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 r18835 = 333.75;
        double r18836 = y;
        double r18837 = 6.0;
        double r18838 = pow(r18836, r18837);
        double r18839 = r18835 * r18838;
        double r18840 = x;
        double r18841 = r18840 * r18840;
        double r18842 = 11.0;
        double r18843 = r18842 * r18840;
        double r18844 = r18843 * r18840;
        double r18845 = r18844 * r18836;
        double r18846 = r18845 * r18836;
        double r18847 = r18846 - r18838;
        double r18848 = 121.0;
        double r18849 = 4.0;
        double r18850 = pow(r18836, r18849);
        double r18851 = r18848 * r18850;
        double r18852 = r18847 - r18851;
        double r18853 = 2.0;
        double r18854 = r18852 - r18853;
        double r18855 = r18841 * r18854;
        double r18856 = r18839 + r18855;
        double r18857 = 5.5;
        double r18858 = 8.0;
        double r18859 = pow(r18836, r18858);
        double r18860 = r18857 * r18859;
        double r18861 = r18856 + r18860;
        double r18862 = r18853 * r18836;
        double r18863 = r18840 / r18862;
        double r18864 = r18861 + r18863;
        return r18864;
}
↓
double f(double x, double y) {
        double r18865 = -2.0;
        double r18866 = x;
        double r18867 = 2.0;
        double r18868 = pow(r18866, r18867);
        double r18869 = r18865 * r18868;
        double r18870 = 2.0;
        double r18871 = y;
        double r18872 = r18870 * r18871;
        double r18873 = r18866 / r18872;
        double r18874 = r18869 + r18873;
        return r18874;
}

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 2019291 
(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))))