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 | F | F | F | F(-1) | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 136 | 79 | 74 | 0 | 0 | 0 | 0 | 0 | 139 | 0 |
N.S. |
1 | 0.58 | 0.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.517 | 0.041 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 84 | 86 | 86 | 0 | 0 | 0 | 0 | 0 | 89 | 0 |
N.S. |
1 | 1.02 | 1.02 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.06 | 0.00 |
time (sec) |
N/A | 0.381 | 0.027 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F(-1) | F | F | F(-1) |
verified | N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 300 | 360 | 42 | 0 | 0 | 282 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.20 | 0.14 | 0.00 | 0.00 | 0.94 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.620 | 0.019 | 0.000 | 0.000 | 0.090 | 0.000 | 0.000 | 200.020 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified | N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 248 | 298 | 42 | 0 | 0 | 266 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.20 | 0.17 | 0.00 | 0.00 | 1.07 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.531 | 0.016 | 0.000 | 0.000 | 0.109 | 0.000 | 0.000 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified | N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 236 | 42 | 0 | 0 | 250 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.20 | 0.21 | 0.00 | 0.00 | 1.28 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.467 | 0.010 | 0.000 | 0.000 | 0.117 | 0.000 | 0.000 | 200.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | A | F | F | F | F(-1) |
verified | N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 137 | 181 | 40 | 0 | 0 | 206 | 0 | 0 | 35 | 0 |
N.S. |
1 | 1.32 | 0.29 | 0.00 | 0.00 | 1.50 | 0.00 | 0.00 | 0.26 | 0.00 |
time (sec) |
N/A | 0.417 | 0.009 | 0.000 | 0.000 | 0.082 | 0.000 | 0.000 | 200.022 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 37 | 37 | 32 | 54 | 0 | 56 | 0 | 0 | 33 | 69 |
N.S. |
1 | 1.00 | 0.86 | 1.46 | 0.00 | 1.51 | 0.00 | 0.00 | 0.89 | 1.86 |
time (sec) |
N/A | 0.233 | 0.011 | 0.234 | 0.000 | 0.070 | 0.000 | 0.000 | 0.161 | 26.643 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 75 | 75 | 48 | 70 | 0 | 78 | 0 | 0 | 65 | 115 |
N.S. |
1 | 1.00 | 0.64 | 0.93 | 0.00 | 1.04 | 0.00 | 0.00 | 0.87 | 1.53 |
time (sec) |
N/A | 0.353 | 0.019 | 0.244 | 0.000 | 0.085 | 0.000 | 0.000 | 0.155 | 26.513 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 112 | 117 | 64 | 86 | 0 | 104 | 0 | 0 | 96 | 165 |
N.S. |
1 | 1.04 | 0.57 | 0.77 | 0.00 | 0.93 | 0.00 | 0.00 | 0.86 | 1.47 |
time (sec) |
N/A | 0.507 | 0.026 | 0.240 | 0.000 | 0.079 | 0.000 | 0.000 | 0.149 | 26.814 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 149 | 159 | 80 | 102 | 0 | 126 | 0 | 0 | 129 | 211 |
N.S. |
1 | 1.07 | 0.54 | 0.68 | 0.00 | 0.85 | 0.00 | 0.00 | 0.87 | 1.42 |
time (sec) |
N/A | 0.625 | 0.030 | 0.253 | 0.000 | 0.082 | 0.000 | 0.000 | 0.177 | 27.091 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 588 | 393 | 74 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.67 | 0.13 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.06 | 0.00 |
time (sec) |
N/A | 0.736 | 0.035 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 458 | 329 | 72 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.72 | 0.16 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.08 | 0.00 |
time (sec) |
N/A | 0.663 | 0.028 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.023 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 341 | 266 | 71 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.78 | 0.21 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.607 | 0.026 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.029 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | F | F(-1) |
verified | N/A | No | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 224 | 210 | 69 | 0 | 0 | 0 | 0 | 0 | 36 | 0 |
N.S. |
1 | 0.94 | 0.31 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.555 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 200.030 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 64 | 55 | 0 | 0 | 0 | 0 | 38 | 49 |
N.S. |
1 | 1.00 | 1.56 | 1.34 | 0.00 | 0.00 | 0.00 | 0.00 | 0.93 | 1.20 |
time (sec) |
N/A | 0.249 | 0.026 | 0.243 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 26.818 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 83 | 83 | 80 | 71 | 0 | 0 | 0 | 0 | 70 | 97 |
N.S. |
1 | 1.00 | 0.96 | 0.86 | 0.00 | 0.00 | 0.00 | 0.00 | 0.84 | 1.17 |
time (sec) |
N/A | 0.377 | 0.044 | 0.258 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 26.680 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 124 | 132 | 96 | 87 | 0 | 0 | 0 | 0 | 101 | 139 |
N.S. |
1 | 1.06 | 0.77 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.81 | 1.12 |
time (sec) |
N/A | 0.533 | 0.054 | 0.246 | 0.000 | 0.000 | 0.000 | 0.000 | 0.174 | 26.765 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F(-2) | F(-1) | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 165 | 181 | 112 | 103 | 0 | 0 | 0 | 0 | 134 | 183 |
N.S. |
1 | 1.10 | 0.68 | 0.62 | 0.00 | 0.00 | 0.00 | 0.00 | 0.81 | 1.11 |
time (sec) |
N/A | 0.715 | 0.056 | 0.257 | 0.000 | 0.000 | 0.000 | 0.000 | 0.161 | 26.892 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F(-1) | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 201 | 106 | 84 | 0 | 0 | 0 | 0 | 0 | 83 | 0 |
N.S. |
1 | 0.53 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.41 | 0.00 |
time (sec) |
N/A | 0.569 | 0.039 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F(-1) | F | B | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 90 | 70 | 0 | 0 | 0 | 0 | 0 | 60 | 0 |
N.S. |
1 | 0.59 | 0.46 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.547 | 0.032 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F(-1) | F | B | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 74 | 74 | 0 | 0 | 0 | 0 | 0 | 61 | 0 |
N.S. |
1 | 0.70 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.58 | 0.00 |
time (sec) |
N/A | 0.434 | 0.059 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.153 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F | F | B | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 106 | 75 | 64 | 0 | 0 | 0 | 0 | 0 | 56 | 0 |
N.S. |
1 | 0.71 | 0.60 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 | 0.00 |
time (sec) |
N/A | 0.370 | 0.012 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F(-1) | F | B | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 144 | 85 | 79 | 0 | 0 | 0 | 0 | 0 | 174 | 0 |
N.S. |
1 | 0.59 | 0.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.21 | 0.00 |
time (sec) |
N/A | 0.518 | 0.031 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | C | F | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 196 | 104 | 86 | 0 | 0 | 0 | 0 | 0 | 83 | 0 |
N.S. |
1 | 0.53 | 0.44 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.42 | 0.00 |
time (sec) |
N/A | 0.527 | 0.034 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.196 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F(-1) | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 252 | 145 | 107 | 0 | 0 | 0 | 0 | 0 | 51 | 0 |
N.S. |
1 | 0.58 | 0.42 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.20 | 0.00 |
time (sec) |
N/A | 0.529 | 0.063 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.596 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F(-1) | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 63 | 54 | 28 | 0 | 0 | 0 | 51 | 52 |
N.S. |
1 | 1.00 | 1.54 | 1.32 | 0.68 | 0.00 | 0.00 | 0.00 | 1.24 | 1.27 |
time (sec) |
N/A | 0.302 | 0.022 | 0.257 | 0.454 | 0.000 | 0.000 | 0.000 | 0.382 | 26.601 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 102 | 93 | 0 | 0 | 0 | 0 | 0 | 126 | 0 |
N.S. |
1 | 0.77 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.95 | 0.00 |
time (sec) |
N/A | 0.433 | 0.040 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.378 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 74 | 74 | 69 | 0 | 0 | 0 | 0 | 0 | 48 | 0 |
N.S. |
1 | 1.00 | 0.93 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.65 | 0.00 |
time (sec) |
N/A | 0.356 | 0.018 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.423 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 78 | 73 | 0 | 0 | 0 | 0 | 0 | 0 | 279 | 0 |
N.S. |
1 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 3.58 | 0.00 |
time (sec) |
N/A | 0.477 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 2.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F(-1) | F(-1) | F | F | F(-1) |
verified | N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 74 | 0 | 0 | 0 | 0 | 0 | 0 | 422 | 0 |
N.S. |
1 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 5.34 | 0.00 |
time (sec) |
N/A | 0.495 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 1.376 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 68 | 70 | 65 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.03 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.47 | 0.00 |
time (sec) |
N/A | 0.263 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 72 | 67 | 0 | 0 | 0 | 0 | 0 | 52 | 0 |
N.S. |
1 | 1.03 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.74 | 0.00 |
time (sec) |
N/A | 0.279 | 0.021 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 72 | 67 | 0 | 0 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 1.03 | 0.96 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.276 | 0.024 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 226 | 211 | 172 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.93 | 0.76 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.500 | 0.125 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 185 | 160 | 120 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.86 | 0.65 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.16 | 0.00 |
time (sec) |
N/A | 0.406 | 0.048 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 86 | 1 | 82 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.01 | 0.95 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.35 | 0.00 |
time (sec) |
N/A | 0.303 | 0.020 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.152 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 94 | 92 | 74 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.98 | 0.79 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.30 | 0.00 |
time (sec) |
N/A | 0.319 | 0.011 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 18 | 33 | 18 | 31 | 28 | 41 | 0 | 18 | 31 |
N.S. |
1 | 1.00 | 1.83 | 1.00 | 1.72 | 1.56 | 2.28 | 0.00 | 1.00 | 1.72 |
time (sec) |
N/A | 0.232 | 0.005 | 1.223 | 0.039 | 0.085 | 0.664 | 0.000 | 0.145 | 26.232 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 90 | 88 | 85 | 0 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 0.98 | 0.94 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.338 | 0.032 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 123 | 119 | 103 | 0 | 0 | 0 | 0 | 0 | 64 | 0 |
N.S. |
1 | 0.97 | 0.84 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.52 | 0.00 |
time (sec) |
N/A | 0.374 | 0.038 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.150 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 376 | 367 | 178 | 0 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.98 | 0.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.648 | 0.089 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 311 | 296 | 145 | 0 | 0 | 0 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.95 | 0.47 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.544 | 0.209 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 79 | 79 | 65 | 62 | 0 | 92 | 0 | 0 | 71 | 93 |
N.S. |
1 | 1.00 | 0.82 | 0.78 | 0.00 | 1.16 | 0.00 | 0.00 | 0.90 | 1.18 |
time (sec) |
N/A | 0.434 | 0.045 | 6.863 | 0.000 | 0.076 | 0.000 | 0.000 | 0.151 | 26.776 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 69 | 108 | 56 | 47 | 0 | 79 | 0 | 0 | 56 | 46 |
N.S. |
1 | 1.57 | 0.81 | 0.68 | 0.00 | 1.14 | 0.00 | 0.00 | 0.81 | 0.67 |
time (sec) |
N/A | 0.526 | 0.033 | 6.837 | 0.000 | 0.074 | 0.000 | 0.000 | 0.145 | 26.720 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 72 | 72 | 68 | 55 | 0 | 80 | 0 | 0 | 65 | 93 |
N.S. |
1 | 1.00 | 0.94 | 0.76 | 0.00 | 1.11 | 0.00 | 0.00 | 0.90 | 1.29 |
time (sec) |
N/A | 0.368 | 0.027 | 6.842 | 0.000 | 0.075 | 0.000 | 0.000 | 0.145 | 26.666 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 190 | 184 | 121 | 0 | 0 | 0 | 0 | 0 | 34 | 0 |
N.S. |
1 | 0.97 | 0.64 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.448 | 0.050 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 239 | 233 | 163 | 0 | 0 | 0 | 0 | 0 | 276 | 0 |
N.S. |
1 | 0.97 | 0.68 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.15 | 0.00 |
time (sec) |
N/A | 0.527 | 0.054 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.157 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 127 | 124 | 111 | 101 | 0 | 175 | 0 | 0 | 147 | 179 |
N.S. |
1 | 0.98 | 0.87 | 0.80 | 0.00 | 1.38 | 0.00 | 0.00 | 1.16 | 1.41 |
time (sec) |
N/A | 0.543 | 0.065 | 25.888 | 0.000 | 0.213 | 0.000 | 0.000 | 0.146 | 26.950 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 197 | 176 | 170 | 167 | 0 | 310 | 0 | 0 | 281 | 301 |
N.S. |
1 | 0.89 | 0.86 | 0.85 | 0.00 | 1.57 | 0.00 | 0.00 | 1.43 | 1.53 |
time (sec) |
N/A | 0.757 | 0.103 | 96.634 | 0.000 | 0.081 | 0.000 | 0.000 | 0.148 | 27.192 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 319 | 209 | 236 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.66 | 0.74 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.618 | 0.400 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.200 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 244 | 195 | 135 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.80 | 0.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.11 | 0.00 |
time (sec) |
N/A | 0.571 | 0.203 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 173 | 145 | 125 | 0 | 0 | 0 | 0 | 0 | 26 | 0 |
N.S. |
1 | 0.84 | 0.72 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.484 | 0.132 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 101 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.24 | 0.00 |
time (sec) |
N/A | 0.385 | 0.044 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.168 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 269 | 225 | 207 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.84 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.639 | 0.159 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.166 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 268 | 211 | 138 | 0 | 0 | 0 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.79 | 0.51 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.10 | 0.00 |
time (sec) |
N/A | 0.601 | 0.142 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 105 | 105 | 102 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.54 | 0.00 |
time (sec) |
N/A | 0.401 | 0.076 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.184 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified | N/A | No | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 340 | 226 | 187 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 0.66 | 0.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 |
time (sec) |
N/A | 0.661 | 0.276 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.179 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 253 | 204 | 141 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 0.81 | 0.56 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.618 | 0.164 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 176 | 151 | 124 | 0 | 0 | 0 | 0 | 0 | 30 | 0 |
N.S. |
1 | 0.86 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.484 | 0.086 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 104 | 104 | 101 | 0 | 0 | 0 | 0 | 0 | 29 | 0 |
N.S. |
1 | 1.00 | 0.97 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.28 | 0.00 |
time (sec) |
N/A | 0.388 | 0.033 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.171 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 101 | 101 | 99 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 1.00 | 0.98 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.32 | 0.00 |
time (sec) |
N/A | 0.481 | 0.040 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.172 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 167 | 139 | 117 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 0.83 | 0.70 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.19 | 0.00 |
time (sec) |
N/A | 0.530 | 0.066 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 242 | 186 | 134 | 0 | 0 | 0 | 0 | 0 | 32 | 0 |
N.S. |
1 | 0.77 | 0.55 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.13 | 0.00 |
time (sec) |
N/A | 0.576 | 0.077 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.183 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F(-2) | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 325 | 212 | 186 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.65 | 0.57 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.672 | 0.215 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.170 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 153 | 153 | 155 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 1.00 | 1.01 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.37 | 0.00 |
time (sec) |
N/A | 0.664 | 0.127 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 81 | 49 | 0 | 83 | 0 | 0 | 55 | 68 |
N.S. |
1 | 1.00 | 1.76 | 1.07 | 0.00 | 1.80 | 0.00 | 0.00 | 1.20 | 1.48 |
time (sec) |
N/A | 0.299 | 0.064 | 0.204 | 0.000 | 0.075 | 0.000 | 0.000 | 0.169 | 26.485 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 46 | 46 | 81 | 49 | 0 | 81 | 0 | 0 | 54 | 65 |
N.S. |
1 | 1.00 | 1.76 | 1.07 | 0.00 | 1.76 | 0.00 | 0.00 | 1.17 | 1.41 |
time (sec) |
N/A | 0.262 | 0.065 | 0.197 | 0.000 | 0.081 | 0.000 | 0.000 | 0.171 | 26.583 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 243 | 192 | 149 | 0 | 0 | 0 | 0 | 0 | 55 | 0 |
N.S. |
1 | 0.79 | 0.61 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.633 | 0.153 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.188 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 321 | 238 | 173 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.74 | 0.54 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.18 | 0.00 |
time (sec) |
N/A | 0.668 | 0.166 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 417 | 291 | 219 | 0 | 0 | 0 | 0 | 0 | 57 | 0 |
N.S. |
1 | 0.70 | 0.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.756 | 0.225 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.182 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F(-2) | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 394 | 275 | 112 | 93 | 0 | 176 | 0 | 0 | 73 | 162 |
N.S. |
1 | 0.70 | 0.28 | 0.24 | 0.00 | 0.45 | 0.00 | 0.00 | 0.19 | 0.41 |
time (sec) |
N/A | 0.679 | 0.199 | 0.204 | 0.000 | 0.091 | 0.000 | 0.000 | 0.174 | 26.623 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 108 | 125 | 96 | 0 | 181 | 0 | 0 | 73 | 162 |
N.S. |
1 | 1.06 | 1.23 | 0.94 | 0.00 | 1.77 | 0.00 | 0.00 | 0.72 | 1.59 |
time (sec) |
N/A | 0.499 | 0.177 | 0.325 | 0.000 | 0.082 | 0.000 | 0.000 | 0.174 | 26.704 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 133 | 144 | 114 | 86 | 0 | 172 | 0 | 0 | 71 | 163 |
N.S. |
1 | 1.08 | 0.86 | 0.65 | 0.00 | 1.29 | 0.00 | 0.00 | 0.53 | 1.23 |
time (sec) |
N/A | 0.605 | 0.184 | 0.203 | 0.000 | 0.133 | 0.000 | 0.000 | 0.177 | 26.745 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 102 | 102 | 123 | 84 | 0 | 166 | 0 | 0 | 70 | 160 |
N.S. |
1 | 1.00 | 1.21 | 0.82 | 0.00 | 1.63 | 0.00 | 0.00 | 0.69 | 1.57 |
time (sec) |
N/A | 0.426 | 0.148 | 0.200 | 0.000 | 0.080 | 0.000 | 0.000 | 0.177 | 26.705 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 417 | 295 | 222 | 0 | 0 | 0 | 0 | 0 | 72 | 0 |
N.S. |
1 | 0.71 | 0.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.17 | 0.00 |
time (sec) |
N/A | 0.784 | 0.220 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.180 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 507 | 351 | 268 | 0 | 0 | 0 | 0 | 0 | 74 | 0 |
N.S. |
1 | 0.69 | 0.53 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.15 | 0.00 |
time (sec) |
N/A | 0.921 | 0.278 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.190 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 623 | 418 | 267 | 0 | 0 | 0 | 0 | 0 | 74 | 0 |
N.S. |
1 | 0.67 | 0.43 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.12 | 0.00 |
time (sec) |
N/A | 0.992 | 0.628 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.193 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | A | F(-1) | F | F | B |
verified | N/A | Yes | No | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 166 | 163 | 182 | 140 | 0 | 292 | 0 | 0 | 92 | 276 |
N.S. |
1 | 0.98 | 1.10 | 0.84 | 0.00 | 1.76 | 0.00 | 0.00 | 0.55 | 1.66 |
time (sec) |
N/A | 0.644 | 0.239 | 0.205 | 0.000 | 0.084 | 0.000 | 0.000 | 0.204 | 27.008 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 44 | 0 | 0 | 0 | 0 | 0 | 0 | 62 | 0 |
N.S. |
1 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.48 | 0.00 |
time (sec) |
N/A | 0.310 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.176 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 40 | 42 | 0 | 0 | 0 | 0 | 0 | 0 | 39 | 0 |
N.S. |
1 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.98 | 0.00 |
time (sec) |
N/A | 0.286 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.164 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | No | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 44 | 106 | 0 | 0 | 0 | 0 | 0 | 43 | 0 |
N.S. |
1 | 1.05 | 2.52 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 1.02 | 0.00 |
time (sec) |
N/A | 0.295 | 0.080 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.158 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 42 | 44 | 0 | 0 | 0 | 0 | 0 | 0 | 275 | 0 |
N.S. |
1 | 1.05 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 6.55 | 0.00 |
time (sec) |
N/A | 0.323 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.159 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 70 | 70 | 0 | 0 | 0 | 0 | 0 | 0 | 27 | 0 |
N.S. |
1 | 1.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.39 | 0.00 |
time (sec) |
N/A | 0.447 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.160 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 177 | 151 | 136 | 0 | 0 | 0 | 0 | 0 | 25 | 0 |
N.S. |
1 | 0.85 | 0.77 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.00 |
time (sec) |
N/A | 0.464 | 0.103 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.165 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | F | F | F | F | F | F | F(-1) |
verified | N/A | Yes | Yes | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 103 | 103 | 102 | 0 | 0 | 0 | 0 | 0 | 24 | 0 |
N.S. |
1 | 1.00 | 0.99 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.23 | 0.00 |
time (sec) |
N/A | 0.363 | 0.021 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.148 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 41 | 41 | 31 | 59 | 34 | 81 | 0 | 0 | 33 | 84 |
N.S. |
1 | 1.00 | 0.76 | 1.44 | 0.83 | 1.98 | 0.00 | 0.00 | 0.80 | 2.05 |
time (sec) |
N/A | 0.272 | 0.009 | 0.582 | 0.038 | 0.082 | 0.000 | 0.000 | 0.163 | 26.299 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 95 | 69 | 58 | 60 | 39 | 82 | 0 | 0 | 34 | 86 |
N.S. |
1 | 0.73 | 0.61 | 0.63 | 0.41 | 0.86 | 0.00 | 0.00 | 0.36 | 0.91 |
time (sec) |
N/A | 0.430 | 0.012 | 0.543 | 0.042 | 0.084 | 0.000 | 0.000 | 0.167 | 26.236 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 49 | 49 | 36 | 38 | 30 | 43 | 0 | 0 | 38 | 43 |
N.S. |
1 | 1.00 | 0.73 | 0.78 | 0.61 | 0.88 | 0.00 | 0.00 | 0.78 | 0.88 |
time (sec) |
N/A | 0.350 | 0.022 | 0.962 | 0.040 | 0.074 | 0.000 | 0.000 | 0.151 | 26.243 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 51 | 51 | 36 | 40 | 33 | 45 | 0 | 0 | 40 | 44 |
N.S. |
1 | 1.00 | 0.71 | 0.78 | 0.65 | 0.88 | 0.00 | 0.00 | 0.78 | 0.86 |
time (sec) |
N/A | 0.341 | 0.024 | 0.526 | 0.039 | 0.075 | 0.000 | 0.000 | 0.156 | 26.110 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | F(-1) | F | F | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 53 | 53 | 89 | 58 | 72 | 78 | 0 | 0 | 65 | 101 |
N.S. |
1 | 1.00 | 1.68 | 1.09 | 1.36 | 1.47 | 0.00 | 0.00 | 1.23 | 1.91 |
time (sec) |
N/A | 0.314 | 0.051 | 3.454 | 0.051 | 0.082 | 0.000 | 0.000 | 0.170 | 26.418 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 30 | 33 | 379 | 379 | 405 | 299 | 277 | 0 |
N.S. |
1 | 1.00 | 0.97 | 1.06 | 12.23 | 12.23 | 13.06 | 9.65 | 8.94 | 0.00 |
time (sec) |
N/A | 0.302 | 0.030 | 0.342 | 0.205 | 0.294 | 1.785 | 0.134 | 0.151 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 30 | 33 | 169 | 169 | 180 | 139 | 125 | 28 |
N.S. |
1 | 1.00 | 0.97 | 1.06 | 5.45 | 5.45 | 5.81 | 4.48 | 4.03 | 0.90 |
time (sec) |
N/A | 0.318 | 0.016 | 0.272 | 0.051 | 0.076 | 0.692 | 0.120 | 0.148 | 1.486 |
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 | 31 | 31 | 30 | 33 | 49 | 49 | 48 | 45 | 37 | 28 |
N.S. |
1 | 1.00 | 0.97 | 1.06 | 1.58 | 1.58 | 1.55 | 1.45 | 1.19 | 0.90 |
time (sec) |
N/A | 0.306 | 0.011 | 0.240 | 0.027 | 0.085 | 0.206 | 0.123 | 0.160 | 0.097 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 30 | 33 | 49 | 49 | 49 | 76 | 37 | 28 |
N.S. |
1 | 1.00 | 0.97 | 1.06 | 1.58 | 1.58 | 1.58 | 2.45 | 1.19 | 0.90 |
time (sec) |
N/A | 0.302 | 0.012 | 0.221 | 0.032 | 0.070 | 0.205 | 0.124 | 0.144 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 30 | 33 | 169 | 169 | 182 | 139 | 125 | 28 |
N.S. |
1 | 1.00 | 0.97 | 1.06 | 5.45 | 5.45 | 5.87 | 4.48 | 4.03 | 0.90 |
time (sec) |
N/A | 0.287 | 0.019 | 0.379 | 0.056 | 0.077 | 0.700 | 0.126 | 0.162 | 28.321 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 59 | 49 | 0 | 496 | 0 | 0 | 199 | 583 |
N.S. |
1 | 1.00 | 0.98 | 0.82 | 0.00 | 8.27 | 0.00 | 0.00 | 3.32 | 9.72 |
time (sec) |
N/A | 0.513 | 0.062 | 0.312 | 0.000 | 1.453 | 0.000 | 0.000 | 0.147 | 27.265 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | B | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 59 | 49 | 0 | 193 | 0 | 0 | 71 | 186 |
N.S. |
1 | 1.00 | 0.98 | 0.82 | 0.00 | 3.22 | 0.00 | 0.00 | 1.18 | 3.10 |
time (sec) |
N/A | 0.505 | 0.032 | 0.321 | 0.000 | 0.093 | 0.000 | 0.000 | 0.146 | 26.509 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | F | F | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 139 | 76 | 76 | 79 | 0 | 0 | 0 | 46 | 57 | 0 |
N.S. |
1 | 0.55 | 0.55 | 0.57 | 0.00 | 0.00 | 0.00 | 0.33 | 0.41 | 0.00 |
time (sec) |
N/A | 0.519 | 0.030 | 0.236 | 0.000 | 0.000 | 0.000 | 0.138 | 0.146 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | F | F | A | B | F(-1) |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 138 | 75 | 72 | 77 | 52 | 0 | 0 | 47 | 58 | 0 |
N.S. |
1 | 0.54 | 0.52 | 0.56 | 0.38 | 0.00 | 0.00 | 0.34 | 0.42 | 0.00 |
time (sec) |
N/A | 0.539 | 0.030 | 0.308 | 0.040 | 0.000 | 0.000 | 0.123 | 0.143 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | B | F(-1) | F | B | B |
verified | N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 60 | 60 | 59 | 49 | 93 | 192 | 0 | 0 | 71 | 187 |
N.S. |
1 | 1.00 | 0.98 | 0.82 | 1.55 | 3.20 | 0.00 | 0.00 | 1.18 | 3.12 |
time (sec) |
N/A | 0.497 | 0.034 | 0.280 | 0.060 | 0.090 | 0.000 | 0.000 | 0.144 | 26.288 |