Average Error: 58.1 → 57.1
Time: 5.2s
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 r18895 = 333.75;
        double r18896 = y;
        double r18897 = 6.0;
        double r18898 = pow(r18896, r18897);
        double r18899 = r18895 * r18898;
        double r18900 = x;
        double r18901 = r18900 * r18900;
        double r18902 = 11.0;
        double r18903 = r18902 * r18900;
        double r18904 = r18903 * r18900;
        double r18905 = r18904 * r18896;
        double r18906 = r18905 * r18896;
        double r18907 = r18906 - r18898;
        double r18908 = 121.0;
        double r18909 = 4.0;
        double r18910 = pow(r18896, r18909);
        double r18911 = r18908 * r18910;
        double r18912 = r18907 - r18911;
        double r18913 = 2.0;
        double r18914 = r18912 - r18913;
        double r18915 = r18901 * r18914;
        double r18916 = r18899 + r18915;
        double r18917 = 5.5;
        double r18918 = 8.0;
        double r18919 = pow(r18896, r18918);
        double r18920 = r18917 * r18919;
        double r18921 = r18916 + r18920;
        double r18922 = r18913 * r18896;
        double r18923 = r18900 / r18922;
        double r18924 = r18921 + r18923;
        return r18924;
}
↓
double f(double x, double y) {
        double r18925 = -2.0;
        double r18926 = x;
        double r18927 = 2.0;
        double r18928 = pow(r18926, r18927);
        double r18929 = r18925 * r18928;
        double r18930 = 2.0;
        double r18931 = y;
        double r18932 = r18930 * r18931;
        double r18933 = r18926 / r18932;
        double r18934 = r18929 + r18933;
        return r18934;
}

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 2019322 
(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))))