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 | A | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 57 | 55 | 54 | 46 | 47 | 117 | 75 | 45 | 47 |
N.S. |
1 | 0.96 | 0.95 | 0.81 | 0.82 | 2.05 | 1.32 | 0.79 | 0.82 |
time (sec) |
N/A | 0.199 | 0.041 | 0.042 | 0.269 | 0.295 | 0.833 | 0.305 | 0.269 |
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 | 18 | 17 | 21 | 24 | 17 | 19 |
N.S. |
1 | 1.00 | 0.74 | 0.67 | 0.63 | 0.78 | 0.89 | 0.63 | 0.70 |
time (sec) |
N/A | 0.171 | 0.031 | 0.081 | 0.253 | 0.284 | 0.094 | 0.298 | 0.030 |
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 | 10 | 10 | 10 | 9 | 8 | 8 | 19 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.90 | 0.80 | 0.80 | 1.90 | 0.80 | 0.80 |
time (sec) |
N/A | 0.169 | 0.021 | 0.031 | 0.271 | 0.288 | 0.050 | 0.306 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 10 | 10 | 10 | 18 | 17 | 17 | 19 | 18 | 17 |
N.S. |
1 | 1.00 | 1.00 | 1.80 | 1.70 | 1.70 | 1.90 | 1.80 | 1.70 |
time (sec) |
N/A | 0.168 | 0.027 | 0.036 | 0.197 | 0.305 | 0.050 | 0.299 | 0.286 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 18 | 15 | 14 | 10 | 14 | 21 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.78 | 0.56 | 0.78 | 1.17 | 0.00 |
time (sec) |
N/A | 0.177 | 2.173 | 0.032 | 0.199 | 0.310 | 0.735 | 0.300 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 47 | 19 | 18 | 26 | 42 | 17 | 33 | 17 |
N.S. |
1 | 2.35 | 0.95 | 0.90 | 1.30 | 2.10 | 0.85 | 1.65 | 0.85 |
time (sec) |
N/A | 0.227 | 0.045 | 0.037 | 0.274 | 0.287 | 0.063 | 0.288 | 0.547 |
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 | 44 | 54 | 24 | 21 | 21 | 21 | 20 | 21 | 21 |
N.S. |
1 | 1.23 | 0.55 | 0.48 | 0.48 | 0.48 | 0.45 | 0.48 | 0.48 |
time (sec) |
N/A | 0.258 | 0.013 | 0.030 | 0.188 | 0.288 | 0.036 | 0.297 | 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 | 52 | 57 | 26 | 23 | 30 | 23 | 24 | 23 | 23 |
N.S. |
1 | 1.10 | 0.50 | 0.44 | 0.58 | 0.44 | 0.46 | 0.44 | 0.44 |
time (sec) |
N/A | 0.256 | 0.023 | 0.034 | 0.186 | 0.285 | 0.038 | 0.312 | 0.053 |
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 | 45 | 23 | 22 | 35 | 24 | 22 | 22 |
N.S. |
1 | 1.00 | 1.36 | 0.70 | 0.67 | 1.06 | 0.73 | 0.67 | 0.67 |
time (sec) |
N/A | 0.176 | 0.070 | 0.040 | 0.276 | 0.293 | 0.303 | 0.292 | 0.274 |
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 | 50 | 54 | 33 | 39 | 37 | 32 | 36 | 53 | 32 |
N.S. |
1 | 1.08 | 0.66 | 0.78 | 0.74 | 0.64 | 0.72 | 1.06 | 0.64 |
time (sec) |
N/A | 0.199 | 0.035 | 0.027 | 0.191 | 0.275 | 0.686 | 0.302 | 0.264 |
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 | 81 | 81 | 48 | 62 | 61 | 50 | 61 | 75 | 38 |
N.S. |
1 | 1.00 | 0.59 | 0.77 | 0.75 | 0.62 | 0.75 | 0.93 | 0.47 |
time (sec) |
N/A | 0.227 | 0.045 | 0.054 | 0.185 | 0.280 | 6.677 | 0.301 | 0.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 55 | 46 | 54 | 45 | 44 | 44 | 49 | 44 | 44 |
N.S. |
1 | 0.84 | 0.98 | 0.82 | 0.80 | 0.80 | 0.89 | 0.80 | 0.80 |
time (sec) |
N/A | 0.276 | 0.035 | 0.072 | 0.195 | 0.298 | 0.060 | 0.291 | 0.250 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 35 | 55 | 27 | 26 | 43 | 26 | 26 | 26 |
N.S. |
1 | 1.00 | 1.57 | 0.77 | 0.74 | 1.23 | 0.74 | 0.74 | 0.74 |
time (sec) |
N/A | 0.342 | 0.068 | 0.086 | 0.273 | 0.288 | 14.887 | 0.307 | 0.332 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 24 | 29 | 24 | 23 | 23 | 24 | 23 | 24 |
N.S. |
1 | 0.75 | 0.91 | 0.75 | 0.72 | 0.72 | 0.75 | 0.72 | 0.75 |
time (sec) |
N/A | 0.389 | 0.053 | 0.063 | 0.188 | 0.302 | 0.062 | 0.291 | 0.268 |
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 | 5 | 5 | 5 | 4 | 3 | 3 | 3 | 3 | 3 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 0.60 | 0.60 | 0.60 | 0.60 | 0.60 |
time (sec) |
N/A | 0.167 | 0.005 | 0.022 | 0.192 | 0.285 | 0.237 | 0.305 | 0.029 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 7 | 7 | 7 | 5 | 4 | 4 | 5 | 0 | 4 |
N.S. |
1 | 1.00 | 1.00 | 0.71 | 0.57 | 0.57 | 0.71 | 0.00 | 0.57 |
time (sec) |
N/A | 0.193 | 0.010 | 0.032 | 0.186 | 0.266 | 0.418 | 0.000 | 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 | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 25 | 23 | 17 | 16 | 19 | 17 | 24 | 8 |
N.S. |
1 | 1.14 | 1.05 | 0.77 | 0.73 | 0.86 | 0.77 | 1.09 | 0.36 |
time (sec) |
N/A | 0.185 | 0.019 | 0.026 | 0.183 | 0.292 | 0.046 | 0.284 | 0.266 |
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 | 4 | 4 | 4 | 4 | 7 | 3 | 15 | 3 | 3 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 1.75 | 0.75 | 3.75 | 0.75 | 0.75 |
time (sec) |
N/A | 0.153 | 0.002 | 0.028 | 0.286 | 0.274 | 0.051 | 0.278 | 0.020 |
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 | 13 | 13 | 13 | 11 | 10 | 10 | 10 | 10 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.77 | 0.77 | 0.77 | 0.77 | 0.92 |
time (sec) |
N/A | 0.162 | 0.012 | 0.032 | 0.193 | 0.281 | 0.031 | 0.308 | 0.076 |
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 | 19 | 15 | 15 | 16 | 15 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 3.17 | 2.50 | 2.50 | 2.67 | 2.50 |
time (sec) |
N/A | 0.157 | 0.001 | 0.020 | 0.189 | 0.297 | 0.050 | 0.326 | 0.060 |
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 | 15 | 15 | 11 | 11 | 10 | 10 | 10 | 10 | 12 |
N.S. |
1 | 1.00 | 0.73 | 0.73 | 0.67 | 0.67 | 0.67 | 0.67 | 0.80 |
time (sec) |
N/A | 0.165 | 0.027 | 0.029 | 0.185 | 0.287 | 0.032 | 0.310 | 0.078 |
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 | 23 | 18 | 21 | 18 | 15 | 17 | 17 |
N.S. |
1 | 1.00 | 1.05 | 0.82 | 0.95 | 0.82 | 0.68 | 0.77 | 0.77 |
time (sec) |
N/A | 0.200 | 0.023 | 0.030 | 0.183 | 0.299 | 0.049 | 0.315 | 0.057 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B |
verified |
N/A | No | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 27 | 30 | 23 | 24 | 25 | 26 | 30 | 22 |
N.S. |
1 | 0.87 | 0.97 | 0.74 | 0.77 | 0.81 | 0.84 | 0.97 | 0.71 |
time (sec) |
N/A | 0.199 | 0.028 | 0.035 | 0.188 | 0.257 | 0.060 | 0.291 | 0.267 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 21 | 21 | 23 | 22 | 21 | 29 | 0 | 21 |
N.S. |
1 | 0.95 | 0.95 | 1.05 | 1.00 | 0.95 | 1.32 | 0.00 | 0.95 |
time (sec) |
N/A | 0.191 | 0.066 | 0.039 | 0.262 | 0.289 | 0.137 | 0.000 | 0.409 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 26 | 23 | 34 | 40 | 25 | 42 | 0 | 0 |
N.S. |
1 | 0.76 | 0.68 | 1.00 | 1.18 | 0.74 | 1.24 | 0.00 | 0.00 |
time (sec) |
N/A | 0.193 | 0.078 | 0.053 | 0.283 | 0.267 | 0.145 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 0 | 0 | 28 | 0 | 0 | 27 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 1.22 | 0.00 | 0.00 | 1.17 |
time (sec) |
N/A | 0.189 | 0.213 | 0.000 | 0.000 | 0.287 | 0.000 | 0.000 | 0.290 |
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 | 66 | 66 | 41 | 51 | 74 | 35 | 54 | 35 | 50 |
N.S. |
1 | 1.00 | 0.62 | 0.77 | 1.12 | 0.53 | 0.82 | 0.53 | 0.76 |
time (sec) |
N/A | 0.353 | 0.138 | 0.054 | 0.186 | 0.278 | 4.448 | 0.315 | 0.360 |
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 | 12 | 12 | 12 | 20 | 19 | 25 | 20 | 20 | 19 |
N.S. |
1 | 1.00 | 1.00 | 1.67 | 1.58 | 2.08 | 1.67 | 1.67 | 1.58 |
time (sec) |
N/A | 0.163 | 0.028 | 0.036 | 0.182 | 0.294 | 0.053 | 0.284 | 0.064 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 13 | 12 | 0 | 11 | 8 | 54 | 11 |
N.S. |
1 | 1.00 | 0.81 | 0.75 | 0.00 | 0.69 | 0.50 | 3.38 | 0.69 |
time (sec) |
N/A | 0.227 | 0.047 | 0.210 | 0.000 | 0.294 | 0.047 | 0.328 | 0.265 |
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 | 16 | 14 | 13 | 13 | 10 | 13 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.81 | 0.81 | 0.62 | 0.81 | 0.88 |
time (sec) |
N/A | 0.192 | 0.089 | 0.352 | 0.191 | 0.290 | 0.041 | 0.276 | 0.278 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 33 | 33 | 23 | 74 | 33 | 27 | 33 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.70 | 2.24 | 1.00 | 0.82 | 1.00 | 0.00 |
time (sec) |
N/A | 0.183 | 0.030 | 0.046 | 0.190 | 0.296 | 0.354 | 0.328 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 9 | 8 | 0 | 8 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.73 | 0.00 | 0.73 | 0.73 | 0.73 |
time (sec) |
N/A | 0.192 | 0.017 | 0.051 | 0.196 | 0.000 | 0.069 | 0.342 | 0.324 |
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 | 6 | 6 | 6 | 6 | 5 | 5 | 5 | 5 | 5 |
N.S. |
1 | 1.00 | 1.00 | 1.00 | 0.83 | 0.83 | 0.83 | 0.83 | 0.83 |
time (sec) |
N/A | 0.184 | 0.010 | 0.020 | 0.210 | 0.272 | 0.038 | 0.278 | 0.037 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 19 | 17 | 19 | 18 | 14 | 0 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 1.00 | 0.95 | 0.74 | 0.00 | 1.11 |
time (sec) |
N/A | 0.175 | 0.017 | 0.024 | 0.210 | 0.294 | 0.148 | 0.000 | 0.230 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 16 | 16 | 36 | 15 | 12 | 20 | 15 |
N.S. |
1 | 1.00 | 0.84 | 0.84 | 1.89 | 0.79 | 0.63 | 1.05 | 0.79 |
time (sec) |
N/A | 0.273 | 0.080 | 0.036 | 0.217 | 0.273 | 0.037 | 0.294 | 0.248 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | A | C | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 56 | 61 | 41 | 60 | 63 | 0 | 97 | 1392 | 62 |
N.S. |
1 | 1.09 | 0.73 | 1.07 | 1.12 | 0.00 | 1.73 | 24.86 | 1.11 |
time (sec) |
N/A | 0.245 | 0.082 | 0.328 | 0.195 | 0.000 | 0.068 | 0.337 | 0.383 |
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 | 15 | 15 | 12 | 12 | 13 | 13 | 10 | 13 | 11 |
N.S. |
1 | 1.00 | 0.80 | 0.80 | 0.87 | 0.87 | 0.67 | 0.87 | 0.73 |
time (sec) |
N/A | 0.158 | 0.023 | 0.031 | 0.189 | 0.299 | 0.039 | 0.311 | 0.253 |
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 | 12 | 12 | 11 | 10 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.86 | 0.79 | 0.71 | 0.79 | 0.79 |
time (sec) |
N/A | 0.154 | 0.003 | 0.051 | 0.189 | 0.322 | 0.063 | 0.301 | 0.249 |
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 | 12 | 11 | 11 | 8 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 1.00 | 0.73 | 1.00 | 1.00 |
time (sec) |
N/A | 0.153 | 0.002 | 0.037 | 0.190 | 0.290 | 0.041 | 0.268 | 0.239 |
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 | 20 | 20 | 20 | 17 | 20 | 17 | 17 | 20 | 17 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 1.00 | 0.85 | 0.85 | 1.00 | 0.85 |
time (sec) |
N/A | 0.155 | 0.012 | 0.028 | 0.188 | 0.287 | 0.049 | 0.293 | 0.067 |
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 | 32 | 32 | 19 | 16 | 34 | 16 | 15 | 16 | 16 |
N.S. |
1 | 1.00 | 0.59 | 0.50 | 1.06 | 0.50 | 0.47 | 0.50 | 0.50 |
time (sec) |
N/A | 0.208 | 0.050 | 0.049 | 0.209 | 0.281 | 0.036 | 0.296 | 0.248 |
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 | 28 | 27 | 40 | 36 | 27 | 26 |
N.S. |
1 | 1.00 | 1.00 | 0.85 | 0.82 | 1.21 | 1.09 | 0.82 | 0.79 |
time (sec) |
N/A | 0.158 | 0.014 | 0.067 | 0.182 | 0.288 | 0.042 | 0.286 | 0.337 |
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 | 12 | 11 | 11 | 10 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.57 | 0.52 | 0.52 | 0.48 | 0.52 | 0.52 |
time (sec) |
N/A | 0.157 | 0.003 | 0.041 | 0.184 | 0.283 | 0.066 | 0.358 | 0.253 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 11 | 9 | 8 | 0 | 0 | 0 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.73 | 0.00 | 0.00 | 0.00 | 0.73 |
time (sec) |
N/A | 0.183 | 0.002 | 0.026 | 0.225 | 0.000 | 0.000 | 0.000 | 0.300 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 10 | 16 | 0 | 0 | 0 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.33 | 0.00 | 0.00 | 0.00 | 0.75 |
time (sec) |
N/A | 0.385 | 0.108 | 0.056 | 0.213 | 0.000 | 0.000 | 0.000 | 0.305 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 10 | 9 | 0 | 0 | 0 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 0.75 | 0.00 | 0.00 | 0.00 | 0.75 |
time (sec) |
N/A | 0.281 | 0.008 | 0.026 | 0.220 | 0.000 | 0.000 | 0.000 | 0.289 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 18 | 12 | 14 | 0 | 15 | 14 | 14 |
N.S. |
1 | 1.00 | 1.12 | 0.75 | 0.88 | 0.00 | 0.94 | 0.88 | 0.88 |
time (sec) |
N/A | 0.402 | 0.168 | 0.000 | 0.227 | 0.000 | 0.744 | 0.299 | 0.305 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 26 | 26 | 28 | 19 | 21 | 0 | 15 | 21 | 21 |
N.S. |
1 | 1.00 | 1.08 | 0.73 | 0.81 | 0.00 | 0.58 | 0.81 | 0.81 |
time (sec) |
N/A | 0.266 | 0.013 | 0.002 | 0.222 | 0.000 | 0.219 | 0.373 | 0.251 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 14 | 14 | 16 | 10 | 12 | 0 | 14 | 12 | 12 |
N.S. |
1 | 1.00 | 1.14 | 0.71 | 0.86 | 0.00 | 1.00 | 0.86 | 0.86 |
time (sec) |
N/A | 0.323 | 0.137 | 0.005 | 0.232 | 0.000 | 0.342 | 0.325 | 0.249 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 20 | 16 | 23 | 0 | 0 | 0 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.80 | 1.15 | 0.00 | 0.00 | 0.00 | 0.75 |
time (sec) |
N/A | 0.630 | 0.748 | 0.082 | 0.228 | 0.000 | 0.000 | 0.000 | 0.446 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 22 | 16 | 18 | 0 | 19 | 18 | 18 |
N.S. |
1 | 1.00 | 1.10 | 0.80 | 0.90 | 0.00 | 0.95 | 0.90 | 0.90 |
time (sec) |
N/A | 0.376 | 0.378 | 0.000 | 0.231 | 0.000 | 0.436 | 0.324 | 0.275 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 9 | 8 | 0 | 12 | 8 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.69 | 0.62 | 0.00 | 0.92 | 0.62 | 0.62 |
time (sec) |
N/A | 0.198 | 0.015 | 0.020 | 0.190 | 0.000 | 0.100 | 0.305 | 0.293 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 13 | 9 | 8 | 0 | 0 | 0 | 8 |
N.S. |
1 | 1.00 | 1.00 | 0.69 | 0.62 | 0.00 | 0.00 | 0.00 | 0.62 |
time (sec) |
N/A | 0.217 | 0.001 | 0.034 | 0.216 | 0.000 | 0.000 | 0.000 | 0.277 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 13 | 8 | 10 | 0 | 10 | 10 | 10 |
N.S. |
1 | 1.00 | 1.18 | 0.73 | 0.91 | 0.00 | 0.91 | 0.91 | 0.91 |
time (sec) |
N/A | 0.248 | 0.045 | 0.000 | 0.213 | 0.000 | 0.242 | 0.297 | 0.238 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 10 | 16 | 0 | 0 | 0 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.33 | 0.00 | 0.00 | 0.00 | 0.75 |
time (sec) |
N/A | 0.510 | 0.102 | 0.025 | 0.233 | 0.000 | 0.000 | 0.000 | 0.311 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 12 | 10 | 16 | 0 | 0 | 0 | 9 |
N.S. |
1 | 1.00 | 1.00 | 0.83 | 1.33 | 0.00 | 0.00 | 0.00 | 0.75 |
time (sec) |
N/A | 0.289 | 0.009 | 0.052 | 0.226 | 0.000 | 0.000 | 0.000 | 0.302 |
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 | 31 | 34 | 31 | 23 | 24 | 27 | 22 | 28 | 22 |
N.S. |
1 | 1.10 | 1.00 | 0.74 | 0.77 | 0.87 | 0.71 | 0.90 | 0.71 |
time (sec) |
N/A | 0.236 | 0.020 | 0.039 | 0.202 | 0.361 | 0.052 | 0.294 | 0.262 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 9 | 9 | 11 | 8 | 10 | 10 | 7 | 10 | 10 |
N.S. |
1 | 1.00 | 1.22 | 0.89 | 1.11 | 1.11 | 0.78 | 1.11 | 1.11 |
time (sec) |
N/A | 0.216 | 3.770 | 0.004 | 0.217 | 0.336 | 0.205 | 0.311 | 0.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | F(-2) | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 15 | 10 | 12 | 0 | 12 | 12 | 12 |
N.S. |
1 | 1.00 | 1.15 | 0.77 | 0.92 | 0.00 | 0.92 | 0.92 | 0.92 |
time (sec) |
N/A | 0.231 | 0.056 | 0.004 | 0.235 | 0.000 | 0.243 | 0.328 | 0.244 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 13 | 9 | 14 | 11 | 8 | 11 | 11 |
N.S. |
1 | 1.00 | 1.18 | 0.82 | 1.27 | 1.00 | 0.73 | 1.00 | 1.00 |
time (sec) |
N/A | 0.216 | 0.013 | 0.003 | 0.217 | 0.353 | 0.212 | 0.299 | 0.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A | N/A |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD |
size | 13 | 13 | 15 | 11 | 18 | 13 | 10 | 13 | 13 |
N.S. |
1 | 1.00 | 1.15 | 0.85 | 1.38 | 1.00 | 0.77 | 1.00 | 1.00 |
time (sec) |
N/A | 0.228 | 0.054 | 0.004 | 0.216 | 0.316 | 0.224 | 0.286 | 0.290 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 36 | 36 | 36 | 37 | 58 | 46 | 78 | 46 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.03 | 1.61 | 1.28 | 2.17 | 1.28 | 0.00 |
time (sec) |
N/A | 0.304 | 0.062 | 0.464 | 0.232 | 0.355 | 0.365 | 0.401 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 241 | 36 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 6.51 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.238 | 0.014 | 0.057 | 0.084 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | F | F | F | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 50 | 50 | 50 | 298 | 50 | 0 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 1.00 | 5.96 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.238 | 0.021 | 0.266 | 0.116 | 0.000 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | F | C | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 37 | 219 | 38 | 0 | 105 | 0 | 58 |
N.S. |
1 | 1.00 | 1.00 | 5.92 | 1.03 | 0.00 | 2.84 | 0.00 | 1.57 |
time (sec) |
N/A | 0.176 | 0.007 | 0.069 | 0.080 | 0.000 | 0.678 | 0.000 | 0.522 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | A | F | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 41 | 267 | 42 | 0 | 0 | 0 | 71 |
N.S. |
1 | 1.00 | 1.00 | 6.51 | 1.02 | 0.00 | 0.00 | 0.00 | 1.73 |
time (sec) |
N/A | 0.177 | 0.007 | 0.142 | 0.081 | 0.000 | 0.000 | 0.000 | 0.542 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 52 | 52 | 52 | 0 | 0 | 0 | 0 | 0 | 77 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.48 |
time (sec) |
N/A | 0.193 | 0.011 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.599 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 56 | 56 | 56 | 0 | 0 | 0 | 0 | 0 | 94 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.68 |
time (sec) |
N/A | 0.197 | 0.010 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.657 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | F | A | F | F | F(-1) |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 80 | 80 | 74 | 0 | 0 | 89 | 0 | 0 | 0 |
N.S. |
1 | 1.00 | 0.92 | 0.00 | 0.00 | 1.11 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.226 | 0.013 | 0.000 | 0.000 | 0.101 | 0.000 | 0.000 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | F(-2) | F | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 0 | 21 | 0 | 0 | 0 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.00 | 1.24 | 0.00 | 0.00 | 0.00 | 0.82 |
time (sec) |
N/A | 0.747 | 0.536 | 0.000 | 0.231 | 0.000 | 0.000 | 0.000 | 0.389 |