Average Error: 58.1 → 57.1
Time: 11.7s
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 r18838 = 333.75;
        double r18839 = y;
        double r18840 = 6.0;
        double r18841 = pow(r18839, r18840);
        double r18842 = r18838 * r18841;
        double r18843 = x;
        double r18844 = r18843 * r18843;
        double r18845 = 11.0;
        double r18846 = r18845 * r18843;
        double r18847 = r18846 * r18843;
        double r18848 = r18847 * r18839;
        double r18849 = r18848 * r18839;
        double r18850 = r18849 - r18841;
        double r18851 = 121.0;
        double r18852 = 4.0;
        double r18853 = pow(r18839, r18852);
        double r18854 = r18851 * r18853;
        double r18855 = r18850 - r18854;
        double r18856 = 2.0;
        double r18857 = r18855 - r18856;
        double r18858 = r18844 * r18857;
        double r18859 = r18842 + r18858;
        double r18860 = 5.5;
        double r18861 = 8.0;
        double r18862 = pow(r18839, r18861);
        double r18863 = r18860 * r18862;
        double r18864 = r18859 + r18863;
        double r18865 = r18856 * r18839;
        double r18866 = r18843 / r18865;
        double r18867 = r18864 + r18866;
        return r18867;
}
↓
double f(double x, double y) {
        double r18868 = -2.0;
        double r18869 = x;
        double r18870 = 2.0;
        double r18871 = pow(r18869, r18870);
        double r18872 = r18868 * r18871;
        double r18873 = 2.0;
        double r18874 = y;
        double r18875 = r18873 * r18874;
        double r18876 = r18869 / r18875;
        double r18877 = r18872 + r18876;
        return r18877;
}

Error

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Your Program's Arguments

Results

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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 2019297 
(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))))