
1 | 1.15 | 1.00 | 0.88 | 0.96 | 0.85 | 0.85 | 0.96 | 0.85 | 0.85 |
time (sec) |
N/A | 0.270 | 0.001 | 0.517 | 0.029 | 0.075 | 0.039 | 0.118 | 0.200 | 0.128 |
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 | 27 | 28 | 27 | 24 | 25 | 27 | 24 | 33 | 27 | 23 |
N.S. |
1 | 1.04 | 1.00 | 0.89 | 0.93 | 1.00 | 0.89 | 1.22 | 1.00 | 0.85 |
time (sec) |
N/A | 0.276 | 0.001 | 0.460 | 0.030 | 0.070 | 0.070 | 0.119 | 0.231 | 0.035 |
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 | 26 | 30 | 26 | 23 | 26 | 28 | 24 | 34 | 28 | 25 |
N.S. |
1 | 1.15 | 1.00 | 0.88 | 1.00 | 1.08 | 0.92 | 1.31 | 1.08 | 0.96 |
time (sec) |
N/A | 0.283 | 0.001 | 0.435 | 0.026 | 0.073 | 0.109 | 0.124 | 0.211 | 0.046 |
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 | 19 | 19 | 30 | 25 | 24 | 24 | 26 | 24 | 26 | 26 |
N.S. |
1 | 1.00 | 1.58 | 1.32 | 1.26 | 1.26 | 1.37 | 1.26 | 1.37 | 1.37 |
time (sec) |
N/A | 0.234 | 0.001 | 0.428 | 0.032 | 0.071 | 0.127 | 0.123 | 0.204 | 0.038 |
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 | 30 | 34 | 30 | 25 | 26 | 26 | 27 | 26 | 26 | 26 |
N.S. |
1 | 1.13 | 1.00 | 0.83 | 0.87 | 0.87 | 0.90 | 0.87 | 0.87 | 0.87 |
time (sec) |
N/A | 0.279 | 0.001 | 0.438 | 0.025 | 0.066 | 0.146 | 0.122 | 0.205 | 0.042 |
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 | 30 | 30 | 30 | 25 | 24 | 24 | 26 | 24 | 26 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.87 | 0.80 | 0.87 | 0.80 |
time (sec) |
N/A | 0.268 | 0.001 | 0.498 | 0.028 | 0.066 | 0.018 | 0.116 | 0.259 | 0.033 |
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 | 30 | 30 | 30 | 25 | 24 | 24 | 26 | 24 | 26 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.87 | 0.80 | 0.87 | 0.80 |
time (sec) |
N/A | 0.270 | 0.001 | 0.501 | 0.031 | 0.071 | 0.020 | 0.120 | 0.227 | 0.033 |
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 | 30 | 30 | 30 | 25 | 24 | 24 | 24 | 24 | 26 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.80 | 0.80 | 0.80 | 0.80 | 0.87 | 0.80 |
time (sec) |
N/A | 0.275 | 0.002 | 0.507 | 0.033 | 0.065 | 0.020 | 0.116 | 0.251 | 0.034 |
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 | 25 | 22 | 21 | 21 | 22 | 21 | 24 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.84 | 0.84 | 0.88 | 0.84 | 0.96 | 0.84 |
time (sec) |
N/A | 0.271 | 0.001 | 0.423 | 0.025 | 0.066 | 0.021 | 0.122 | 0.200 | 0.033 |
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 | 28 | 25 | 24 | 26 | 22 | 24 | 26 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.86 | 0.93 | 0.79 | 0.86 | 0.93 | 0.89 |
time (sec) |
N/A | 0.274 | 0.001 | 0.448 | 0.028 | 0.068 | 0.061 | 0.121 | 0.202 | 0.037 |
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 | 27 | 27 | 27 | 24 | 23 | 25 | 22 | 23 | 25 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.85 | 0.93 | 0.81 | 0.85 | 0.93 | 0.93 |
time (sec) |
N/A | 0.271 | 0.001 | 0.441 | 0.031 | 0.072 | 0.056 | 0.128 | 0.195 | 0.037 |
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 | 26 | 26 | 26 | 23 | 22 | 26 | 22 | 22 | 26 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.85 | 1.00 | 0.85 | 0.85 | 1.00 | 0.85 |
time (sec) |
N/A | 0.270 | 0.001 | 0.612 | 0.029 | 0.072 | 0.053 | 0.123 | 0.227 | 0.038 |
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 | 34 | 38 | 43 | 36 | 35 | 35 | 37 | 35 | 37 | 35 |
N.S. |
1 | 1.12 | 1.26 | 1.06 | 1.03 | 1.03 | 1.09 | 1.03 | 1.09 | 1.03 |
time (sec) |
N/A | 0.288 | 0.004 | 0.487 | 0.033 | 0.072 | 0.022 | 0.121 | 0.196 | 0.045 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 43 | 15 | 14 | 35 | 37 | 14 | 36 | 35 |
N.S. |
1 | 1.00 | 2.69 | 0.94 | 0.88 | 2.19 | 2.31 | 0.88 | 2.25 | 2.19 |
time (sec) |
N/A | 0.233 | 0.002 | 0.473 | 0.034 | 0.066 | 0.026 | 0.117 | 0.215 | 0.044 |
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 | 43 | 39 | 34 | 36 | 33 | 37 | 36 | 33 | 33 |
N.S. |
1 | 1.10 | 1.00 | 0.87 | 0.92 | 0.85 | 0.95 | 0.92 | 0.85 | 0.85 |
time (sec) |
N/A | 0.290 | 0.004 | 0.453 | 0.036 | 0.072 | 0.069 | 0.111 | 0.202 | 0.039 |
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 | 42 | 40 | 35 | 36 | 38 | 37 | 46 | 38 | 34 |
N.S. |
1 | 1.05 | 1.00 | 0.88 | 0.90 | 0.95 | 0.92 | 1.15 | 0.95 | 0.85 |
time (sec) |
N/A | 0.291 | 0.005 | 0.508 | 0.025 | 0.064 | 0.083 | 0.116 | 0.205 | 0.037 |
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 | 41 | 40 | 35 | 37 | 39 | 37 | 46 | 39 | 37 |
N.S. |
1 | 1.02 | 1.00 | 0.88 | 0.92 | 0.98 | 0.92 | 1.15 | 0.98 | 0.92 |
time (sec) |
N/A | 0.300 | 0.007 | 0.450 | 0.033 | 0.067 | 0.127 | 0.121 | 0.195 | 0.132 |
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 | 43 | 39 | 34 | 39 | 39 | 37 | 47 | 39 | 36 |
N.S. |
1 | 1.10 | 1.00 | 0.87 | 1.00 | 1.00 | 0.95 | 1.21 | 1.00 | 0.92 |
time (sec) |
N/A | 0.297 | 0.004 | 0.438 | 0.025 | 0.070 | 0.159 | 0.121 | 0.205 | 0.143 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 43 | 36 | 35 | 35 | 37 | 35 | 37 | 37 |
N.S. |
1 | 1.00 | 2.26 | 1.89 | 1.84 | 1.84 | 1.95 | 1.84 | 1.95 | 1.95 |
time (sec) |
N/A | 0.228 | 0.004 | 0.437 | 0.031 | 0.067 | 0.183 | 0.123 | 0.215 | 0.032 |
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 | 43 | 36 | 37 | 37 | 39 | 37 | 37 | 37 |
N.S. |
1 | 1.10 | 1.08 | 0.90 | 0.92 | 0.92 | 0.98 | 0.92 | 0.92 | 0.92 |
time (sec) |
N/A | 0.250 | 0.006 | 0.441 | 0.035 | 0.063 | 0.218 | 0.122 | 0.237 | 0.134 |
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 | 43 | 43 | 43 | 36 | 35 | 35 | 37 | 35 | 37 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.81 | 0.81 | 0.86 | 0.81 | 0.86 | 0.81 |
time (sec) |
N/A | 0.277 | 0.002 | 0.493 | 0.032 | 0.066 | 0.025 | 0.117 | 0.194 | 0.045 |
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 | 43 | 43 | 43 | 36 | 35 | 35 | 39 | 35 | 37 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.81 | 0.81 | 0.91 | 0.81 | 0.86 | 0.81 |
time (sec) |
N/A | 0.275 | 0.002 | 0.493 | 0.026 | 0.071 | 0.024 | 0.123 | 0.201 | 0.045 |
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 | 43 | 43 | 43 | 36 | 35 | 35 | 37 | 35 | 37 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.81 | 0.81 | 0.86 | 0.81 | 0.86 | 0.81 |
time (sec) |
N/A | 0.279 | 0.002 | 0.490 | 0.025 | 0.072 | 0.023 | 0.118 | 0.196 | 0.044 |
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 | 38 | 38 | 38 | 33 | 32 | 32 | 34 | 32 | 35 | 32 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.84 | 0.84 | 0.89 | 0.84 | 0.92 | 0.84 |
time (sec) |
N/A | 0.275 | 0.001 | 0.428 | 0.025 | 0.067 | 0.020 | 0.122 | 0.203 | 0.044 |
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 | 38 | 38 | 38 | 35 | 34 | 37 | 32 | 34 | 37 | 34 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.89 | 0.97 | 0.84 | 0.89 | 0.97 | 0.89 |
time (sec) |
N/A | 0.282 | 0.005 | 0.460 | 0.026 | 0.069 | 0.044 | 0.123 | 0.199 | 0.044 |
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 | 43 | 43 | 43 | 36 | 35 | 36 | 37 | 35 | 36 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.81 | 0.84 | 0.86 | 0.81 | 0.84 | 0.81 |
time (sec) |
N/A | 0.292 | 0.005 | 0.454 | 0.033 | 0.068 | 0.049 | 0.113 | 0.222 | 0.045 |
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 | 34 | 33 | 37 | 36 | 33 | 37 | 33 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.85 | 0.95 | 0.92 | 0.85 | 0.95 | 0.85 |
time (sec) |
N/A | 0.289 | 0.003 | 0.454 | 0.025 | 0.072 | 0.083 | 0.112 | 0.220 | 0.045 |
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 | 38 | 38 | 38 | 35 | 35 | 37 | 36 | 35 | 37 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.92 | 0.97 | 0.95 | 0.92 | 0.97 | 0.97 |
time (sec) |
N/A | 0.289 | 0.005 | 0.458 | 0.031 | 0.065 | 0.118 | 0.121 | 0.194 | 0.135 |
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 | 43 | 43 | 43 | 36 | 36 | 36 | 39 | 36 | 36 | 38 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.84 | 0.84 | 0.91 | 0.84 | 0.84 | 0.88 |
time (sec) |
N/A | 0.285 | 0.004 | 0.454 | 0.026 | 0.066 | 0.084 | 0.118 | 0.181 | 0.137 |
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 | 37 | 37 | 37 | 34 | 34 | 37 | 36 | 34 | 37 | 35 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 0.92 | 1.00 | 0.97 | 0.92 | 1.00 | 0.95 |
time (sec) |
N/A | 0.287 | 0.004 | 0.443 | 0.028 | 0.066 | 0.101 | 0.117 | 0.200 | 0.040 |
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 | 39 | 40 | 34 | 34 | 33 | 32 | 35 | 71 | 33 |
N.S. |
1 | 0.98 | 1.00 | 0.85 | 0.85 | 0.82 | 0.80 | 0.88 | 1.78 | 0.82 |
time (sec) |
N/A | 0.293 | 0.007 | 0.642 | 0.032 | 0.068 | 0.106 | 0.123 | 0.228 | 0.151 |
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 | 27 | 26 | 27 | 23 | 23 | 22 | 20 | 24 | 58 | 22 |
N.S. |
1 | 0.96 | 1.00 | 0.85 | 0.85 | 0.81 | 0.74 | 0.89 | 2.15 | 0.81 |
time (sec) |
N/A | 0.265 | 0.006 | 0.572 | 0.035 | 0.063 | 0.123 | 0.123 | 0.234 | 0.042 |
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 | 15 | 15 | 15 | 14 | 13 | 13 | 10 | 14 | 47 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.93 | 0.87 | 0.87 | 0.67 | 0.93 | 3.13 | 0.87 |
time (sec) |
N/A | 0.231 | 0.004 | 0.555 | 0.025 | 0.077 | 0.088 | 0.122 | 0.195 | 0.128 |
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 | 22 | 26 | 22 | 21 | 23 | 18 | 15 | 24 | 55 | 18 |
N.S. |
1 | 1.18 | 1.00 | 0.95 | 1.05 | 0.82 | 0.68 | 1.09 | 2.50 | 0.82 |
time (sec) |
N/A | 0.245 | 0.005 | 0.562 | 0.038 | 0.070 | 0.139 | 0.123 | 0.196 | 0.095 |
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 | 35 | 36 | 35 | 32 | 33 | 33 | 31 | 43 | 71 | 31 |
N.S. |
1 | 1.03 | 1.00 | 0.91 | 0.94 | 0.94 | 0.89 | 1.23 | 2.03 | 0.89 |
time (sec) |
N/A | 0.299 | 0.006 | 0.589 | 0.033 | 0.071 | 0.235 | 0.117 | 0.205 | 0.185 |
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 | 51 | 50 | 48 | 43 | 42 | 107 | 87 | 45 | 88 | 37 |
N.S. |
1 | 0.98 | 0.94 | 0.84 | 0.82 | 2.10 | 1.71 | 0.88 | 1.73 | 0.73 |
time (sec) |
N/A | 0.314 | 0.022 | 0.596 | 0.119 | 0.079 | 0.111 | 0.124 | 0.202 | 0.083 |
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 | 39 | 40 | 32 | 31 | 89 | 63 | 31 | 75 | 28 |
N.S. |
1 | 0.98 | 1.00 | 0.80 | 0.78 | 2.22 | 1.58 | 0.78 | 1.88 | 0.70 |
time (sec) |
N/A | 0.263 | 0.010 | 0.585 | 0.107 | 0.076 | 0.104 | 0.124 | 0.195 | 0.142 |
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 | 29 | 29 | 29 | 19 | 18 | 72 | 56 | 18 | 67 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.66 | 0.62 | 2.48 | 1.93 | 0.62 | 2.31 | 0.66 |
time (sec) |
N/A | 0.248 | 0.005 | 0.572 | 0.109 | 0.084 | 0.081 | 0.123 | 0.216 | 0.148 |
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 | 40 | 79 | 32 | 31 | 90 | 71 | 31 | 82 | 28 |
N.S. |
1 | 1.00 | 1.98 | 0.80 | 0.78 | 2.25 | 1.78 | 0.78 | 2.05 | 0.70 |
time (sec) |
N/A | 0.265 | 0.027 | 0.628 | 0.106 | 0.078 | 0.149 | 0.125 | 0.218 | 0.056 |
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 | 51 | 57 | 88 | 43 | 43 | 110 | 90 | 43 | 95 | 40 |
N.S. |
1 | 1.12 | 1.73 | 0.84 | 0.84 | 2.16 | 1.76 | 0.84 | 1.86 | 0.78 |
time (sec) |
N/A | 0.285 | 0.028 | 0.630 | 0.109 | 0.079 | 0.168 | 0.125 | 0.208 | 0.158 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 217 | 176 | 37 | 183 | 150 | 34 | 175 | 147 | 51 |
N.S. |
1 | 1.51 | 1.22 | 0.26 | 1.27 | 1.04 | 0.24 | 1.22 | 1.02 | 0.35 |
time (sec) |
N/A | 0.686 | 0.025 | 0.687 | 0.107 | 0.079 | 0.099 | 0.127 | 0.211 | 0.209 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 212 | 173 | 34 | 179 | 107 | 22 | 172 | 144 | 48 |
N.S. |
1 | 1.53 | 1.24 | 0.24 | 1.29 | 0.77 | 0.16 | 1.24 | 1.04 | 0.35 |
time (sec) |
N/A | 0.637 | 0.020 | 0.622 | 0.110 | 0.087 | 0.086 | 0.129 | 0.213 | 0.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 200 | 134 | 27 | 169 | 124 | 26 | 179 | 112 | 35 |
N.S. |
1 | 1.49 | 1.00 | 0.20 | 1.26 | 0.93 | 0.19 | 1.34 | 0.84 | 0.26 |
time (sec) |
N/A | 0.637 | 0.016 | 0.615 | 0.109 | 0.076 | 0.084 | 0.128 | 0.222 | 0.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 134 | 200 | 134 | 27 | 169 | 112 | 20 | 179 | 112 | 33 |
N.S. |
1 | 1.49 | 1.00 | 0.20 | 1.26 | 0.84 | 0.15 | 1.34 | 0.84 | 0.25 |
time (sec) |
N/A | 0.603 | 0.013 | 0.569 | 0.113 | 0.079 | 0.085 | 0.121 | 0.211 | 0.088 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 142 | 215 | 179 | 50 | 183 | 128 | 29 | 187 | 150 | 51 |
N.S. |
1 | 1.51 | 1.26 | 0.35 | 1.29 | 0.90 | 0.20 | 1.32 | 1.06 | 0.36 |
time (sec) |
N/A | 0.661 | 0.023 | 0.650 | 0.109 | 0.080 | 0.104 | 0.131 | 0.221 | 0.117 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 217 | 188 | 56 | 184 | 153 | 32 | 175 | 159 | 51 |
N.S. |
1 | 1.51 | 1.31 | 0.39 | 1.28 | 1.06 | 0.22 | 1.22 | 1.10 | 0.35 |
time (sec) |
N/A | 0.642 | 0.027 | 0.648 | 0.113 | 0.085 | 0.117 | 0.123 | 0.217 | 0.109 |
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 | 43 | 38 | 41 | 43 | 56 | 41 | 49 | 135 | 45 |
N.S. |
1 | 0.93 | 0.83 | 0.89 | 0.93 | 1.22 | 0.89 | 1.07 | 2.93 | 0.98 |
time (sec) |
N/A | 0.311 | 0.020 | 0.631 | 0.029 | 0.067 | 0.187 | 0.116 | 0.203 | 0.157 |
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 | 33 | 31 | 27 | 30 | 32 | 35 | 29 | 48 | 117 | 29 |
N.S. |
1 | 0.94 | 0.82 | 0.91 | 0.97 | 1.06 | 0.88 | 1.45 | 3.55 | 0.88 |
time (sec) |
N/A | 0.289 | 0.011 | 0.487 | 0.032 | 0.066 | 0.156 | 0.114 | 0.197 | 0.151 |
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 | 16 | 15 | 14 | 15 | 15 | 14 | 17 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.94 | 0.94 | 0.88 | 1.06 | 0.88 |
time (sec) |
N/A | 0.228 | 0.004 | 0.470 | 0.038 | 0.064 | 0.129 | 0.123 | 0.201 | 0.026 |
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 | 38 | 39 | 33 | 35 | 37 | 47 | 34 | 47 | 134 | 34 |
N.S. |
1 | 1.03 | 0.87 | 0.92 | 0.97 | 1.24 | 0.89 | 1.24 | 3.53 | 0.89 |
time (sec) |
N/A | 0.308 | 0.010 | 0.452 | 0.034 | 0.085 | 0.259 | 0.120 | 0.241 | 0.165 |
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 | 52 | 41 | 54 | 53 | 73 | 53 | 52 | 162 | 53 |
N.S. |
1 | 1.00 | 0.79 | 1.04 | 1.02 | 1.40 | 1.02 | 1.00 | 3.12 | 1.02 |
time (sec) |
N/A | 0.315 | 0.030 | 0.453 | 0.035 | 0.074 | 0.299 | 0.120 | 0.206 | 0.098 |
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 | 71 | 77 | 64 | 60 | 65 | 172 | 112 | 67 | 189 | 62 |
N.S. |
1 | 1.08 | 0.90 | 0.85 | 0.92 | 2.42 | 1.58 | 0.94 | 2.66 | 0.87 |
time (sec) |
N/A | 0.327 | 0.034 | 0.464 | 0.104 | 0.077 | 0.201 | 0.132 | 0.185 | 0.109 |
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 | 60 | 66 | 60 | 49 | 52 | 144 | 92 | 49 | 172 | 50 |
N.S. |
1 | 1.10 | 1.00 | 0.82 | 0.87 | 2.40 | 1.53 | 0.82 | 2.87 | 0.83 |
time (sec) |
N/A | 0.289 | 0.033 | 0.460 | 0.106 | 0.076 | 0.218 | 0.125 | 0.184 | 0.211 |
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 | 49 | 53 | 49 | 40 | 40 | 127 | 83 | 39 | 167 | 37 |
N.S. |
1 | 1.08 | 1.00 | 0.82 | 0.82 | 2.59 | 1.69 | 0.80 | 3.41 | 0.76 |
time (sec) |
N/A | 0.269 | 0.021 | 0.490 | 0.103 | 0.076 | 0.167 | 0.120 | 0.218 | 0.176 |
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 | 49 | 53 | 49 | 40 | 39 | 129 | 83 | 39 | 166 | 37 |
N.S. |
1 | 1.08 | 1.00 | 0.82 | 0.80 | 2.63 | 1.69 | 0.80 | 3.39 | 0.76 |
time (sec) |
N/A | 0.266 | 0.021 | 0.484 | 0.110 | 0.073 | 0.178 | 0.117 | 0.212 | 0.144 |
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 | 60 | 67 | 94 | 49 | 53 | 148 | 97 | 51 | 178 | 50 |
N.S. |
1 | 1.12 | 1.57 | 0.82 | 0.88 | 2.47 | 1.62 | 0.85 | 2.97 | 0.83 |
time (sec) |
N/A | 0.293 | 0.044 | 0.469 | 0.106 | 0.077 | 0.221 | 0.124 | 0.186 | 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 | 70 | 84 | 104 | 59 | 66 | 176 | 117 | 63 | 195 | 60 |
N.S. |
1 | 1.20 | 1.49 | 0.84 | 0.94 | 2.51 | 1.67 | 0.90 | 2.79 | 0.86 |
time (sec) |
N/A | 0.311 | 0.054 | 0.480 | 0.130 | 0.078 | 0.302 | 0.127 | 0.237 | 0.201 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 164 | 244 | 196 | 55 | 204 | 226 | 60 | 193 | 312 | 76 |
N.S. |
1 | 1.49 | 1.20 | 0.34 | 1.24 | 1.38 | 0.37 | 1.18 | 1.90 | 0.46 |
time (sec) |
N/A | 0.688 | 0.086 | 0.472 | 0.108 | 0.085 | 0.184 | 0.129 | 0.236 | 0.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 157 | 239 | 192 | 50 | 198 | 196 | 48 | 188 | 310 | 71 |
N.S. |
1 | 1.52 | 1.22 | 0.32 | 1.26 | 1.25 | 0.31 | 1.20 | 1.97 | 0.45 |
time (sec) |
N/A | 0.676 | 0.079 | 0.471 | 0.112 | 0.080 | 0.171 | 0.129 | 0.192 | 0.253 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 227 | 185 | 45 | 192 | 192 | 44 | 196 | 307 | 60 |
N.S. |
1 | 1.48 | 1.21 | 0.29 | 1.25 | 1.25 | 0.29 | 1.28 | 2.01 | 0.39 |
time (sec) |
N/A | 0.638 | 0.077 | 0.470 | 0.110 | 0.077 | 0.196 | 0.121 | 0.193 | 0.237 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 225 | 182 | 43 | 190 | 181 | 39 | 194 | 303 | 58 |
N.S. |
1 | 1.49 | 1.21 | 0.28 | 1.26 | 1.20 | 0.26 | 1.28 | 2.01 | 0.38 |
time (sec) |
N/A | 0.643 | 0.076 | 0.488 | 0.107 | 0.086 | 0.150 | 0.125 | 0.198 | 0.130 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 227 | 184 | 48 | 191 | 196 | 46 | 196 | 305 | 60 |
N.S. |
1 | 1.48 | 1.20 | 0.31 | 1.25 | 1.28 | 0.30 | 1.28 | 1.99 | 0.39 |
time (sec) |
N/A | 0.666 | 0.067 | 0.490 | 0.127 | 0.081 | 0.137 | 0.124 | 0.217 | 0.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 151 | 225 | 183 | 46 | 189 | 183 | 39 | 194 | 305 | 58 |
N.S. |
1 | 1.49 | 1.21 | 0.30 | 1.25 | 1.21 | 0.26 | 1.28 | 2.02 | 0.38 |
time (sec) |
N/A | 0.649 | 0.068 | 0.437 | 0.111 | 0.079 | 0.154 | 0.121 | 0.222 | 0.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 242 | 196 | 70 | 203 | 204 | 56 | 205 | 316 | 69 |
N.S. |
1 | 1.49 | 1.21 | 0.43 | 1.25 | 1.26 | 0.35 | 1.27 | 1.95 | 0.43 |
time (sec) |
N/A | 0.713 | 0.090 | 0.481 | 0.110 | 0.090 | 0.189 | 0.122 | 0.199 | 0.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 162 | 244 | 194 | 76 | 206 | 230 | 58 | 191 | 324 | 73 |
N.S. |
1 | 1.51 | 1.20 | 0.47 | 1.27 | 1.42 | 0.36 | 1.18 | 2.00 | 0.45 |
time (sec) |
N/A | 0.726 | 0.098 | 0.469 | 0.122 | 0.089 | 0.227 | 0.124 | 0.213 | 0.122 |
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 | 65 | 62 | 48 | 54 | 66 | 91 | 68 | 62 | 217 | 68 |
N.S. |
1 | 0.95 | 0.74 | 0.83 | 1.02 | 1.40 | 1.05 | 0.95 | 3.34 | 1.05 |
time (sec) |
N/A | 0.341 | 0.043 | 0.461 | 0.031 | 0.076 | 0.333 | 0.124 | 0.204 | 0.249 |
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 | 51 | 39 | 43 | 55 | 69 | 53 | 42 | 200 | 53 |
N.S. |
1 | 0.98 | 0.75 | 0.83 | 1.06 | 1.33 | 1.02 | 0.81 | 3.85 | 1.02 |
time (sec) |
N/A | 0.315 | 0.014 | 0.443 | 0.031 | 0.066 | 0.261 | 0.124 | 0.209 | 0.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 24 | 23 | 36 | 36 | 36 | 22 | 28 | 37 |
N.S. |
1 | 1.00 | 1.26 | 1.21 | 1.89 | 1.89 | 1.89 | 1.16 | 1.47 | 1.95 |
time (sec) |
N/A | 0.233 | 0.010 | 0.441 | 0.036 | 0.067 | 0.237 | 0.128 | 0.208 | 0.161 |
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 | 16 | 15 | 14 | 26 | 27 | 14 | 25 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 1.62 | 1.69 | 0.88 | 1.56 | 1.56 |
time (sec) |
N/A | 0.235 | 0.005 | 0.438 | 0.030 | 0.076 | 0.180 | 0.122 | 0.250 | 0.142 |
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 | 54 | 55 | 43 | 46 | 60 | 90 | 56 | 59 | 228 | 56 |
N.S. |
1 | 1.02 | 0.80 | 0.85 | 1.11 | 1.67 | 1.04 | 1.09 | 4.22 | 1.04 |
time (sec) |
N/A | 0.321 | 0.025 | 0.458 | 0.030 | 0.076 | 0.303 | 0.124 | 0.205 | 0.199 |
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 | 69 | 69 | 59 | 65 | 77 | 119 | 80 | 82 | 258 | 75 |
N.S. |
1 | 1.00 | 0.86 | 0.94 | 1.12 | 1.72 | 1.16 | 1.19 | 3.74 | 1.09 |
time (sec) |
N/A | 0.351 | 0.039 | 0.458 | 0.032 | 0.080 | 0.442 | 0.128 | 0.213 | 0.115 |
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 | 68 | 80 | 58 | 52 | 63 | 196 | 116 | 49 | 273 | 60 |
N.S. |
1 | 1.18 | 0.85 | 0.76 | 0.93 | 2.88 | 1.71 | 0.72 | 4.01 | 0.88 |
time (sec) |
N/A | 0.318 | 0.037 | 0.476 | 0.111 | 0.078 | 0.263 | 0.126 | 0.194 | 0.116 |
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 | 71 | 80 | 62 | 54 | 66 | 199 | 116 | 54 | 272 | 58 |
N.S. |
1 | 1.13 | 0.87 | 0.76 | 0.93 | 2.80 | 1.63 | 0.76 | 3.83 | 0.82 |
time (sec) |
N/A | 0.302 | 0.024 | 0.483 | 0.111 | 0.076 | 0.250 | 0.126 | 0.229 | 0.215 |
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 | 68 | 80 | 58 | 63 | 62 | 196 | 110 | 49 | 273 | 59 |
N.S. |
1 | 1.18 | 0.85 | 0.93 | 0.91 | 2.88 | 1.62 | 0.72 | 4.01 | 0.87 |
time (sec) |
N/A | 0.290 | 0.034 | 0.497 | 0.107 | 0.077 | 0.239 | 0.117 | 0.223 | 0.188 |
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 | 80 | 94 | 105 | 58 | 75 | 214 | 121 | 61 | 284 | 72 |
N.S. |
1 | 1.18 | 1.31 | 0.72 | 0.94 | 2.68 | 1.51 | 0.76 | 3.55 | 0.90 |
time (sec) |
N/A | 0.329 | 0.062 | 0.501 | 0.118 | 0.082 | 0.330 | 0.128 | 0.218 | 0.248 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 254 | 205 | 56 | 215 | 264 | 70 | 206 | 476 | 83 |
N.S. |
1 | 1.48 | 1.19 | 0.33 | 1.25 | 1.53 | 0.41 | 1.20 | 2.77 | 0.48 |
time (sec) |
N/A | 0.740 | 0.070 | 0.487 | 0.109 | 0.082 | 0.267 | 0.129 | 0.210 | 0.245 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 170 | 252 | 201 | 54 | 213 | 262 | 68 | 204 | 474 | 81 |
N.S. |
1 | 1.48 | 1.18 | 0.32 | 1.25 | 1.54 | 0.40 | 1.20 | 2.79 | 0.48 |
time (sec) |
N/A | 0.726 | 0.064 | 0.500 | 0.133 | 0.085 | 0.275 | 0.131 | 0.201 | 0.139 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 175 | 254 | 207 | 58 | 219 | 277 | 71 | 209 | 476 | 81 |
N.S. |
1 | 1.45 | 1.18 | 0.33 | 1.25 | 1.58 | 0.41 | 1.19 | 2.72 | 0.46 |
time (sec) |
N/A | 0.733 | 0.079 | 0.507 | 0.109 | 0.087 | 0.253 | 0.133 | 0.194 | 0.258 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 171 | 250 | 203 | 56 | 216 | 267 | 66 | 206 | 474 | 80 |
N.S. |
1 | 1.46 | 1.19 | 0.33 | 1.26 | 1.56 | 0.39 | 1.20 | 2.77 | 0.47 |
time (sec) |
N/A | 0.719 | 0.079 | 0.484 | 0.108 | 0.079 | 0.233 | 0.123 | 0.190 | 0.268 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | C | A | C | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 172 | 254 | 204 | 59 | 214 | 269 | 71 | 206 | 476 | 82 |
N.S. |
1 | 1.48 | 1.19 | 0.34 | 1.24 | 1.56 | 0.41 | 1.20 | 2.77 | 0.48 |
time (sec) |
N/A | 0.722 | 0.069 | 0.513 | 0.111 | 0.089 | 0.224 | 0.129 | 0.210 | 0.119 |