Average Error: 58.1 → 57.1
Time: 8.2s
Precision: 64
\[x = 77617 \land y = 33096\]
\[\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]
↓
\[-2 \cdot {x}^{2} + \frac{x}{2 \cdot y}\]
\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}
↓
-2 \cdot {x}^{2} + \frac{x}{2 \cdot y}
double f(double x, double y) {
        double r18839 = 333.75;
        double r18840 = y;
        double r18841 = 6.0;
        double r18842 = pow(r18840, r18841);
        double r18843 = r18839 * r18842;
        double r18844 = x;
        double r18845 = r18844 * r18844;
        double r18846 = 11.0;
        double r18847 = r18846 * r18844;
        double r18848 = r18847 * r18844;
        double r18849 = r18848 * r18840;
        double r18850 = r18849 * r18840;
        double r18851 = r18850 - r18842;
        double r18852 = 121.0;
        double r18853 = 4.0;
        double r18854 = pow(r18840, r18853);
        double r18855 = r18852 * r18854;
        double r18856 = r18851 - r18855;
        double r18857 = 2.0;
        double r18858 = r18856 - r18857;
        double r18859 = r18845 * r18858;
        double r18860 = r18843 + r18859;
        double r18861 = 5.5;
        double r18862 = 8.0;
        double r18863 = pow(r18840, r18862);
        double r18864 = r18861 * r18863;
        double r18865 = r18860 + r18864;
        double r18866 = r18857 * r18840;
        double r18867 = r18844 / r18866;
        double r18868 = r18865 + r18867;
        return r18868;
}
↓
double f(double x, double y) {
        double r18869 = -2.0;
        double r18870 = x;
        double r18871 = 2.0;
        double r18872 = pow(r18870, r18871);
        double r18873 = r18869 * r18872;
        double r18874 = 2.0;
        double r18875 = y;
        double r18876 = r18874 * r18875;
        double r18877 = r18870 / r18876;
        double r18878 = r18873 + r18877;
        return r18878;
}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.1

    \[\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]

  2. Taylor expanded around 0 57.1

    \[\leadsto \color{blue}{-2 \cdot {x}^{2}} + \frac{x}{2 \cdot y}\]

  3. Final simplification57.1

    \[\leadsto -2 \cdot {x}^{2} + \frac{x}{2 \cdot y}\]

Reproduce

herbie shell --seed 2019308 
(FPCore (x y)
  :name "Rump's expression from Stadtherr's award speech"
  :precision binary64
  :pre (and (== x 77617) (== y 33096))
  (+ (+ (+ (* 333.75 (pow y 6)) (* (* x x) (- (- (- (* (* (* (* 11 x) x) y) y) (pow y 6)) (* 121 (pow y 4))) 2))) (* 5.5 (pow y 8))) (/ x (* 2 y))))