Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 27 | 27 | 24 | 28 | 23 | 26 | 30 | 27 | 0 |
N.S. |
1 | 1.00 | 1.00 | 0.89 | 1.04 | 0.85 | 0.96 | 1.11 | 1.00 | 0.00 |
time (sec) |
N/A | 0.595 | 0.034 | 1.293 | 0.166 | 0.079 | 0.385 | 0.291 | 0.154 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 111 | 30 | 23 | 0 | 29 | 36 | 0 | 711 | 31 |
N.S. |
1 | 3.70 | 1.00 | 0.77 | 0.00 | 0.97 | 1.20 | 0.00 | 23.70 | 1.03 |
time (sec) |
N/A | 0.430 | 0.262 | 0.678 | 0.000 | 0.097 | 4.411 | 0.000 | 0.604 | 3.322 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 29 | 25 | 19 | 18 | 18 | 17 | 30 | 21 | 18 |
N.S. |
1 | 1.16 | 1.00 | 0.76 | 0.72 | 0.72 | 0.68 | 1.20 | 0.84 | 0.72 |
time (sec) |
N/A | 0.738 | 0.319 | 0.300 | 0.066 | 0.101 | 0.123 | 0.137 | 0.168 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 31 | 30 | 28 | 28 | 37 | 36 | 42 | 47 |
N.S. |
1 | 0.00 | 1.41 | 1.36 | 1.27 | 1.27 | 1.68 | 1.64 | 1.91 | 2.14 |
time (sec) |
N/A | 0.000 | 0.174 | 1.799 | 0.065 | 0.084 | 0.400 | 0.140 | 0.185 | 3.316 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 20 | 80 | 23 | 23 | 23 | 27 | 25 | 22 | 23 |
N.S. |
1 | 0.91 | 3.64 | 1.05 | 1.05 | 1.05 | 1.23 | 1.14 | 1.00 | 1.05 |
time (sec) |
N/A | 0.182 | 0.039 | 0.074 | 0.031 | 0.085 | 0.335 | 0.121 | 0.162 | 0.112 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 74 | 37 | 28 | 40 | 30 | 29 | 0 | 27 | 0 |
N.S. |
1 | 3.36 | 1.68 | 1.27 | 1.82 | 1.36 | 1.32 | 0.00 | 1.23 | 0.00 |
time (sec) |
N/A | 1.299 | 0.364 | 1.142 | 0.094 | 0.100 | 0.153 | 0.000 | 0.163 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 26 | 24 | 29 | 27 | 56 | 26 | 23 |
N.S. |
1 | 0.00 | 1.00 | 0.93 | 0.86 | 1.04 | 0.96 | 2.00 | 0.93 | 0.82 |
time (sec) |
N/A | 0.000 | 0.917 | 0.473 | 0.069 | 0.102 | 0.068 | 0.134 | 0.161 | 3.224 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 30 | 36 | 31 | 29 | 32 | 39 | 33 | 31 | 30 |
N.S. |
1 | 1.50 | 1.80 | 1.55 | 1.45 | 1.60 | 1.95 | 1.65 | 1.55 | 1.50 |
time (sec) |
N/A | 0.266 | 0.009 | 0.088 | 0.027 | 0.086 | 0.095 | 0.113 | 0.157 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 591 | 54 | 25 | 6875 | 565 | 8716 | 9072 | 21 | 20 |
N.S. |
1 | 24.62 | 2.25 | 1.04 | 286.46 | 23.54 | 363.17 | 378.00 | 0.88 | 0.83 |
time (sec) |
N/A | 7.461 | 0.284 | 0.574 | 0.108 | 0.116 | 6.574 | 0.149 | 0.161 | 3.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 49 | 17 | 14 | 11 | 11 | 15 | 0 | 16 | 11 |
N.S. |
1 | 2.88 | 1.00 | 0.82 | 0.65 | 0.65 | 0.88 | 0.00 | 0.94 | 0.65 |
time (sec) |
N/A | 0.228 | 0.068 | 0.083 | 0.075 | 0.091 | 0.116 | 0.000 | 0.152 | 3.189 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-2) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 26 | 25 | 24 | 263 | 24 | 0 | 25 | 25 | 36 |
N.S. |
1 | 1.37 | 1.32 | 1.26 | 13.84 | 1.26 | 0.00 | 1.32 | 1.32 | 1.89 |
time (sec) |
N/A | 1.104 | 0.090 | 0.183 | 0.169 | 0.105 | 0.000 | 0.112 | 0.144 | 0.211 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 285 | 406 | 70 | 105 | 95 | 107 | 82 | 119 | 0 |
N.S. |
1 | 11.40 | 16.24 | 2.80 | 4.20 | 3.80 | 4.28 | 3.28 | 4.76 | 0.00 |
time (sec) |
N/A | 1.005 | 0.168 | 0.282 | 0.046 | 0.095 | 4.761 | 0.127 | 0.144 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 17 | 16 | 157 | 33 | 15 | 0 | 190 | 20 |
N.S. |
1 | 0.00 | 0.81 | 0.76 | 7.48 | 1.57 | 0.71 | 0.00 | 9.05 | 0.95 |
time (sec) |
N/A | 0.000 | 0.465 | 0.011 | 0.338 | 0.107 | 0.155 | 0.000 | 0.162 | 4.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 26 | 21 | 20 | 26 | 17 | 53 | 24 | 22 |
N.S. |
1 | 0.00 | 0.90 | 0.72 | 0.69 | 0.90 | 0.59 | 1.83 | 0.83 | 0.76 |
time (sec) |
N/A | 0.000 | 0.184 | 0.139 | 0.067 | 0.110 | 0.093 | 0.124 | 0.145 | 4.264 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 0 | 14 | 15 | 38 | 38 | 20 | 43 | 33 | 26 |
N.S. |
1 | 0.00 | 1.00 | 1.07 | 2.71 | 2.71 | 1.43 | 3.07 | 2.36 | 1.86 |
time (sec) |
N/A | 0.000 | 0.157 | 0.357 | 0.067 | 0.105 | 0.048 | 0.118 | 0.150 | 4.319 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | C | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 54 | 32 | 28 | 361 | 26 | 26 | 48 | 45 | 41 |
N.S. |
1 | 2.57 | 1.52 | 1.33 | 17.19 | 1.24 | 1.24 | 2.29 | 2.14 | 1.95 |
time (sec) |
N/A | 0.373 | 0.661 | 0.447 | 0.189 | 0.099 | 0.087 | 0.177 | 0.149 | 4.301 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 30 | 23 | 21 | 0 | 40 | 15 | 38 | 39 | 20 |
N.S. |
1 | 0.88 | 0.68 | 0.62 | 0.00 | 1.18 | 0.44 | 1.12 | 1.15 | 0.59 |
time (sec) |
N/A | 0.721 | 0.365 | 0.412 | 0.000 | 0.106 | 0.086 | 0.118 | 0.156 | 0.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 81 | 22 | 20 | 0 | 22 | 26 | 0 | 31 | 22 |
N.S. |
1 | 3.38 | 0.92 | 0.83 | 0.00 | 0.92 | 1.08 | 0.00 | 1.29 | 0.92 |
time (sec) |
N/A | 0.386 | 0.024 | 0.283 | 0.000 | 0.112 | 1.616 | 0.000 | 0.150 | 4.456 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | A | A | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 45 | 25 | 29 | 0 | 24 | 29 | 28 | 33 | 0 |
N.S. |
1 | 1.88 | 1.04 | 1.21 | 0.00 | 1.00 | 1.21 | 1.17 | 1.38 | 0.00 |
time (sec) |
N/A | 0.351 | 0.385 | 137.345 | 0.000 | 0.112 | 0.255 | 0.148 | 1.389 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | B | A | A | A | F | B |
verified | N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 36 | 0 | 28 | 54 | 37 | 37 | 37 | 370 | 37 |
N.S. |
1 | 1.57 | 0.00 | 1.22 | 2.35 | 1.61 | 1.61 | 1.61 | 16.09 | 1.61 |
time (sec) |
N/A | 5.303 | 0.000 | 1.099 | 0.621 | 0.113 | 0.271 | 0.144 | 0.479 | 0.259 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 27 | 29 | 279 | 298 | 427 | 849 | 622 | 0 |
N.S. |
1 | 0.00 | 0.96 | 1.04 | 9.96 | 10.64 | 15.25 | 30.32 | 22.21 | 0.00 |
time (sec) |
N/A | 0.000 | 0.514 | 24.498 | 1.575 | 0.139 | 0.751 | 0.614 | 28.810 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 33 | 35 | 38 | 38 | 48 | 38 | 38 | 0 |
N.S. |
1 | 0.00 | 1.22 | 1.30 | 1.41 | 1.41 | 1.78 | 1.41 | 1.41 | 0.00 |
time (sec) |
N/A | 0.000 | 0.031 | 0.324 | 0.029 | 0.101 | 0.957 | 0.125 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 30 | 30 | 34 | 35 | 31 | 35 | 933 | 0 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 1.13 | 1.17 | 1.03 | 1.17 | 31.10 | 0.00 |
time (sec) |
N/A | 0.000 | 3.273 | 0.471 | 1.774 | 0.104 | 4.289 | 0.140 | 0.174 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 26 | 26 | 27 | 26 | 26 | 26 | 27 | 26 | 26 |
N.S. |
1 | 1.08 | 1.08 | 1.12 | 1.08 | 1.08 | 1.08 | 1.12 | 1.08 | 1.08 |
time (sec) |
N/A | 0.325 | 0.002 | 0.024 | 0.030 | 0.083 | 0.038 | 0.112 | 0.148 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | A | B | B | B | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 49 | 46 | 53 | 45 | 53 | 50 | 424 | 50 |
N.S. |
1 | 0.00 | 2.04 | 1.92 | 2.21 | 1.88 | 2.21 | 2.08 | 17.67 | 2.08 |
time (sec) |
N/A | 0.000 | 0.409 | 0.349 | 0.078 | 0.094 | 0.172 | 0.138 | 0.164 | 4.784 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 43 | 21 | 22 | 48 | 54 | 65 | 48 | 55 | 38 |
N.S. |
1 | 2.15 | 1.05 | 1.10 | 2.40 | 2.70 | 3.25 | 2.40 | 2.75 | 1.90 |
time (sec) |
N/A | 0.198 | 0.002 | 0.093 | 0.045 | 0.112 | 0.024 | 0.108 | 0.151 | 4.375 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | B | F(-1) | B | F | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 35 | 5397 | 132 | 64 | 0 | 211 | 1351 | 45 |
N.S. |
1 | 0.00 | 1.00 | 154.20 | 3.77 | 1.83 | 0.00 | 6.03 | 38.60 | 1.29 |
time (sec) |
N/A | 0.000 | 0.214 | 0.058 | 0.716 | 0.118 | 0.000 | 0.395 | 0.434 | 4.998 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 27 | 25 | 22 | 17 | 21 | 20 | 17 | 31 | 19 |
N.S. |
1 | 0.90 | 0.83 | 0.73 | 0.57 | 0.70 | 0.67 | 0.57 | 1.03 | 0.63 |
time (sec) |
N/A | 0.476 | 0.185 | 0.137 | 0.115 | 0.089 | 0.115 | 0.125 | 0.165 | 4.492 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 29 | 33 | 26 | 31 | 26 | 31 | 52 | 56 |
N.S. |
1 | 0.00 | 1.00 | 1.14 | 0.90 | 1.07 | 0.90 | 1.07 | 1.79 | 1.93 |
time (sec) |
N/A | 0.000 | 2.251 | 0.237 | 0.168 | 0.088 | 0.091 | 0.185 | 0.160 | 4.543 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 25 | 19 | 17 | 92 | 19 | 15 | 19 | 31 | 17 |
N.S. |
1 | 1.32 | 1.00 | 0.89 | 4.84 | 1.00 | 0.79 | 1.00 | 1.63 | 0.89 |
time (sec) |
N/A | 0.218 | 0.027 | 0.099 | 0.156 | 0.109 | 0.055 | 0.117 | 0.154 | 0.069 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 65 | 56 | 72 | 73 | 65 | 58 | 444 | 92 |
N.S. |
1 | 0.00 | 2.50 | 2.15 | 2.77 | 2.81 | 2.50 | 2.23 | 17.08 | 3.54 |
time (sec) |
N/A | 0.000 | 11.399 | 0.765 | 0.095 | 0.103 | 0.667 | 0.187 | 0.171 | 0.349 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 41 | 39 | 38 | 35 | 39 | 38 | 38 | 38 |
N.S. |
1 | 0.00 | 1.78 | 1.70 | 1.65 | 1.52 | 1.70 | 1.65 | 1.65 | 1.65 |
time (sec) |
N/A | 0.000 | 0.106 | 0.159 | 0.074 | 0.089 | 0.140 | 0.132 | 0.156 | 4.601 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 25 | 19 | 27 | 0 | 24 | 20 | 26 | 30 | 20 |
N.S. |
1 | 1.14 | 0.86 | 1.23 | 0.00 | 1.09 | 0.91 | 1.18 | 1.36 | 0.91 |
time (sec) |
N/A | 0.772 | 0.090 | 0.279 | 0.000 | 0.112 | 0.073 | 0.111 | 0.154 | 4.557 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 24 | 24 | 25 | 23 | 21 | 24 | 22 | 26 | 21 |
N.S. |
1 | 1.04 | 1.04 | 1.09 | 1.00 | 0.91 | 1.04 | 0.96 | 1.13 | 0.91 |
time (sec) |
N/A | 0.148 | 0.004 | 0.121 | 0.027 | 0.099 | 0.034 | 0.107 | 0.154 | 0.093 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-2) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 30 | 24 | 29 | 23 | 26 | 0 | 25 | 96 | 28 |
N.S. |
1 | 1.25 | 1.00 | 1.21 | 0.96 | 1.08 | 0.00 | 1.04 | 4.00 | 1.17 |
time (sec) |
N/A | 1.864 | 0.052 | 17.363 | 0.085 | 0.108 | 0.000 | 0.518 | 0.163 | 5.808 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 111 | 29 | 76 | 149 | 67 | 53 | 221 | 72 | 56 |
N.S. |
1 | 4.27 | 1.12 | 2.92 | 5.73 | 2.58 | 2.04 | 8.50 | 2.77 | 2.15 |
time (sec) |
N/A | 0.492 | 0.020 | 3.831 | 0.030 | 0.097 | 0.120 | 0.125 | 0.148 | 4.564 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 8 | 9 | 9 | 9 | 9 | 7 | 9 | 8 | 9 |
N.S. |
1 | 0.73 | 0.82 | 0.82 | 0.82 | 0.82 | 0.64 | 0.82 | 0.73 | 0.82 |
time (sec) |
N/A | 0.132 | 0.000 | 0.012 | 0.023 | 0.068 | 0.015 | 0.114 | 0.142 | 0.002 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 29 | 22 | 39 | 31 | 27 | 0 | 546 | 31 |
N.S. |
1 | 0.00 | 1.45 | 1.10 | 1.95 | 1.55 | 1.35 | 0.00 | 27.30 | 1.55 |
time (sec) |
N/A | 0.000 | 0.071 | 18.488 | 0.132 | 0.103 | 7.690 | 0.000 | 6.607 | 4.798 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | B | B | C | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 147 | 82 | 101 | 130 | 84 | 110 | 110 | 123 | 90 |
N.S. |
1 | 4.59 | 2.56 | 3.16 | 4.06 | 2.62 | 3.44 | 3.44 | 3.84 | 2.81 |
time (sec) |
N/A | 0.988 | 0.085 | 1.362 | 0.067 | 0.109 | 0.128 | 0.118 | 0.144 | 4.760 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | A | A | A | A | A | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 31 | 33 | 28 | 27 | 32 | 29 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.03 | 1.10 | 0.93 | 0.90 | 1.07 | 0.97 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 1.169 | 0.152 | 0.107 | 0.174 | 0.417 | 0.149 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | B | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 132 | 57 | 41 | 69 | 69 | 37 | 157 | 96 | 42 |
N.S. |
1 | 3.77 | 1.63 | 1.17 | 1.97 | 1.97 | 1.06 | 4.49 | 2.74 | 1.20 |
time (sec) |
N/A | 3.455 | 0.295 | 0.013 | 0.071 | 0.115 | 0.152 | 0.163 | 0.149 | 0.134 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 21 | 19 | 19 | 22 | 22 | 24 | 22 | 20 | 16 |
N.S. |
1 | 0.95 | 0.86 | 0.86 | 1.00 | 1.00 | 1.09 | 1.00 | 0.91 | 0.73 |
time (sec) |
N/A | 0.161 | 0.005 | 0.039 | 0.025 | 0.103 | 0.048 | 0.105 | 0.140 | 4.762 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 33 | 22 | 25 | 30 | 35 | 32 | 30 | 566 | 34 |
N.S. |
1 | 1.50 | 1.00 | 1.14 | 1.36 | 1.59 | 1.45 | 1.36 | 25.73 | 1.55 |
time (sec) |
N/A | 0.913 | 0.091 | 182.009 | 0.279 | 0.090 | 0.333 | 0.214 | 9.143 | 4.871 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 18 | 18 | 18 | 17 | 17 | 19 | 18 | 18 | 17 |
N.S. |
1 | 0.90 | 0.90 | 0.90 | 0.85 | 0.85 | 0.95 | 0.90 | 0.90 | 0.85 |
time (sec) |
N/A | 0.205 | 0.009 | 0.089 | 0.024 | 0.102 | 0.190 | 0.114 | 0.153 | 0.095 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 24 | 22 | 24 | 23 | 23 | 22 | 23 | 24 | 23 |
N.S. |
1 | 1.00 | 0.92 | 1.00 | 0.96 | 0.96 | 0.92 | 0.96 | 1.00 | 0.96 |
time (sec) |
N/A | 0.266 | 0.019 | 0.227 | 0.028 | 0.100 | 0.076 | 0.110 | 0.144 | 4.834 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 21 | 13 | 12 | 13 | 13 | 12 | 15 | 39 | 11 |
N.S. |
1 | 1.24 | 0.76 | 0.71 | 0.76 | 0.76 | 0.71 | 0.88 | 2.29 | 0.65 |
time (sec) |
N/A | 0.323 | 0.004 | 0.046 | 0.029 | 0.074 | 0.041 | 0.114 | 0.153 | 4.802 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 35 | 20 | 29 | 26 | 26 | 58 | 26 | 31 | 28 |
N.S. |
1 | 1.94 | 1.11 | 1.61 | 1.44 | 1.44 | 3.22 | 1.44 | 1.72 | 1.56 |
time (sec) |
N/A | 0.291 | 0.013 | 0.179 | 0.029 | 0.098 | 0.067 | 0.117 | 0.149 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 18 | 24 | 18 | 0 | 27 | 12 | 24 | 30 | 18 |
N.S. |
1 | 0.58 | 0.77 | 0.58 | 0.00 | 0.87 | 0.39 | 0.77 | 0.97 | 0.58 |
time (sec) |
N/A | 0.659 | 0.522 | 0.157 | 0.000 | 0.089 | 0.048 | 0.115 | 0.151 | 0.070 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 30 | 28 | 31 | 28 | 30 | 31 | 32 | 32 | 30 |
N.S. |
1 | 1.20 | 1.12 | 1.24 | 1.12 | 1.20 | 1.24 | 1.28 | 1.28 | 1.20 |
time (sec) |
N/A | 0.742 | 0.119 | 0.227 | 0.203 | 0.083 | 0.067 | 0.117 | 0.148 | 0.291 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | C | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 39 | 39 | 41 | 82 | 54 | 313 | 443 | 41 | 38 |
N.S. |
1 | 1.30 | 1.30 | 1.37 | 2.73 | 1.80 | 10.43 | 14.77 | 1.37 | 1.27 |
time (sec) |
N/A | 1.402 | 0.068 | 43.128 | 0.166 | 0.110 | 33.817 | 1.124 | 0.154 | 5.696 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 18 | 18 | 19 | 46 | 16 | 17 | 11 | 24 | 11 |
N.S. |
1 | 0.90 | 0.90 | 0.95 | 2.30 | 0.80 | 0.85 | 0.55 | 1.20 | 0.55 |
time (sec) |
N/A | 0.381 | 0.032 | 0.164 | 0.075 | 0.087 | 0.114 | 0.114 | 0.140 | 4.996 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | B | B | B | B | B |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 36 | 120 | 61 | 61 | 65 | 65 | 68 | 892 |
N.S. |
1 | 0.00 | 1.20 | 4.00 | 2.03 | 2.03 | 2.17 | 2.17 | 2.27 | 29.73 |
time (sec) |
N/A | 0.000 | 0.143 | 7.937 | 0.125 | 0.126 | 0.168 | 0.190 | 0.149 | 5.680 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 27 | 25 | 20 | 110 | 19 | 20 | 19 | 23 | 19 |
N.S. |
1 | 1.23 | 1.14 | 0.91 | 5.00 | 0.86 | 0.91 | 0.86 | 1.05 | 0.86 |
time (sec) |
N/A | 0.323 | 0.017 | 13.479 | 0.026 | 0.101 | 0.079 | 0.112 | 0.139 | 4.926 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 15 | 21 | 31 | 39 | 41 | 39 | 27 | 27 | 38 |
N.S. |
1 | 0.83 | 1.17 | 1.72 | 2.17 | 2.28 | 2.17 | 1.50 | 1.50 | 2.11 |
time (sec) |
N/A | 0.179 | 0.007 | 0.063 | 0.034 | 0.095 | 0.135 | 0.111 | 0.144 | 0.086 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 48 | 50 | 34 | 37 | 35 | 37 | 35 | 38 | 33 |
N.S. |
1 | 2.09 | 2.17 | 1.48 | 1.61 | 1.52 | 1.61 | 1.52 | 1.65 | 1.43 |
time (sec) |
N/A | 1.238 | 0.120 | 1.207 | 0.162 | 0.104 | 0.196 | 0.122 | 0.146 | 4.881 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 17 | 15 | 14 | 13 | 15 | 10 | 13 | 17 | 13 |
N.S. |
1 | 0.89 | 0.79 | 0.74 | 0.68 | 0.79 | 0.53 | 0.68 | 0.89 | 0.68 |
time (sec) |
N/A | 0.201 | 0.001 | 0.033 | 0.028 | 0.072 | 0.036 | 0.117 | 0.145 | 0.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 24 | 26 | 22 | 23 | 23 | 19 | 23 | 25 | 20 |
N.S. |
1 | 1.14 | 1.24 | 1.05 | 1.10 | 1.10 | 0.90 | 1.10 | 1.19 | 0.95 |
time (sec) |
N/A | 0.250 | 0.004 | 0.049 | 0.035 | 0.089 | 0.025 | 0.114 | 0.151 | 4.682 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 22 | 21 | 20 | 21 | 19 | 29 | 21 | 21 |
N.S. |
1 | 0.00 | 0.79 | 0.75 | 0.71 | 0.75 | 0.68 | 1.04 | 0.75 | 0.75 |
time (sec) |
N/A | 0.000 | 0.180 | 0.113 | 0.063 | 0.089 | 0.089 | 0.113 | 0.156 | 3.701 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 0 | 25 | 40 | 38 | 37 | 37 | 62 | 41 | 28 |
N.S. |
1 | 0.00 | 0.66 | 1.05 | 1.00 | 0.97 | 0.97 | 1.63 | 1.08 | 0.74 |
time (sec) |
N/A | 0.000 | 5.027 | 0.153 | 0.147 | 0.087 | 0.074 | 0.115 | 0.159 | 3.702 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 40 | 24 | 18 | 0 | 17 | 26 | 41 | 18 | 21 |
N.S. |
1 | 1.67 | 1.00 | 0.75 | 0.00 | 0.71 | 1.08 | 1.71 | 0.75 | 0.88 |
time (sec) |
N/A | 0.289 | 0.197 | 0.208 | 0.000 | 0.094 | 0.112 | 0.119 | 0.154 | 3.795 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 10 | 10 | 8 | 12 | 7 | 8 | 7 | 8 | 7 |
N.S. |
1 | 0.77 | 0.77 | 0.62 | 0.92 | 0.54 | 0.62 | 0.54 | 0.62 | 0.54 |
time (sec) |
N/A | 0.187 | 0.001 | 0.050 | 0.056 | 0.078 | 0.039 | 0.111 | 0.154 | 3.673 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 0 | 23 | 24 | 37 | 23 | 22 | 23 | 62 | 23 |
N.S. |
1 | 0.00 | 1.28 | 1.33 | 2.06 | 1.28 | 1.22 | 1.28 | 3.44 | 1.28 |
time (sec) |
N/A | 0.000 | 0.293 | 0.326 | 0.079 | 0.089 | 0.108 | 0.139 | 0.153 | 3.899 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 47 | 39 | 40 | 48 | 40 | 37 | 39 | 28 | 14 |
N.S. |
1 | 2.61 | 2.17 | 2.22 | 2.67 | 2.22 | 2.06 | 2.17 | 1.56 | 0.78 |
time (sec) |
N/A | 0.223 | 0.008 | 0.215 | 0.025 | 0.085 | 0.060 | 0.108 | 0.151 | 3.765 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 16 | 16 | 14 | 13 | 13 | 0 | 13 | 16 | 13 |
N.S. |
1 | 1.00 | 1.00 | 0.88 | 0.81 | 0.81 | 0.00 | 0.81 | 1.00 | 0.81 |
time (sec) |
N/A | 0.146 | 0.000 | 0.093 | 0.029 | 0.093 | 0.000 | 0.111 | 0.155 | 3.539 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 51 | 19 | 25 | 0 | 22 | 26 | 24 | 27 | 18 |
N.S. |
1 | 2.43 | 0.90 | 1.19 | 0.00 | 1.05 | 1.24 | 1.14 | 1.29 | 0.86 |
time (sec) |
N/A | 0.847 | 0.224 | 0.307 | 0.000 | 0.099 | 0.091 | 0.120 | 0.151 | 3.695 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 13 | 13 | 14 | 13 | 17 | 7 | 13 | 21 | 13 |
N.S. |
1 | 0.48 | 0.48 | 0.52 | 0.48 | 0.63 | 0.26 | 0.48 | 0.78 | 0.48 |
time (sec) |
N/A | 0.178 | 0.005 | 0.030 | 0.023 | 0.075 | 0.033 | 0.115 | 0.150 | 3.608 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 36 | 23 | 21 | 29 | 23 | 17 | 23 | 28 | 20 |
N.S. |
1 | 1.71 | 1.10 | 1.00 | 1.38 | 1.10 | 0.81 | 1.10 | 1.33 | 0.95 |
time (sec) |
N/A | 0.616 | 0.392 | 0.126 | 0.077 | 0.084 | 0.062 | 0.119 | 0.164 | 3.652 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 17 | 17 | 28 | 35 | 26 | 14 | 17 | 27 | 17 |
N.S. |
1 | 0.94 | 0.94 | 1.56 | 1.94 | 1.44 | 0.78 | 0.94 | 1.50 | 0.94 |
time (sec) |
N/A | 0.588 | 0.019 | 0.664 | 0.079 | 0.090 | 0.086 | 0.604 | 0.160 | 3.742 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | C | B | B | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 28 | 65 | 105 | 59 | 100 | 70 | 89 | 94 |
N.S. |
1 | 0.00 | 1.12 | 2.60 | 4.20 | 2.36 | 4.00 | 2.80 | 3.56 | 3.76 |
time (sec) |
N/A | 0.000 | 0.366 | 0.554 | 0.179 | 0.100 | 0.254 | 0.133 | 0.160 | 3.866 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 16 | 10 | 10 | 8 | 7 | 9 | 7 | 7 | 8 | 8 |
N.S. |
1 | 0.62 | 0.62 | 0.50 | 0.44 | 0.56 | 0.44 | 0.44 | 0.50 | 0.50 |
time (sec) |
N/A | 0.163 | 0.000 | 0.019 | 0.025 | 0.067 | 0.014 | 0.113 | 0.157 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 16 | 16 | 18 | 17 | 19 | 19 | 17 | 19 | 16 |
N.S. |
1 | 0.94 | 0.94 | 1.06 | 1.00 | 1.12 | 1.12 | 1.00 | 1.12 | 0.94 |
time (sec) |
N/A | 0.233 | 0.000 | 0.039 | 0.032 | 0.081 | 0.013 | 0.103 | 0.161 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | B | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 0 | 14 | 13 | 13 | 43 | 14 | 43 | 16 | 12 |
N.S. |
1 | 0.00 | 0.93 | 0.87 | 0.87 | 2.87 | 0.93 | 2.87 | 1.07 | 0.80 |
time (sec) |
N/A | 0.000 | 0.054 | 0.179 | 0.147 | 0.091 | 0.217 | 0.140 | 0.161 | 3.755 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 21 | 25 | 27 | 21 | 19 | 21 | 25 | 22 |
N.S. |
1 | 0.00 | 0.91 | 1.09 | 1.17 | 0.91 | 0.83 | 0.91 | 1.09 | 0.96 |
time (sec) |
N/A | 0.000 | 0.013 | 0.107 | 0.106 | 0.086 | 0.048 | 0.111 | 0.159 | 3.658 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 31 | 21 | 21 | 21 | 25 | 15 | 21 | 25 | 21 |
N.S. |
1 | 1.24 | 0.84 | 0.84 | 0.84 | 1.00 | 0.60 | 0.84 | 1.00 | 0.84 |
time (sec) |
N/A | 0.252 | 0.007 | 0.036 | 0.025 | 0.087 | 0.039 | 0.118 | 0.163 | 3.595 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | B | A | F | F | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 0 | 35 | 17 | 27 | 43 | 14 | 0 | 256 | 28 |
N.S. |
1 | 0.00 | 1.75 | 0.85 | 1.35 | 2.15 | 0.70 | 0.00 | 12.80 | 1.40 |
time (sec) |
N/A | 0.000 | 0.280 | 0.201 | 0.242 | 0.091 | 0.133 | 0.000 | 0.204 | 0.132 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | C | B | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 116 | 78 | 81 | 86 | 71 | 151 | 106 | 0 |
N.S. |
1 | 0.00 | 3.87 | 2.60 | 2.70 | 2.87 | 2.37 | 5.03 | 3.53 | 0.00 |
time (sec) |
N/A | 0.000 | 0.194 | 0.029 | 0.102 | 0.093 | 0.304 | 0.178 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 37 | 20 | 18 | 17 | 20 | 17 | 20 | 34 | 19 |
N.S. |
1 | 1.61 | 0.87 | 0.78 | 0.74 | 0.87 | 0.74 | 0.87 | 1.48 | 0.83 |
time (sec) |
N/A | 0.287 | 0.006 | 0.055 | 0.026 | 0.083 | 0.196 | 0.114 | 0.164 | 0.050 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 0 | 17 | 16 | 13 | 26 | 15 | 28 | 17 | 15 |
N.S. |
1 | 0.00 | 1.00 | 0.94 | 0.76 | 1.53 | 0.88 | 1.65 | 1.00 | 0.88 |
time (sec) |
N/A | 0.000 | 0.185 | 0.211 | 0.068 | 0.110 | 0.140 | 0.128 | 0.158 | 3.823 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 11 | 9 | 9 | 8 | 7 | 7 | 7 | 7 | 11 | 8 |
N.S. |
1 | 0.82 | 0.82 | 0.73 | 0.64 | 0.64 | 0.64 | 0.64 | 1.00 | 0.73 |
time (sec) |
N/A | 0.171 | 0.007 | 0.029 | 0.025 | 0.094 | 0.049 | 0.116 | 0.161 | 0.032 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | B | B | F | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 0 | 44 | 59 | 123 | 118 | 126 | 364 | 0 | 0 |
N.S. |
1 | 0.00 | 1.26 | 1.69 | 3.51 | 3.37 | 3.60 | 10.40 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 4.585 | 0.893 | 0.241 | 0.092 | 0.354 | 0.232 | 0.211 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 22 | 20 | 15 | 0 | 14 | 15 | 0 | 16 | 12 |
N.S. |
1 | 1.10 | 1.00 | 0.75 | 0.00 | 0.70 | 0.75 | 0.00 | 0.80 | 0.60 |
time (sec) |
N/A | 0.274 | 0.013 | 0.072 | 0.000 | 0.088 | 0.070 | 0.000 | 0.167 | 3.524 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | F | A | F(-2) | F(-1) | F | B | F(-1) |
verified | N/A | N/A | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 41 | 0 | 33 | 0 | 0 | 0 | 40 | 0 |
N.S. |
1 | 0.00 | 1.32 | 0.00 | 1.06 | 0.00 | 0.00 | 0.00 | 1.29 | 0.00 |
time (sec) |
N/A | 0.000 | 0.554 | 0.000 | 0.107 | 0.000 | 0.000 | 0.000 | 0.199 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 60 | 39 | 36 | 96 | 33 | 42 | 33 | 57 | 51 |
N.S. |
1 | 2.14 | 1.39 | 1.29 | 3.43 | 1.18 | 1.50 | 1.18 | 2.04 | 1.82 |
time (sec) |
N/A | 0.528 | 2.321 | 0.185 | 0.034 | 0.088 | 0.077 | 0.112 | 0.161 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | A | A | F(-1) | A | B | F(-1) |
verified | N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 0 | 29 | 329 | 27 | 28 | 0 | 32 | 39 | 0 |
N.S. |
1 | 0.00 | 0.94 | 10.61 | 0.87 | 0.90 | 0.00 | 1.03 | 1.26 | 0.00 |
time (sec) |
N/A | 0.000 | 0.055 | 15.860 | 0.333 | 0.098 | 0.000 | 1.787 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | A | F | B | B |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 36 | 29 | 92 | 40 | 37 | 0 | 85 | 96 |
N.S. |
1 | 0.00 | 1.44 | 1.16 | 3.68 | 1.60 | 1.48 | 0.00 | 3.40 | 3.84 |
time (sec) |
N/A | 0.000 | 0.127 | 0.575 | 0.322 | 0.091 | 0.300 | 0.000 | 67.478 | 0.184 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 30 | 15 | 13 | 0 | 12 | 14 | 12 | 19 | 12 |
N.S. |
1 | 2.00 | 1.00 | 0.87 | 0.00 | 0.80 | 0.93 | 0.80 | 1.27 | 0.80 |
time (sec) |
N/A | 0.590 | 0.204 | 0.133 | 0.000 | 0.083 | 0.071 | 0.112 | 0.162 | 0.047 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 66 | 65 | 64 | 58 | 53 | 57 | 62 | 0 |
N.S. |
1 | 0.00 | 2.54 | 2.50 | 2.46 | 2.23 | 2.04 | 2.19 | 2.38 | 0.00 |
time (sec) |
N/A | 0.000 | 0.134 | 0.017 | 0.131 | 0.103 | 1.774 | 0.339 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 12 | 9 | 9 | 9 | 8 | 8 | 7 | 8 | 9 | 8 |
N.S. |
1 | 0.75 | 0.75 | 0.75 | 0.67 | 0.67 | 0.58 | 0.67 | 0.75 | 0.67 |
time (sec) |
N/A | 0.144 | 0.001 | 0.029 | 0.028 | 0.093 | 0.034 | 0.106 | 0.164 | 0.019 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 35 | 31 | 25 | 28 | 34 | 24 | 23 | 24 | 23 |
N.S. |
1 | 1.35 | 1.19 | 0.96 | 1.08 | 1.31 | 0.92 | 0.88 | 0.92 | 0.88 |
time (sec) |
N/A | 0.249 | 0.008 | 0.036 | 0.022 | 0.073 | 0.051 | 0.111 | 0.157 | 3.291 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 26 | 21 | 17 | 22 | 16 | 19 | 16 | 17 | 16 |
N.S. |
1 | 1.13 | 0.91 | 0.74 | 0.96 | 0.70 | 0.83 | 0.70 | 0.74 | 0.70 |
time (sec) |
N/A | 0.194 | 0.009 | 0.170 | 0.029 | 0.089 | 0.069 | 0.111 | 0.151 | 0.030 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 17 | 17 | 17 | 16 | 18 | 15 | 18 | 17 | 17 |
N.S. |
1 | 0.81 | 0.81 | 0.81 | 0.76 | 0.86 | 0.71 | 0.86 | 0.81 | 0.81 |
time (sec) |
N/A | 0.236 | 0.007 | 0.116 | 0.028 | 0.078 | 0.137 | 0.117 | 0.151 | 0.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 38 | 45 | 37 | 40 | 24 | 50 | 52 | 0 |
N.S. |
1 | 0.00 | 1.27 | 1.50 | 1.23 | 1.33 | 0.80 | 1.67 | 1.73 | 0.00 |
time (sec) |
N/A | 0.000 | 0.061 | 0.839 | 0.164 | 0.096 | 0.194 | 0.128 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | B | B | B | B | B | B | F(-1) |
verified | N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 0 | 44 | 65 | 63 | 46 | 44 | 50 | 0 |
N.S. |
1 | 0.00 | 0.00 | 2.00 | 2.95 | 2.86 | 2.09 | 2.00 | 2.27 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.141 | 0.140 | 0.089 | 0.586 | 0.119 | 0.156 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | A | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 33 | 30 | 26 | 0 | 37 | 27 | 0 | 66 | 27 |
N.S. |
1 | 1.22 | 1.11 | 0.96 | 0.00 | 1.37 | 1.00 | 0.00 | 2.44 | 1.00 |
time (sec) |
N/A | 1.424 | 1.032 | 0.638 | 0.000 | 0.098 | 0.461 | 0.000 | 200.022 | 3.392 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 38 | 26 | 23 | 25 | 26 | 26 | 23 | 35 | 23 |
N.S. |
1 | 1.31 | 0.90 | 0.79 | 0.86 | 0.90 | 0.90 | 0.79 | 1.21 | 0.79 |
time (sec) |
N/A | 0.282 | 0.011 | 0.130 | 0.033 | 0.077 | 0.480 | 0.115 | 0.173 | 3.402 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 17 | 17 | 16 | 30 | 15 | 12 | 15 | 15 | 15 |
N.S. |
1 | 0.74 | 0.74 | 0.70 | 1.30 | 0.65 | 0.52 | 0.65 | 0.65 | 0.65 |
time (sec) |
N/A | 0.920 | 0.149 | 0.379 | 0.317 | 0.088 | 0.076 | 0.134 | 0.159 | 3.398 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | B | A | B | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 849 | 40 | 33 | 912 | 42 | 54 | 48 | 89 | 55 |
N.S. |
1 | 29.28 | 1.38 | 1.14 | 31.45 | 1.45 | 1.86 | 1.66 | 3.07 | 1.90 |
time (sec) |
N/A | 2.023 | 3.137 | 1.814 | 0.084 | 0.097 | 0.414 | 0.160 | 0.157 | 3.669 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | F(-1) |
verified | N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 29 | 32 | 29 | 29 | 20 | 29 | 31 | 0 |
N.S. |
1 | 0.00 | 0.97 | 1.07 | 0.97 | 0.97 | 0.67 | 0.97 | 1.03 | 0.00 |
time (sec) |
N/A | 0.000 | 0.062 | 1.501 | 0.090 | 0.083 | 0.161 | 0.246 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | C | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 104 | 35 | 33 | 42 | 36 | 26 | 32 | 34 | 34 |
N.S. |
1 | 3.35 | 1.13 | 1.06 | 1.35 | 1.16 | 0.84 | 1.03 | 1.10 | 1.10 |
time (sec) |
N/A | 0.871 | 0.058 | 0.643 | 0.141 | 0.101 | 0.094 | 0.145 | 0.163 | 0.106 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 17 | 14 | 15 | 15 | 14 | 12 | 18 | 15 | 14 |
N.S. |
1 | 0.74 | 0.61 | 0.65 | 0.65 | 0.61 | 0.52 | 0.78 | 0.65 | 0.61 |
time (sec) |
N/A | 0.256 | 0.005 | 0.037 | 0.029 | 0.078 | 0.054 | 0.110 | 0.152 | 0.038 |