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 | Mupad | |
grade |
N/A | A | A | A | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 26 | 31 | 25 | 20 | 33 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.86 | 2.21 | 1.79 | 1.43 | 2.36 | 1.00 |
time (sec) |
N/A | 0.006 | 0.005 | 0.189 | 0.199 | 0.254 | 0.058 | 0.280 | 0.055 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 15 | 14 | 14 | 26 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 1.00 | 1.86 | 1.00 | 1.00 |
time (sec) |
N/A | 0.003 | 0.004 | 0.220 | 0.283 | 0.243 | 0.054 | 0.276 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 18 | 17 | 26 | 27 | 40 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.38 | 1.31 | 2.00 | 2.08 | 3.08 | 0.85 |
time (sec) |
N/A | 0.005 | 0.003 | 0.125 | 0.182 | 0.297 | 0.067 | 0.279 | 0.252 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 23 | 8 | 19 | 23 | 22 | 21 | 7 |
N.S. |
1 | 1.00 | 2.09 | 0.73 | 1.73 | 2.09 | 2.00 | 1.91 | 0.64 |
time (sec) |
N/A | 0.003 | 0.033 | 0.135 | 0.192 | 0.259 | 0.059 | 0.271 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 21 | 27 | 29 | 22 | 29 | 24 |
N.S. |
1 | 1.00 | 1.00 | 1.40 | 1.80 | 1.93 | 1.47 | 1.93 | 1.60 |
time (sec) |
N/A | 0.004 | 0.009 | 0.293 | 0.214 | 0.255 | 0.092 | 0.280 | 0.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 2 | 2 | 2 | 3 | 4 | 4 | 3 | 4 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.50 | 2.00 | 2.00 | 1.50 | 2.00 | 6.00 |
time (sec) |
N/A | 0.005 | 0.002 | 0.069 | 0.194 | 0.254 | 0.020 | 0.313 | 0.331 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 4 | 4 | 4 | 5 | 6 | 6 | 5 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 1.25 | 1.50 | 1.50 | 1.25 | 1.50 | 1.50 |
time (sec) |
N/A | 0.007 | 0.002 | 0.052 | 0.196 | 0.261 | 0.037 | 0.284 | 0.253 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 6 | 5 | 27 | 4 | 7 | 4 | 4 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 4.50 | 0.67 | 1.17 | 0.67 | 0.67 |
time (sec) |
N/A | 0.018 | 0.026 | 0.102 | 0.231 | 0.248 | 0.319 | 0.293 | 0.205 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 6 | 5 | 9 | 9 | 3 | 30 | 4 |
N.S. |
1 | 1.00 | 0.67 | 0.56 | 1.00 | 1.00 | 0.33 | 3.33 | 0.44 |
time (sec) |
N/A | 0.007 | 0.003 | 0.059 | 0.192 | 0.247 | 0.086 | 0.287 | 0.211 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 8 | 9 | 10 | 10 | 7 | 8 | 6 |
N.S. |
1 | 1.00 | 0.67 | 0.75 | 0.83 | 0.83 | 0.58 | 0.67 | 0.50 |
time (sec) |
N/A | 0.009 | 0.002 | 0.069 | 0.204 | 0.240 | 0.163 | 0.285 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 13 | 13 | 12 | 15 | 14 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.08 | 1.00 | 1.25 | 1.17 | 1.08 |
time (sec) |
N/A | 0.018 | 0.048 | 0.237 | 0.226 | 0.252 | 0.092 | 0.306 | 0.220 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 16 | 15 | 15 | 31 | 15 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 1.00 | 2.07 | 1.00 | 1.00 |
time (sec) |
N/A | 0.026 | 0.013 | 0.692 | 0.288 | 0.282 | 0.222 | 0.288 | 0.049 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 33 | 33 | 26 | 44 | 35 | 15 |
N.S. |
1 | 1.00 | 1.00 | 2.20 | 2.20 | 1.73 | 2.93 | 2.33 | 1.00 |
time (sec) |
N/A | 0.023 | 0.013 | 0.500 | 0.212 | 0.252 | 0.252 | 0.275 | 0.204 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 18 | 17 | 21 | 32 | 17 | 48 |
N.S. |
1 | 1.00 | 1.00 | 1.06 | 1.00 | 1.24 | 1.88 | 1.00 | 2.82 |
time (sec) |
N/A | 0.030 | 0.012 | 6.745 | 0.224 | 0.265 | 0.872 | 0.298 | 0.597 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 20 | 20 | 23 | 34 | 21 | 48 |
N.S. |
1 | 1.00 | 1.00 | 1.05 | 1.05 | 1.21 | 1.79 | 1.11 | 2.53 |
time (sec) |
N/A | 0.039 | 0.013 | 6.177 | 0.226 | 0.275 | 0.914 | 0.280 | 0.592 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 22 | 22 | 19 | 18 | 18 | 34 | 18 | 58 |
N.S. |
1 | 1.22 | 1.22 | 1.06 | 1.00 | 1.00 | 1.89 | 1.00 | 3.22 |
time (sec) |
N/A | 0.039 | 0.018 | 10.257 | 0.214 | 0.265 | 0.872 | 0.279 | 0.462 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 22 | 22 | 19 | 19 | 19 | 32 | 20 | 58 |
N.S. |
1 | 1.22 | 1.22 | 1.06 | 1.06 | 1.06 | 1.78 | 1.11 | 3.22 |
time (sec) |
N/A | 0.035 | 0.016 | 9.131 | 0.207 | 0.270 | 0.937 | 0.287 | 0.470 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 19 | 14 | 13 | 31 | 61 | 46 | 26 |
N.S. |
1 | 1.00 | 0.46 | 0.34 | 0.32 | 0.76 | 1.49 | 1.12 | 0.63 |
time (sec) |
N/A | 0.017 | 0.109 | 0.151 | 0.306 | 0.271 | 0.223 | 0.299 | 0.257 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 6 | 6 | 6 | 6 | 15 | 15 | 15 | 16 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 2.50 | 2.50 | 2.50 | 2.67 | 2.50 |
time (sec) |
N/A | 0.015 | 0.001 | 0.033 | 0.221 | 0.251 | 0.048 | 0.284 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 3 | 3 | 3 | 4 | 3 | 3 | 3 | 4 | 3 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.00 | 1.00 | 1.00 | 1.33 | 1.00 |
time (sec) |
N/A | 0.010 | 0.001 | 0.025 | 0.197 | 0.243 | 0.035 | 0.271 | 0.206 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 3 | 3 | 3 | 4 | 3 | 3 | 15 | 3 | 3 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 1.00 | 1.00 | 5.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.015 | 0.005 | 0.103 | 0.285 | 0.268 | 0.068 | 0.293 | 0.411 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 7 | 8 | 7 | 7 | 7 | 22 | 7 |
N.S. |
1 | 1.00 | 0.78 | 0.89 | 0.78 | 0.78 | 0.78 | 2.44 | 0.78 |
time (sec) |
N/A | 0.015 | 0.034 | 0.040 | 0.210 | 0.235 | 0.039 | 0.325 | 0.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 9 | 10 | 9 | 9 | 7 | 9 | 9 |
N.S. |
1 | 1.00 | 1.00 | 1.11 | 1.00 | 1.00 | 0.78 | 1.00 | 1.00 |
time (sec) |
N/A | 0.017 | 0.035 | 0.033 | 0.201 | 0.241 | 0.041 | 0.285 | 0.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 22 | 22 | 24 | 22 | 23 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.88 | 0.96 | 0.88 | 0.92 | 0.96 |
time (sec) |
N/A | 0.019 | 0.026 | 0.066 | 0.209 | 0.248 | 0.151 | 0.294 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 21 | 20 | 22 | 31 | 21 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.70 | 0.67 | 0.73 | 1.03 | 0.70 | 0.73 |
time (sec) |
N/A | 0.085 | 0.034 | 0.027 | 0.196 | 0.237 | 0.933 | 0.274 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 9 | 10 | 10 | 8 | 11 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 1.00 | 1.00 | 0.80 | 1.10 | 0.80 |
time (sec) |
N/A | 0.005 | 0.003 | 0.155 | 0.200 | 0.244 | 0.024 | 0.287 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 47 | 24 | 36 | 40 | 42 | 37 | 47 |
N.S. |
1 | 1.00 | 1.00 | 0.51 | 0.77 | 0.85 | 0.89 | 0.79 | 1.00 |
time (sec) |
N/A | 0.021 | 0.034 | 0.194 | 0.284 | 0.248 | 0.045 | 0.274 | 0.138 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 30 | 24 | 23 | 23 | 27 | 21 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.77 | 0.77 | 0.90 | 0.70 | 0.70 |
time (sec) |
N/A | 0.007 | 0.016 | 0.190 | 0.289 | 0.255 | 0.044 | 0.278 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 14 | 13 | 24 | 22 | 17 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.62 | 1.14 | 1.05 | 0.81 | 0.62 |
time (sec) |
N/A | 0.007 | 0.052 | 0.249 | 0.199 | 0.246 | 0.128 | 0.301 | 0.190 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 12 | 11 | 24 | 26 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.73 | 1.60 | 1.73 | 0.73 | 0.73 |
time (sec) |
N/A | 0.008 | 0.002 | 0.237 | 0.210 | 0.254 | 0.127 | 0.282 | 0.059 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 20 | 186 | 89 | 138 | 18 | 118 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 8.86 | 4.24 | 6.57 | 0.86 | 5.62 |
time (sec) |
N/A | 0.038 | 0.088 | 0.240 | 0.299 | 0.273 | 0.560 | 0.286 | 1.426 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 11 | 10 | 10 | 10 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.71 | 0.71 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.005 | 0.002 | 0.059 | 0.197 | 0.245 | 0.022 | 0.269 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 11 | 10 | 10 | 10 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.71 | 0.71 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.006 | 0.002 | 0.063 | 0.198 | 0.241 | 0.016 | 0.271 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 6 | 6 | 7 | 6 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.88 | 0.75 | 1.50 |
time (sec) |
N/A | 0.010 | 0.002 | 0.125 | 0.203 | 0.249 | 0.017 | 0.303 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 15 | 14 | 22 | 15 | 14 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.36 | 1.27 | 2.00 | 1.36 | 1.27 | 1.00 |
time (sec) |
N/A | 0.012 | 0.010 | 0.308 | 0.216 | 0.238 | 0.033 | 0.290 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 7 | 7 | 6 | 11 | 9 | 18 | 12 | 9 | 6 |
N.S. |
1 | 1.00 | 0.86 | 1.57 | 1.29 | 2.57 | 1.71 | 1.29 | 0.86 |
time (sec) |
N/A | 0.018 | 0.003 | 0.287 | 0.201 | 0.247 | 0.024 | 0.293 | 0.254 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 28 | 17 | 12 | 23 | 19 | 18 | 10 |
N.S. |
1 | 1.00 | 2.00 | 1.21 | 0.86 | 1.64 | 1.36 | 1.29 | 0.71 |
time (sec) |
N/A | 0.007 | 0.017 | 0.052 | 0.273 | 0.240 | 0.025 | 0.435 | 0.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 26 | 19 | 12 | 20 | 17 | 22 | 18 |
N.S. |
1 | 1.00 | 1.62 | 1.19 | 0.75 | 1.25 | 1.06 | 1.38 | 1.12 |
time (sec) |
N/A | 0.013 | 0.017 | 0.059 | 0.287 | 0.247 | 0.058 | 0.304 | 0.331 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 29 | 11 | 12 | 19 | 10 | 12 | 12 |
N.S. |
1 | 1.00 | 2.90 | 1.10 | 1.20 | 1.90 | 1.00 | 1.20 | 1.20 |
time (sec) |
N/A | 0.027 | 0.014 | 0.183 | 0.274 | 0.240 | 0.143 | 0.291 | 0.285 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 15 | 14 | 25 | 10 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 1.07 | 1.00 | 1.79 | 0.71 | 1.00 | 1.00 |
time (sec) |
N/A | 0.062 | 0.009 | 0.438 | 0.279 | 0.248 | 0.325 | 0.296 | 0.297 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | C | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 25 | 15 | 28 | 24 | 29 | 12 | 12 |
N.S. |
1 | 1.00 | 2.27 | 1.36 | 2.55 | 2.18 | 2.64 | 1.09 | 1.09 |
time (sec) |
N/A | 0.021 | 0.046 | 0.101 | 0.290 | 0.251 | 0.230 | 0.292 | 0.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 31 | 17 | 23 | 14 | 8 | 12 | 10 |
N.S. |
1 | 1.00 | 1.94 | 1.06 | 1.44 | 0.88 | 0.50 | 0.75 | 0.62 |
time (sec) |
N/A | 0.025 | 0.094 | 0.093 | 0.272 | 0.268 | 0.211 | 0.292 | 0.180 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 33 | 19 | 18 | 22 | 19 | 18 | 18 |
N.S. |
1 | 1.00 | 1.32 | 0.76 | 0.72 | 0.88 | 0.76 | 0.72 | 0.72 |
time (sec) |
N/A | 0.025 | 0.033 | 0.052 | 0.197 | 0.242 | 0.046 | 0.286 | 0.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 14 | 13 | 13 | 12 | 15 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.62 | 0.62 | 0.57 | 0.71 | 0.38 |
time (sec) |
N/A | 0.004 | 0.004 | 0.224 | 0.208 | 0.249 | 0.042 | 0.292 | 0.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 14 | 11 | 10 | 10 | 10 | 10 | 10 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.71 | 0.71 | 0.71 | 0.71 | 0.71 |
time (sec) |
N/A | 0.017 | 0.008 | 0.078 | 0.271 | 0.228 | 0.043 | 0.277 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 47 | 29 | 35 | 45 | 42 | 44 | 34 |
N.S. |
1 | 1.00 | 0.92 | 0.57 | 0.69 | 0.88 | 0.82 | 0.86 | 0.67 |
time (sec) |
N/A | 0.016 | 0.027 | 0.283 | 0.271 | 0.260 | 0.050 | 0.277 | 0.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 26 | 25 | 25 | 29 | 25 | 25 |
N.S. |
1 | 1.00 | 1.00 | 0.79 | 0.76 | 0.76 | 0.88 | 0.76 | 0.76 |
time (sec) |
N/A | 0.009 | 0.022 | 0.136 | 0.200 | 0.232 | 0.056 | 0.290 | 0.246 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 29 | 29 | 19 | 18 | 68 | 73 | 18 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.66 | 0.62 | 2.34 | 2.52 | 0.62 | 0.66 |
time (sec) |
N/A | 0.012 | 0.025 | 0.181 | 0.289 | 0.244 | 0.377 | 0.284 | 0.217 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 20 | 17 | 22 | 19 | 37 | 19 | 20 |
N.S. |
1 | 1.00 | 0.74 | 0.63 | 0.81 | 0.70 | 1.37 | 0.70 | 0.74 |
time (sec) |
N/A | 0.011 | 0.019 | 0.178 | 0.284 | 0.236 | 0.135 | 0.300 | 0.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 28 | 19 | 18 | 25 | 29 | 10 | 18 |
N.S. |
1 | 1.00 | 1.27 | 0.86 | 0.82 | 1.14 | 1.32 | 0.45 | 0.82 |
time (sec) |
N/A | 0.007 | 0.127 | 0.256 | 0.281 | 0.243 | 0.498 | 0.309 | 0.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 21 | 12 | 26 | 22 | 20 | 24 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.55 | 1.18 | 1.00 | 0.91 | 1.09 |
time (sec) |
N/A | 0.010 | 0.026 | 0.438 | 0.286 | 0.261 | 0.498 | 0.287 | 0.311 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | A | C | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 53 | 37 | 34 | 25 | 22 | 43 | 21 |
N.S. |
1 | 1.00 | 2.30 | 1.61 | 1.48 | 1.09 | 0.96 | 1.87 | 0.91 |
time (sec) |
N/A | 0.012 | 0.051 | 0.208 | 0.210 | 0.243 | 0.522 | 0.305 | 0.554 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 49 | 35 | 12 | 40 | 7 | 37 | 26 |
N.S. |
1 | 1.00 | 2.33 | 1.67 | 0.57 | 1.90 | 0.33 | 1.76 | 1.24 |
time (sec) |
N/A | 0.010 | 0.041 | 0.221 | 0.201 | 0.245 | 0.508 | 0.310 | 0.107 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 21 | 7 | 8 | 30 | 8 | 26 | 6 |
N.S. |
1 | 1.00 | 1.75 | 0.58 | 0.67 | 2.50 | 0.67 | 2.17 | 0.50 |
time (sec) |
N/A | 0.005 | 0.082 | 0.250 | 0.275 | 0.246 | 0.229 | 0.292 | 0.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 33 | 15 | 16 | 38 | 20 | 53 | 26 |
N.S. |
1 | 1.00 | 1.74 | 0.79 | 0.84 | 2.00 | 1.05 | 2.79 | 1.37 |
time (sec) |
N/A | 0.009 | 0.086 | 0.796 | 0.286 | 0.264 | 0.260 | 0.298 | 0.382 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 40 | 7 | 6 | 16 | 5 | 25 | 6 |
N.S. |
1 | 1.00 | 5.00 | 0.88 | 0.75 | 2.00 | 0.62 | 3.12 | 0.75 |
time (sec) |
N/A | 0.002 | 0.044 | 0.424 | 0.308 | 0.244 | 0.192 | 0.286 | 0.219 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 36 | 22 | 21 | 43 | 22 | 21 | 40 |
N.S. |
1 | 1.00 | 1.33 | 0.81 | 0.78 | 1.59 | 0.81 | 0.78 | 1.48 |
time (sec) |
N/A | 0.009 | 0.128 | 0.254 | 0.323 | 0.278 | 0.358 | 0.289 | 0.419 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 32 | 30 | 25 | 33 | 39 | 0 | 71 | 28 |
N.S. |
1 | 1.00 | 0.94 | 0.78 | 1.03 | 1.22 | 0.00 | 2.22 | 0.88 |
time (sec) |
N/A | 0.008 | 0.108 | 0.250 | 0.300 | 0.258 | 0.000 | 0.305 | 0.427 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 23 | 21 | 16 | 17 | 17 | 0 | 28 | 19 |
N.S. |
1 | 1.10 | 1.00 | 0.76 | 0.81 | 0.81 | 0.00 | 1.33 | 0.90 |
time (sec) |
N/A | 0.004 | 0.139 | 0.276 | 0.298 | 0.245 | 0.000 | 0.318 | 0.301 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 54 | 21 | 33 | 39 | 22 | 31 | 22 |
N.S. |
1 | 1.00 | 1.93 | 0.75 | 1.18 | 1.39 | 0.79 | 1.11 | 0.79 |
time (sec) |
N/A | 0.117 | 0.160 | 0.216 | 0.221 | 0.271 | 0.299 | 0.292 | 0.361 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 48 | 17 | 14 | 13 | 31 | 0 | 46 | 26 |
N.S. |
1 | 1.30 | 0.46 | 0.38 | 0.35 | 0.84 | 0.00 | 1.24 | 0.70 |
time (sec) |
N/A | 0.023 | 0.541 | 0.155 | 0.313 | 0.258 | 0.000 | 0.285 | 0.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 21 | 11 | 47 | 32 | 27 | 11 | 10 |
N.S. |
1 | 1.00 | 1.50 | 0.79 | 3.36 | 2.29 | 1.93 | 0.79 | 0.71 |
time (sec) |
N/A | 0.029 | 0.064 | 0.200 | 0.221 | 0.255 | 0.499 | 0.273 | 0.281 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 9 | 4 | 15 | 45 | 15 | 17 | 3 |
N.S. |
1 | 1.00 | 0.82 | 0.36 | 1.36 | 4.09 | 1.36 | 1.55 | 0.27 |
time (sec) |
N/A | 0.030 | 0.007 | 0.063 | 0.218 | 0.252 | 0.061 | 0.280 | 0.392 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 19 | 19 | 15 | 14 | 14 | 0 | 14 | 14 |
N.S. |
1 | 1.06 | 1.06 | 0.83 | 0.78 | 0.78 | 0.00 | 0.78 | 0.78 |
time (sec) |
N/A | 0.045 | 0.021 | 0.184 | 0.213 | 0.267 | 0.000 | 0.269 | 0.424 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 15 | 17 | 14 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 0.83 | 0.94 | 0.78 | 0.78 |
time (sec) |
N/A | 0.054 | 0.024 | 0.257 | 0.216 | 0.269 | 0.795 | 0.259 | 0.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | F | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 16 | 15 | 15 | 0 | 15 | 37 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.88 | 0.00 | 0.88 | 2.18 |
time (sec) |
N/A | 0.015 | 0.036 | 0.132 | 0.296 | 0.251 | 0.000 | 0.279 | 0.355 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | A | A | A | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 0 | 18 | 16 | 19 | 16 | 16 |
N.S. |
1 | 1.00 | 1.10 | 0.00 | 0.90 | 0.80 | 0.95 | 0.80 | 0.80 |
time (sec) |
N/A | 0.021 | 0.039 | 0.000 | 0.215 | 0.256 | 0.281 | 0.273 | 0.411 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 13 | 12 | 12 | 15 | 12 | 12 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 1.00 | 1.00 | 1.25 | 1.00 | 1.00 |
time (sec) |
N/A | 0.024 | 0.008 | 0.546 | 0.221 | 0.256 | 0.833 | 0.268 | 0.296 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | F | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 42 | 42 | 42 | 38 | 0 | 38 | 0 | 15 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.00 | 0.90 | 0.00 | 0.36 | 0.00 |
time (sec) |
N/A | 0.029 | 0.049 | 0.247 | 0.000 | 0.256 | 0.000 | 0.285 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 8 | 8 | 8 | 7 | 6 | 6 | 7 | 6 | 6 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.75 | 0.75 | 0.88 | 0.75 | 0.75 |
time (sec) |
N/A | 0.018 | 0.009 | 0.168 | 0.305 | 0.254 | 0.411 | 0.260 | 0.394 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 28 | 28 | 23 | 17 | 22 | 22 | 22 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.61 | 0.79 | 0.79 | 0.79 | 0.61 |
time (sec) |
N/A | 0.008 | 0.000 | 0.021 | 0.211 | 0.239 | 0.040 | 0.287 | 0.034 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 11 | 13 | 11 | 15 | 13 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.65 | 0.76 | 0.65 | 0.88 | 0.76 | 0.53 |
time (sec) |
N/A | 0.005 | 0.003 | 0.034 | 0.210 | 0.252 | 0.040 | 0.269 | 0.229 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 38 | 38 | 29 | 28 | 28 | 26 | 70 | 40 |
N.S. |
1 | 1.06 | 1.06 | 0.81 | 0.78 | 0.78 | 0.72 | 1.94 | 1.11 |
time (sec) |
N/A | 0.021 | 0.009 | 0.108 | 0.212 | 0.257 | 0.048 | 0.285 | 0.413 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 17 | 15 | 18 | 17 | 15 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 0.79 | 0.95 | 0.89 | 0.79 | 1.11 |
time (sec) |
N/A | 0.006 | 0.001 | 0.302 | 0.204 | 0.262 | 0.022 | 0.276 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 34 | 30 | 23 | 18 | 25 | 31 | 22 | 26 |
N.S. |
1 | 1.00 | 0.88 | 0.68 | 0.53 | 0.74 | 0.91 | 0.65 | 0.76 |
time (sec) |
N/A | 0.026 | 0.001 | 0.318 | 0.207 | 0.255 | 0.017 | 0.270 | 0.024 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | B | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 71 | 26 | 42 | 69 | 46 | 38 | 33 |
N.S. |
1 | 1.00 | 2.73 | 1.00 | 1.62 | 2.65 | 1.77 | 1.46 | 1.27 |
time (sec) |
N/A | 0.012 | 0.014 | 0.329 | 0.210 | 0.250 | 0.069 | 0.269 | 0.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 14 | 12 | 11 | 17 | 17 | 11 | 11 |
N.S. |
1 | 1.00 | 0.61 | 0.52 | 0.48 | 0.74 | 0.74 | 0.48 | 0.48 |
time (sec) |
N/A | 0.009 | 0.015 | 0.125 | 0.207 | 0.248 | 0.163 | 0.277 | 0.022 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 22 | 20 | 19 | 21 | 26 | 19 | 19 |
N.S. |
1 | 1.00 | 0.81 | 0.74 | 0.70 | 0.78 | 0.96 | 0.70 | 0.70 |
time (sec) |
N/A | 0.008 | 0.053 | 0.132 | 0.206 | 0.257 | 0.093 | 0.270 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | C | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 20 | 21 | 24 | 20 | 107 | 329 | 20 |
N.S. |
1 | 1.00 | 0.65 | 0.68 | 0.77 | 0.65 | 3.45 | 10.61 | 0.65 |
time (sec) |
N/A | 0.010 | 0.022 | 0.161 | 0.215 | 0.243 | 0.269 | 0.304 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 11 | 10 | 13 | 15 | 13 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.65 | 0.59 | 0.76 | 0.88 | 0.76 | 0.76 |
time (sec) |
N/A | 0.004 | 0.003 | 0.073 | 0.207 | 0.259 | 0.127 | 0.271 | 0.240 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 13 | 94 | 22 | 15 | 12 | 35 |
N.S. |
1 | 1.00 | 1.00 | 1.08 | 7.83 | 1.83 | 1.25 | 1.00 | 2.92 |
time (sec) |
N/A | 0.018 | 0.019 | 0.565 | 0.286 | 0.246 | 17.259 | 0.282 | 0.506 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 20 | 107 | 21 | 19 | 23 | 13 |
N.S. |
1 | 1.00 | 1.00 | 1.33 | 7.13 | 1.40 | 1.27 | 1.53 | 0.87 |
time (sec) |
N/A | 0.014 | 0.006 | 0.031 | 0.296 | 0.248 | 0.073 | 0.270 | 0.026 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 21 | 33 | 39 | 22 | 38 | 20 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 1.50 | 1.77 | 1.00 | 1.73 | 0.91 |
time (sec) |
N/A | 0.014 | 0.001 | 0.013 | 0.290 | 0.268 | 0.980 | 0.267 | 0.023 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 24 | 23 | 23 | 22 | 23 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 0.92 | 0.92 | 0.88 | 0.92 | 0.88 |
time (sec) |
N/A | 0.032 | 0.003 | 0.040 | 0.284 | 0.246 | 0.074 | 0.284 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 20 | 24 | 19 | 19 | 19 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 1.04 | 0.83 | 0.83 | 0.83 | 0.83 |
time (sec) |
N/A | 0.049 | 0.019 | 0.234 | 0.292 | 0.249 | 0.108 | 0.282 | 0.294 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | F(-2) | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 57 | 49 | 45 | 78 | 30 | 58 | 0 | 0 |
N.S. |
1 | 1.50 | 1.29 | 1.18 | 2.05 | 0.79 | 1.53 | 0.00 | 0.00 |
time (sec) |
N/A | 0.034 | 0.056 | 0.053 | 0.300 | 0.257 | 4.078 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 21 | 21 | 21 | 22 | 21 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 0.84 | 0.84 | 0.88 | 0.84 | 0.84 |
time (sec) |
N/A | 0.005 | 0.003 | 0.161 | 0.209 | 0.235 | 0.018 | 0.286 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 39 | 39 | 39 | 29 | 29 | 29 | 34 | 29 | 29 |
N.S. |
1 | 1.00 | 1.00 | 0.74 | 0.74 | 0.74 | 0.87 | 0.74 | 0.74 |
time (sec) |
N/A | 0.011 | 0.001 | 0.238 | 0.201 | 0.232 | 0.021 | 0.274 | 0.036 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 29 | 23 | 27 | 78 | 23 | 23 |
N.S. |
1 | 1.00 | 1.00 | 1.26 | 1.00 | 1.17 | 3.39 | 1.00 | 1.00 |
time (sec) |
N/A | 0.008 | 0.037 | 0.865 | 0.212 | 0.248 | 12.029 | 0.279 | 0.817 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 30 | 27 | 21 | 22 | 22 | 20 | 23 | 20 |
N.S. |
1 | 1.00 | 0.90 | 0.70 | 0.73 | 0.73 | 0.67 | 0.77 | 0.67 |
time (sec) |
N/A | 0.010 | 0.010 | 0.168 | 0.214 | 0.258 | 0.026 | 0.282 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 35 | 27 | 26 | 32 | 34 | 26 | 32 |
N.S. |
1 | 1.00 | 0.85 | 0.66 | 0.63 | 0.78 | 0.83 | 0.63 | 0.78 |
time (sec) |
N/A | 0.010 | 0.013 | 0.182 | 0.298 | 0.238 | 0.036 | 0.278 | 0.044 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 21 | 21 | 14 | 15 | 15 | 14 | 17 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.67 | 0.71 | 0.71 | 0.67 | 0.81 | 0.38 |
time (sec) |
N/A | 0.005 | 0.004 | 0.226 | 0.220 | 0.244 | 0.042 | 0.268 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 32 | 29 | 28 | 28 | 36 | 28 | 30 |
N.S. |
1 | 1.00 | 0.97 | 0.88 | 0.85 | 0.85 | 1.09 | 0.85 | 0.91 |
time (sec) |
N/A | 0.013 | 0.008 | 0.710 | 0.291 | 0.255 | 0.047 | 0.273 | 0.046 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 22 | 21 | 21 | 22 | 21 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.84 | 0.84 | 0.88 | 0.84 | 0.84 |
time (sec) |
N/A | 0.014 | 0.005 | 0.301 | 0.284 | 0.239 | 0.045 | 0.283 | 0.048 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 47 | 47 | 47 | 39 | 38 | 38 | 46 | 38 | 40 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.81 | 0.81 | 0.98 | 0.81 | 0.85 |
time (sec) |
N/A | 0.051 | 0.019 | 0.411 | 0.293 | 0.263 | 0.046 | 0.275 | 0.284 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 25 | 25 | 18 | 17 | 17 | 17 | 20 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.72 | 0.68 | 0.68 | 0.68 | 0.80 | 0.68 |
time (sec) |
N/A | 0.029 | 0.007 | 0.039 | 0.202 | 0.239 | 0.054 | 0.279 | 0.261 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 29 | 26 | 25 | 25 | 26 | 28 | 25 |
N.S. |
1 | 1.00 | 0.88 | 0.79 | 0.76 | 0.76 | 0.79 | 0.85 | 0.76 |
time (sec) |
N/A | 0.039 | 0.019 | 0.053 | 0.213 | 0.242 | 0.117 | 0.276 | 0.109 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 61 | 37 | 26 | 25 | 25 | 29 | 29 | 29 |
N.S. |
1 | 1.65 | 1.00 | 0.70 | 0.68 | 0.68 | 0.78 | 0.78 | 0.78 |
time (sec) |
N/A | 0.032 | 0.008 | 0.047 | 0.203 | 0.256 | 0.077 | 0.290 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 69 | 26 | 43 | 51 | 60 | 59 | 25 |
N.S. |
1 | 1.00 | 2.23 | 0.84 | 1.39 | 1.65 | 1.94 | 1.90 | 0.81 |
time (sec) |
N/A | 0.011 | 0.020 | 0.060 | 0.287 | 0.251 | 0.289 | 0.291 | 0.098 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 41 | 26 | 25 | 25 | 26 | 29 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.63 | 0.61 | 0.61 | 0.63 | 0.71 | 0.37 |
time (sec) |
N/A | 0.019 | 0.008 | 0.259 | 0.206 | 0.242 | 0.075 | 0.273 | 0.272 |