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 | 24 | 24 | 24 | 21 | 19 | 23 | 22 | 22 | 21 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.79 | 0.96 | 0.92 | 0.92 | 0.88 |
time (sec) |
N/A | 0.527 | 0.167 | 0.127 | 0.289 | 0.257 | 0.186 | 0.276 | 9.290 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 21 | 71 | 57 | 31 | 0 | 75 |
N.S. |
1 | 0.00 | 1.00 | 0.84 | 2.84 | 2.28 | 1.24 | 0.00 | 3.00 |
time (sec) |
N/A | 0.000 | 5.098 | 54.609 | 0.499 | 0.259 | 4.442 | 0.000 | 9.368 |
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 | 38 | 38 | 38 | 34 | 34 | 42 | 34 | 35 |
N.S. |
1 | 1.36 | 1.36 | 1.36 | 1.21 | 1.21 | 1.50 | 1.21 | 1.25 |
time (sec) |
N/A | 0.214 | 0.029 | 0.135 | 0.196 | 0.241 | 0.082 | 0.266 | 9.298 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 28 | 69 | 63 | 61 | 60 | 66 | 70 | 66 | 55 |
N.S. |
1 | 2.46 | 2.25 | 2.18 | 2.14 | 2.36 | 2.50 | 2.36 | 1.96 |
time (sec) |
N/A | 1.650 | 0.466 | 0.332 | 0.335 | 0.255 | 0.149 | 0.267 | 9.516 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | B | F | B | F(-2) | F(-2) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 65 | 61 | 0 | 59 | 0 | 0 | 109 |
N.S. |
1 | 0.00 | 2.24 | 2.10 | 0.00 | 2.03 | 0.00 | 0.00 | 3.76 |
time (sec) |
N/A | 0.000 | 0.351 | 297.766 | 0.000 | 0.255 | 0.000 | 0.000 | 12.732 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 21 | 19 | 24 | 18 | 20 | 18 | 20 |
N.S. |
1 | 0.00 | 0.84 | 0.76 | 0.96 | 0.72 | 0.80 | 0.72 | 0.80 |
time (sec) |
N/A | 0.000 | 0.098 | 9.875 | 0.400 | 0.267 | 1.855 | 0.319 | 9.861 |
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 | 14 | 12 | 12 | 12 | 19 | 14 | 12 | 11 | 11 |
N.S. |
1 | 0.86 | 0.86 | 0.86 | 1.36 | 1.00 | 0.86 | 0.79 | 0.79 |
time (sec) |
N/A | 0.173 | 0.083 | 0.239 | 0.230 | 0.247 | 0.059 | 0.256 | 0.097 |
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 | 9 | 9 | 10 | 7 | 9 | 8 | 12 | 9 |
N.S. |
1 | 0.43 | 0.43 | 0.48 | 0.33 | 0.43 | 0.38 | 0.57 | 0.43 |
time (sec) |
N/A | 0.149 | 0.045 | 0.051 | 0.208 | 0.260 | 0.058 | 0.256 | 9.075 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | C | A | B | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 11 | 11 | 290 | 13 | 82 | 18 | 15 | 71 | 17 |
N.S. |
1 | 1.00 | 26.36 | 1.18 | 7.45 | 1.64 | 1.36 | 6.45 | 1.55 |
time (sec) |
N/A | 0.351 | 0.184 | 0.449 | 0.290 | 0.246 | 0.095 | 0.276 | 9.810 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | B | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 16 | 14 | 28 | 21 | 21 | 36 | 21 | 11 |
N.S. |
1 | 0.89 | 0.78 | 1.56 | 1.17 | 1.17 | 2.00 | 1.17 | 0.61 |
time (sec) |
N/A | 0.131 | 0.003 | 0.056 | 0.199 | 0.256 | 0.029 | 0.264 | 9.729 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 29 | 31 | 32 | 29 | 29 | 33 | 29 |
N.S. |
1 | 0.00 | 1.71 | 1.82 | 1.88 | 1.71 | 1.71 | 1.94 | 1.71 |
time (sec) |
N/A | 0.000 | 0.070 | 92.085 | 0.284 | 0.259 | 1.492 | 0.467 | 10.649 |
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 | 18 | 18 | 21 | 17 | 18 | 26 | 27 | 20 |
N.S. |
1 | 0.90 | 0.90 | 1.05 | 0.85 | 0.90 | 1.30 | 1.35 | 1.00 |
time (sec) |
N/A | 0.272 | 0.051 | 0.504 | 0.293 | 0.252 | 0.077 | 0.273 | 1.096 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 318 | 73 | 54 | 221 | 221 | 282 | 221 | 207 |
N.S. |
1 | 11.78 | 2.70 | 2.00 | 8.19 | 8.19 | 10.44 | 8.19 | 7.67 |
time (sec) |
N/A | 0.405 | 0.037 | 0.591 | 0.205 | 0.252 | 0.057 | 0.257 | 9.020 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 23 | 23 | 22 | 28 | 26 | 22 | 20 |
N.S. |
1 | 0.00 | 0.88 | 0.88 | 0.85 | 1.08 | 1.00 | 0.85 | 0.77 |
time (sec) |
N/A | 0.000 | 0.279 | 0.228 | 0.327 | 0.272 | 0.128 | 0.269 | 8.846 |
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 | 14 | 14 | 15 | 14 | 14 | 14 | 14 | 11 |
N.S. |
1 | 0.78 | 0.78 | 0.83 | 0.78 | 0.78 | 0.78 | 0.78 | 0.61 |
time (sec) |
N/A | 0.137 | 0.001 | 0.018 | 0.222 | 0.257 | 0.038 | 0.265 | 8.532 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 27 | 59 | 37 | 33 | 50 | 25 | 41 | 25 | 31 |
N.S. |
1 | 2.19 | 1.37 | 1.22 | 1.85 | 0.93 | 1.52 | 0.93 | 1.15 |
time (sec) |
N/A | 0.540 | 1.393 | 0.941 | 0.271 | 0.257 | 0.141 | 0.266 | 0.280 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | C | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 55 | 24 | 22 | 176 | 21 | 22 | 26 | 21 |
N.S. |
1 | 2.20 | 0.96 | 0.88 | 7.04 | 0.84 | 0.88 | 1.04 | 0.84 |
time (sec) |
N/A | 0.363 | 0.184 | 0.075 | 0.255 | 0.251 | 0.105 | 0.265 | 8.683 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 39 | 18 | 119 | 30 | 12 | 39 | 42 |
N.S. |
1 | 0.00 | 2.05 | 0.95 | 6.26 | 1.58 | 0.63 | 2.05 | 2.21 |
time (sec) |
N/A | 0.000 | 0.109 | 0.159 | 0.202 | 0.254 | 0.093 | 0.265 | 9.073 |
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 | 24 | 24 | 24 | 23 | 47 | 22 | 24 | 52 | 22 |
N.S. |
1 | 1.00 | 1.00 | 0.96 | 1.96 | 0.92 | 1.00 | 2.17 | 0.92 |
time (sec) |
N/A | 0.174 | 0.015 | 0.184 | 0.188 | 0.256 | 0.077 | 0.253 | 8.955 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 24 | 32 | 22 | 31 | 29 | 56 | 59 |
N.S. |
1 | 0.00 | 0.92 | 1.23 | 0.85 | 1.19 | 1.12 | 2.15 | 2.27 |
time (sec) |
N/A | 0.000 | 0.065 | 0.590 | 0.436 | 0.272 | 0.159 | 0.404 | 9.751 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | A | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 21 | 51 | 26 | 43 | 15 | 0 | 31 |
N.S. |
1 | 0.00 | 0.88 | 2.12 | 1.08 | 1.79 | 0.62 | 0.00 | 1.29 |
time (sec) |
N/A | 0.000 | 0.265 | 1.087 | 0.199 | 0.261 | 0.155 | 0.000 | 8.926 |
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 | 11 | 5 | 6 | 5 | 5 | 3 | 5 | 5 |
N.S. |
1 | 0.69 | 0.31 | 0.38 | 0.31 | 0.31 | 0.19 | 0.31 | 0.31 |
time (sec) |
N/A | 0.126 | 0.000 | 0.003 | 0.183 | 0.240 | 0.016 | 0.321 | 0.041 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | A | A | F(-2) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 30 | 80 | 35 | 43 | 0 | 223 | 36 |
N.S. |
1 | 0.00 | 1.00 | 2.67 | 1.17 | 1.43 | 0.00 | 7.43 | 1.20 |
time (sec) |
N/A | 0.000 | 0.166 | 226.961 | 0.307 | 0.271 | 0.000 | 179.547 | 11.477 |
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 | 17 | 17 | 22 | 22 | 26 | 18 | 17 |
N.S. |
1 | 1.00 | 0.85 | 0.85 | 1.10 | 1.10 | 1.30 | 0.90 | 0.85 |
time (sec) |
N/A | 0.215 | 0.044 | 0.074 | 0.187 | 0.256 | 0.071 | 0.251 | 0.159 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | B | B | B | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 19 | 38 | 43 | 44 | 63 | 65 | 0 |
N.S. |
1 | 0.00 | 1.06 | 2.11 | 2.39 | 2.44 | 3.50 | 3.61 | 0.00 |
time (sec) |
N/A | 0.000 | 0.446 | 1.101 | 0.234 | 0.257 | 0.252 | 0.297 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 35 | 32 | 35 | 31 | 27 | 31 | 49 |
N.S. |
1 | 0.00 | 1.09 | 1.00 | 1.09 | 0.97 | 0.84 | 0.97 | 1.53 |
time (sec) |
N/A | 0.000 | 0.164 | 0.439 | 0.244 | 0.258 | 0.133 | 0.262 | 8.964 |
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 | 19 | 24 | 23 | 20 | 41 | 19 | 17 | 19 | 15 |
N.S. |
1 | 1.26 | 1.21 | 1.05 | 2.16 | 1.00 | 0.89 | 1.00 | 0.79 |
time (sec) |
N/A | 0.288 | 0.046 | 0.315 | 0.331 | 0.244 | 0.078 | 0.255 | 9.164 |
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 | 17 | 15 | 14 | 13 | 13 | 14 | 13 | 13 |
N.S. |
1 | 1.13 | 1.00 | 0.93 | 0.87 | 0.87 | 0.93 | 0.87 | 0.87 |
time (sec) |
N/A | 0.145 | 0.004 | 0.047 | 0.190 | 0.239 | 0.066 | 0.254 | 9.606 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 38 | 0 | 34 | 67 | 45 | 39 | 26 | 37 | 35 |
N.S. |
1 | 0.00 | 0.89 | 1.76 | 1.18 | 1.03 | 0.68 | 0.97 | 0.92 |
time (sec) |
N/A | 0.000 | 0.122 | 2.876 | 0.320 | 0.274 | 0.290 | 0.341 | 10.948 |
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 | 25 | 25 | 19 | 37 | 34 | 17 | 34 | 18 |
N.S. |
1 | 0.89 | 0.89 | 0.68 | 1.32 | 1.21 | 0.61 | 1.21 | 0.64 |
time (sec) |
N/A | 0.776 | 0.471 | 0.217 | 0.231 | 0.260 | 0.065 | 0.255 | 9.783 |
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 | 29 | 24 | 24 | 23 | 22 | 22 | 19 | 24 | 35 |
N.S. |
1 | 0.83 | 0.83 | 0.79 | 0.76 | 0.76 | 0.66 | 0.83 | 1.21 |
time (sec) |
N/A | 0.357 | 0.156 | 0.426 | 0.236 | 0.251 | 0.076 | 0.257 | 9.646 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 29 | 17 | 26 | 26 | 15 | 0 | 26 |
N.S. |
1 | 0.00 | 1.61 | 0.94 | 1.44 | 1.44 | 0.83 | 0.00 | 1.44 |
time (sec) |
N/A | 0.000 | 0.238 | 4.108 | 0.433 | 0.249 | 0.137 | 0.000 | 9.546 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | C | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 58 | 54 | 57 | 54 | 53 | 57 | 51 |
N.S. |
1 | 0.00 | 2.00 | 1.86 | 1.97 | 1.86 | 1.83 | 1.97 | 1.76 |
time (sec) |
N/A | 0.000 | 0.616 | 0.315 | 0.241 | 0.270 | 0.162 | 0.263 | 9.320 |
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 | 21 | 21 | 19 | 20 | 23 | 62 | 24 | 25 | 17 |
N.S. |
1 | 1.00 | 0.90 | 0.95 | 1.10 | 2.95 | 1.14 | 1.19 | 0.81 |
time (sec) |
N/A | 0.762 | 0.240 | 0.634 | 0.240 | 0.265 | 0.087 | 0.410 | 9.431 |
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 | 14 | 14 | 14 | 12 | 30 | 11 | 12 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 2.14 | 0.79 | 0.86 | 0.79 | 0.79 |
time (sec) |
N/A | 0.207 | 0.008 | 0.055 | 0.192 | 0.259 | 0.047 | 0.259 | 9.629 |
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 | 27 | 27 | 22 | 34 | 38 | 22 | 40 | 31 |
N.S. |
1 | 1.08 | 1.08 | 0.88 | 1.36 | 1.52 | 0.88 | 1.60 | 1.24 |
time (sec) |
N/A | 0.592 | 0.216 | 0.597 | 0.226 | 0.238 | 0.057 | 0.261 | 9.538 |
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 | 24 | 38 | 27 | 26 | 33 | 23 | 27 | 26 | 24 |
N.S. |
1 | 1.58 | 1.12 | 1.08 | 1.38 | 0.96 | 1.12 | 1.08 | 1.00 |
time (sec) |
N/A | 0.257 | 0.282 | 0.039 | 0.223 | 0.240 | 0.068 | 0.257 | 9.774 |
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 | 49 | 24 | 31 | 35 | 28 | 31 | 42 | 42 |
N.S. |
1 | 1.75 | 0.86 | 1.11 | 1.25 | 1.00 | 1.11 | 1.50 | 1.50 |
time (sec) |
N/A | 0.282 | 0.342 | 0.247 | 0.338 | 0.252 | 0.087 | 0.263 | 0.174 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | C | C | A | B | A | A | A | B |
verified |
N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 3581 | 184188 | 32 | 165 | 42 | 26 | 30 | 25 |
N.S. |
1 | 115.52 | 5941.55 | 1.03 | 5.32 | 1.35 | 0.84 | 0.97 | 0.81 |
time (sec) |
N/A | 18.226 | 48.768 | 0.207 | 3.613 | 0.246 | 0.137 | 0.524 | 9.825 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 71 | 22 | 22 | 35 | 34 | 32 | 66 | 66 |
N.S. |
1 | 2.73 | 0.85 | 0.85 | 1.35 | 1.31 | 1.23 | 2.54 | 2.54 |
time (sec) |
N/A | 0.341 | 0.106 | 0.237 | 0.212 | 0.252 | 0.654 | 0.257 | 0.210 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | C | B | B | F(-1) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 24 | 80 | 74 | 56 | 134 | 0 | 94 |
N.S. |
1 | 0.00 | 0.92 | 3.08 | 2.85 | 2.15 | 5.15 | 0.00 | 3.62 |
time (sec) |
N/A | 0.000 | 5.107 | 0.580 | 0.257 | 0.269 | 0.329 | 0.000 | 9.898 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 20 | 19 | 28 | 20 | 0 | 21 |
N.S. |
1 | 0.00 | 1.00 | 0.77 | 0.73 | 1.08 | 0.77 | 0.00 | 0.81 |
time (sec) |
N/A | 0.000 | 1.110 | 0.687 | 0.636 | 0.250 | 6.805 | 0.000 | 9.380 |
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 | 24 | 26 | 21 | 20 | 20 | 22 | 20 | 21 |
N.S. |
1 | 0.89 | 0.96 | 0.78 | 0.74 | 0.74 | 0.81 | 0.74 | 0.78 |
time (sec) |
N/A | 0.296 | 0.020 | 0.091 | 0.194 | 0.234 | 0.231 | 0.268 | 0.156 |
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 | 22 | 24 | 20 | 38 | 24 | 24 | 24 | 37 | 0 |
N.S. |
1 | 1.09 | 0.91 | 1.73 | 1.09 | 1.09 | 1.09 | 1.68 | 0.00 |
time (sec) |
N/A | 6.108 | 0.712 | 0.607 | 0.263 | 0.259 | 0.143 | 0.361 | 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 | 23 | 23 | 19 | 18 | 22 | 19 | 27 | 18 |
N.S. |
1 | 0.92 | 0.92 | 0.76 | 0.72 | 0.88 | 0.76 | 1.08 | 0.72 |
time (sec) |
N/A | 0.596 | 0.030 | 0.092 | 0.193 | 0.256 | 0.104 | 0.273 | 9.596 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | F | A | F(-2) | F(-1) | F | B |
verified |
N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 25 | 24 | 24 | 0 | 17 | 0 | 0 | 0 | 16 |
N.S. |
1 | 0.96 | 0.96 | 0.00 | 0.68 | 0.00 | 0.00 | 0.00 | 0.64 |
time (sec) |
N/A | 0.293 | 0.053 | 0.000 | 0.399 | 0.000 | 0.000 | 0.000 | 9.506 |
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 | 27 | 33 | 17 | 21 | 24 | 19 | 17 | 18 |
N.S. |
1 | 1.35 | 1.65 | 0.85 | 1.05 | 1.20 | 0.95 | 0.85 | 0.90 |
time (sec) |
N/A | 0.330 | 0.653 | 0.089 | 0.247 | 0.270 | 0.110 | 0.263 | 0.249 |
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 | 16 | 16 | 15 | 18 | 16 | 16 | 14 | 16 | 0 |
N.S. |
1 | 1.00 | 0.94 | 1.12 | 1.00 | 1.00 | 0.88 | 1.00 | 0.00 |
time (sec) |
N/A | 0.367 | 0.023 | 0.886 | 0.313 | 0.251 | 0.084 | 0.265 | 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 | 27 | 31 | 29 | 24 | 26 | 26 | 31 | 26 | 24 |
N.S. |
1 | 1.15 | 1.07 | 0.89 | 0.96 | 0.96 | 1.15 | 0.96 | 0.89 |
time (sec) |
N/A | 0.165 | 0.031 | 0.119 | 0.190 | 0.255 | 0.075 | 0.258 | 10.378 |
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 | 20 | 15 | 19 | 17 | 15 | 19 | 20 |
N.S. |
1 | 1.00 | 1.18 | 0.88 | 1.12 | 1.00 | 0.88 | 1.12 | 1.18 |
time (sec) |
N/A | 0.287 | 0.118 | 0.189 | 0.249 | 0.252 | 0.076 | 0.263 | 10.195 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | B | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 157 | 28 | 47 | 47 | 22 | 47 | 47 |
N.S. |
1 | 0.00 | 4.76 | 0.85 | 1.42 | 1.42 | 0.67 | 1.42 | 1.42 |
time (sec) |
N/A | 0.000 | 0.165 | 0.227 | 0.305 | 0.266 | 0.079 | 0.261 | 10.098 |
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 | 18 | 19 | 27 | 17 | 24 | 16 | 17 | 20 | 16 |
N.S. |
1 | 1.06 | 1.50 | 0.94 | 1.33 | 0.89 | 0.94 | 1.11 | 0.89 |
time (sec) |
N/A | 0.762 | 1.233 | 0.333 | 0.248 | 0.255 | 0.061 | 0.255 | 9.840 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | B | F | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 32 | 90 | 0 | 94 | 704 | 107 | 657 |
N.S. |
1 | 0.00 | 1.39 | 3.91 | 0.00 | 4.09 | 30.61 | 4.65 | 28.57 |
time (sec) |
N/A | 0.000 | 0.107 | 1.286 | 0.000 | 0.259 | 0.288 | 0.279 | 9.903 |
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 | 31 | 24 | 32 | 33 | 33 | 32 | 33 | 31 |
N.S. |
1 | 1.41 | 1.09 | 1.45 | 1.50 | 1.50 | 1.45 | 1.50 | 1.41 |
time (sec) |
N/A | 0.197 | 0.017 | 0.209 | 0.185 | 0.243 | 0.170 | 0.280 | 0.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 28 | 44 | 42 | 39 | 39 | 43 | 43 |
N.S. |
1 | 0.00 | 0.85 | 1.33 | 1.27 | 1.18 | 1.18 | 1.30 | 1.30 |
time (sec) |
N/A | 0.000 | 0.052 | 9.957 | 0.312 | 0.245 | 0.079 | 0.270 | 9.424 |
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 | 24 | 17 | 17 | 16 | 17 | 27 | 12 | 18 | 17 |
N.S. |
1 | 0.71 | 0.71 | 0.67 | 0.71 | 1.12 | 0.50 | 0.75 | 0.71 |
time (sec) |
N/A | 0.221 | 0.012 | 0.062 | 0.185 | 0.247 | 0.043 | 0.256 | 8.987 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 31 | 34 | 35 | 34 | 44 | 36 | 33 |
N.S. |
1 | 0.00 | 1.24 | 1.36 | 1.40 | 1.36 | 1.76 | 1.44 | 1.32 |
time (sec) |
N/A | 0.000 | 0.715 | 0.648 | 0.319 | 0.259 | 0.239 | 0.299 | 10.143 |
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 | 41 | 43 | 28 | 31 | 37 | 24 | 36 | 32 |
N.S. |
1 | 1.24 | 1.30 | 0.85 | 0.94 | 1.12 | 0.73 | 1.09 | 0.97 |
time (sec) |
N/A | 0.462 | 0.333 | 0.053 | 0.274 | 0.251 | 0.087 | 0.268 | 0.149 |
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 | 20 | 19 | 33 | 17 | 35 | 19 |
N.S. |
1 | 1.00 | 1.00 | 0.95 | 0.90 | 1.57 | 0.81 | 1.67 | 0.90 |
time (sec) |
N/A | 0.199 | 0.032 | 0.084 | 0.189 | 0.257 | 0.069 | 0.261 | 9.706 |
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 | 17 | 18 | 15 | 16 | 16 | 24 | 14 | 14 |
N.S. |
1 | 0.81 | 0.86 | 0.71 | 0.76 | 0.76 | 1.14 | 0.67 | 0.67 |
time (sec) |
N/A | 0.152 | 0.006 | 2.282 | 0.195 | 0.253 | 0.147 | 0.261 | 0.125 |
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 | 12 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 1.09 | 1.00 | 1.00 | 1.09 | 1.00 | 1.00 |
time (sec) |
N/A | 0.405 | 0.042 | 0.310 | 0.302 | 0.246 | 0.057 | 0.264 | 9.663 |
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 | 40 | 21 | 20 | 23 | 23 | 22 | 23 | 23 |
N.S. |
1 | 1.60 | 0.84 | 0.80 | 0.92 | 0.92 | 0.88 | 0.92 | 0.92 |
time (sec) |
N/A | 0.435 | 0.019 | 0.396 | 0.302 | 0.241 | 0.324 | 0.264 | 9.660 |
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 | 19 | 16 | 21 | 31 | 14 | 19 | 15 |
N.S. |
1 | 1.00 | 1.00 | 0.84 | 1.11 | 1.63 | 0.74 | 1.00 | 0.79 |
time (sec) |
N/A | 0.355 | 0.224 | 0.234 | 0.214 | 0.240 | 0.053 | 0.261 | 0.113 |
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 | 18 | 18 | 16 | 15 | 22 | 17 | 16 | 15 |
N.S. |
1 | 0.78 | 0.78 | 0.70 | 0.65 | 0.96 | 0.74 | 0.70 | 0.65 |
time (sec) |
N/A | 0.164 | 0.009 | 0.079 | 0.193 | 0.234 | 0.065 | 0.252 | 0.038 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | A | C | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 19 | 17 | 21 | 84 | 19 | 42 | 20 | 18 |
N.S. |
1 | 1.00 | 0.89 | 1.11 | 4.42 | 1.00 | 2.21 | 1.05 | 0.95 |
time (sec) |
N/A | 0.351 | 0.099 | 0.843 | 0.276 | 0.257 | 0.262 | 0.281 | 9.683 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | B | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 28 | 33 | 46 | 86 | 26 | 0 | 60 |
N.S. |
1 | 0.00 | 1.17 | 1.38 | 1.92 | 3.58 | 1.08 | 0.00 | 2.50 |
time (sec) |
N/A | 0.000 | 0.217 | 22.767 | 0.926 | 0.257 | 0.391 | 0.000 | 9.350 |
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 | 13 | 13 | 13 | 12 | 35 | 11 | 12 | 11 | 11 |
N.S. |
1 | 1.00 | 1.00 | 0.92 | 2.69 | 0.85 | 0.92 | 0.85 | 0.85 |
time (sec) |
N/A | 0.183 | 0.008 | 0.089 | 0.192 | 0.247 | 0.059 | 0.258 | 9.524 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F(-1) | B | B | B | B | B |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 26 | 0 | 183 | 144 | 175 | 180 | 230 |
N.S. |
1 | 0.00 | 0.79 | 0.00 | 5.55 | 4.36 | 5.30 | 5.45 | 6.97 |
time (sec) |
N/A | 0.000 | 2.317 | 0.000 | 1.116 | 0.255 | 1.639 | 1.598 | 10.807 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 26 | 38 | 24 | 34 | 34 | 27 | 26 |
N.S. |
1 | 0.00 | 0.76 | 1.12 | 0.71 | 1.00 | 1.00 | 0.79 | 0.76 |
time (sec) |
N/A | 0.000 | 0.241 | 3.063 | 0.427 | 0.239 | 0.148 | 1.906 | 10.274 |
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 | 15 | 19 | 13 | 17 | 16 | 16 | 17 | 16 | 18 |
N.S. |
1 | 1.27 | 0.87 | 1.13 | 1.07 | 1.07 | 1.13 | 1.07 | 1.20 |
time (sec) |
N/A | 0.299 | 0.082 | 0.137 | 0.298 | 0.273 | 0.097 | 0.265 | 9.263 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | B | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 17 | 30 | 35 | 29 | 27 | 35 | 25 |
N.S. |
1 | 0.00 | 0.89 | 1.58 | 1.84 | 1.53 | 1.42 | 1.84 | 1.32 |
time (sec) |
N/A | 0.000 | 0.374 | 4.041 | 0.318 | 0.265 | 0.726 | 0.316 | 9.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | A | B | A | A | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 12 | 12 | 44 | 12 | 36 | 11 | 10 | 19 | 10 |
N.S. |
1 | 1.00 | 3.67 | 1.00 | 3.00 | 0.92 | 0.83 | 1.58 | 0.83 |
time (sec) |
N/A | 0.200 | 0.057 | 0.305 | 0.193 | 0.238 | 0.078 | 0.264 | 10.406 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 26 | 33 | 22 | 31 | 37 | 0 | 36 |
N.S. |
1 | 0.00 | 0.87 | 1.10 | 0.73 | 1.03 | 1.23 | 0.00 | 1.20 |
time (sec) |
N/A | 0.000 | 4.585 | 0.648 | 0.260 | 0.259 | 0.129 | 0.000 | 10.929 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | C | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 27 | 30 | 42 | 42 | 24 | 24 | 77 |
N.S. |
1 | 0.00 | 1.04 | 1.15 | 1.62 | 1.62 | 0.92 | 0.92 | 2.96 |
time (sec) |
N/A | 0.000 | 1.499 | 3.123 | 0.325 | 0.260 | 0.090 | 0.433 | 10.047 |
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 | 26 | 18 | 16 | 15 | 14 | 17 | 10 | 14 | 15 |
N.S. |
1 | 0.69 | 0.62 | 0.58 | 0.54 | 0.65 | 0.38 | 0.54 | 0.58 |
time (sec) |
N/A | 0.166 | 0.002 | 0.037 | 0.181 | 0.242 | 0.032 | 0.257 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 29 | 27 | 34 | 34 | 19 | 28 | 26 |
N.S. |
1 | 0.00 | 1.26 | 1.17 | 1.48 | 1.48 | 0.83 | 1.22 | 1.13 |
time (sec) |
N/A | 0.000 | 0.239 | 0.544 | 0.226 | 0.257 | 0.072 | 0.269 | 9.908 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 44 | 36 | 38 | 36 | 39 | 1093 | 0 |
N.S. |
1 | 0.00 | 1.26 | 1.03 | 1.09 | 1.03 | 1.11 | 31.23 | 0.00 |
time (sec) |
N/A | 0.000 | 0.109 | 0.889 | 0.349 | 0.259 | 0.145 | 0.381 | 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 | 21 | 20 | 20 | 22 | 27 | 27 | 17 | 27 | 21 |
N.S. |
1 | 0.95 | 0.95 | 1.05 | 1.29 | 1.29 | 0.81 | 1.29 | 1.00 |
time (sec) |
N/A | 0.486 | 0.155 | 0.555 | 0.221 | 0.254 | 0.046 | 0.267 | 10.016 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 22 | 29 | 23 | 27 | 29 | 51 | 20 |
N.S. |
1 | 0.00 | 1.00 | 1.32 | 1.05 | 1.23 | 1.32 | 2.32 | 0.91 |
time (sec) |
N/A | 0.000 | 0.984 | 2.128 | 0.216 | 0.263 | 0.211 | 0.284 | 10.468 |
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 | 16 | 26 | 15 | 14 | 14 | 10 | 16 | 12 |
N.S. |
1 | 0.89 | 1.44 | 0.83 | 0.78 | 0.78 | 0.56 | 0.89 | 0.67 |
time (sec) |
N/A | 0.195 | 0.007 | 0.344 | 0.200 | 0.255 | 0.039 | 0.270 | 9.986 |
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 | 25 | 26 | 28 | 22 | 46 | 16 | 22 | 22 | 16 |
N.S. |
1 | 1.04 | 1.12 | 0.88 | 1.84 | 0.64 | 0.88 | 0.88 | 0.64 |
time (sec) |
N/A | 0.260 | 0.041 | 0.309 | 0.186 | 0.242 | 0.063 | 0.264 | 10.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | B | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 55 | 29 | 28 | 242 | 27 | 27 | 27 | 15 |
N.S. |
1 | 3.44 | 1.81 | 1.75 | 15.12 | 1.69 | 1.69 | 1.69 | 0.94 |
time (sec) |
N/A | 0.586 | 0.077 | 0.329 | 0.203 | 0.249 | 0.078 | 0.273 | 10.511 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | A | C | B | B | B | B | F(-1) |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 23 | 23 | 23 | 35 | 65 | 75 | 90 | 81 | 0 |
N.S. |
1 | 1.00 | 1.00 | 1.52 | 2.83 | 3.26 | 3.91 | 3.52 | 0.00 |
time (sec) |
N/A | 1.019 | 0.078 | 256.501 | 0.489 | 0.259 | 0.245 | 1.350 | 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 | 27 | 26 | 27 | 34 | 24 | 29 | 26 | 29 | 24 |
N.S. |
1 | 0.96 | 1.00 | 1.26 | 0.89 | 1.07 | 0.96 | 1.07 | 0.89 |
time (sec) |
N/A | 0.979 | 0.341 | 0.339 | 0.233 | 0.260 | 0.153 | 0.280 | 11.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | F | B | A | A | F | B |
verified |
N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 26 | 0 | 71 | 28 | 24 | 0 | 29 |
N.S. |
1 | 0.00 | 0.90 | 0.00 | 2.45 | 0.97 | 0.83 | 0.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.158 | 0.000 | 0.550 | 0.276 | 76.375 | 0.000 | 10.972 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | A | A | A | A | B | A | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 21 | 43 | 41 | 34 | 31 | 41 | 34 | 41 | 32 |
N.S. |
1 | 2.05 | 1.95 | 1.62 | 1.48 | 1.95 | 1.62 | 1.95 | 1.52 |
time (sec) |
N/A | 0.247 | 0.197 | 0.249 | 0.194 | 0.250 | 0.082 | 0.267 | 0.084 |
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 | 27 | 24 | 25 | 19 | 24 | 24 | 19 | 23 |
N.S. |
1 | 1.35 | 1.20 | 1.25 | 0.95 | 1.20 | 1.20 | 0.95 | 1.15 |
time (sec) |
N/A | 0.410 | 0.086 | 0.121 | 0.282 | 0.237 | 0.084 | 0.258 | 10.484 |
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 | 29 | 22 | 22 | 22 | 22 | 20 | 22 | 20 |
N.S. |
1 | 1.07 | 0.81 | 0.81 | 0.81 | 0.81 | 0.74 | 0.81 | 0.74 |
time (sec) |
N/A | 0.371 | 0.026 | 0.276 | 0.194 | 0.237 | 0.615 | 0.265 | 10.431 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 16 | 0 | 21 | 21 | 20 | 20 | 20 | 39 | 20 |
N.S. |
1 | 0.00 | 1.31 | 1.31 | 1.25 | 1.25 | 1.25 | 2.44 | 1.25 |
time (sec) |
N/A | 0.000 | 1.655 | 0.304 | 0.224 | 0.253 | 0.064 | 0.265 | 10.405 |
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 | 28 | 19 | 17 | 25 | 25 | 19 | 27 | 16 |
N.S. |
1 | 1.22 | 0.83 | 0.74 | 1.09 | 1.09 | 0.83 | 1.17 | 0.70 |
time (sec) |
N/A | 0.187 | 0.013 | 0.100 | 0.188 | 0.246 | 0.058 | 0.254 | 9.955 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 46 | 53 | 49 | 49 | 51 | 52 | 0 |
N.S. |
1 | 0.00 | 1.48 | 1.71 | 1.58 | 1.58 | 1.65 | 1.68 | 0.00 |
time (sec) |
N/A | 0.000 | 0.160 | 7.424 | 0.251 | 0.268 | 0.206 | 0.428 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | B | F(-1) | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 33 | 32 | 33 | 35 | 60 | 0 | 31 |
N.S. |
1 | 0.00 | 1.06 | 1.03 | 1.06 | 1.13 | 1.94 | 0.00 | 1.00 |
time (sec) |
N/A | 0.000 | 0.099 | 0.721 | 0.244 | 0.262 | 1.378 | 0.000 | 9.675 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 19 | 32 | 40 | 58 | 53 | 56 | 58 | 58 | 55 |
N.S. |
1 | 1.68 | 2.11 | 3.05 | 2.79 | 2.95 | 3.05 | 3.05 | 2.89 |
time (sec) |
N/A | 0.226 | 0.023 | 0.088 | 0.190 | 0.232 | 0.089 | 0.261 | 0.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 34 | 28 | 46 | 46 | 27 | 49 | 28 |
N.S. |
1 | 0.00 | 0.97 | 0.80 | 1.31 | 1.31 | 0.77 | 1.40 | 0.80 |
time (sec) |
N/A | 0.000 | 2.106 | 0.201 | 0.205 | 0.256 | 0.133 | 0.268 | 10.037 |
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 | 17 | 17 | 17 | 14 | 13 | 19 | 15 | 14 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.82 | 0.76 | 1.12 | 0.88 | 0.82 | 0.76 |
time (sec) |
N/A | 0.170 | 0.002 | 0.038 | 0.194 | 0.232 | 0.050 | 0.251 | 0.033 |
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 | 10 | 10 | 11 | 10 | 10 | 10 | 10 | 10 |
N.S. |
1 | 0.56 | 0.56 | 0.61 | 0.56 | 0.56 | 0.56 | 0.56 | 0.56 |
time (sec) |
N/A | 0.334 | 0.073 | 0.274 | 0.216 | 0.249 | 0.048 | 0.253 | 10.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 13 | 35 | 29 | 27 | 30 | 30 | 27 | 30 | 26 |
N.S. |
1 | 2.69 | 2.23 | 2.08 | 2.31 | 2.31 | 2.08 | 2.31 | 2.00 |
time (sec) |
N/A | 0.167 | 0.007 | 0.088 | 0.193 | 0.244 | 0.028 | 0.257 | 0.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD |
size | 33 | 0 | 28 | 29 | 25 | 28 | 24 | 0 | 25 |
N.S. |
1 | 0.00 | 0.85 | 0.88 | 0.76 | 0.85 | 0.73 | 0.00 | 0.76 |
time (sec) |
N/A | 0.000 | 0.438 | 0.535 | 0.269 | 0.250 | 1.243 | 0.000 | 9.999 |
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 | 24 | 37 | 24 | 28 | 33 | 33 | 37 | 40 | 41 |
N.S. |
1 | 1.54 | 1.00 | 1.17 | 1.38 | 1.38 | 1.54 | 1.67 | 1.71 |
time (sec) |
N/A | 0.275 | 0.016 | 0.317 | 0.187 | 0.249 | 0.483 | 0.254 | 0.194 |
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 | 17 | 16 | 16 | 15 | 34 | 14 | 14 | 14 | 16 |
N.S. |
1 | 0.94 | 0.94 | 0.88 | 2.00 | 0.82 | 0.82 | 0.82 | 0.94 |
time (sec) |
N/A | 0.288 | 0.119 | 0.074 | 0.176 | 0.248 | 0.046 | 0.254 | 9.457 |