Average Error: 58.1 → 57.1
Time: 7.0s
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 r10812 = 333.75;
        double r10813 = y;
        double r10814 = 6.0;
        double r10815 = pow(r10813, r10814);
        double r10816 = r10812 * r10815;
        double r10817 = x;
        double r10818 = r10817 * r10817;
        double r10819 = 11.0;
        double r10820 = r10819 * r10817;
        double r10821 = r10820 * r10817;
        double r10822 = r10821 * r10813;
        double r10823 = r10822 * r10813;
        double r10824 = r10823 - r10815;
        double r10825 = 121.0;
        double r10826 = 4.0;
        double r10827 = pow(r10813, r10826);
        double r10828 = r10825 * r10827;
        double r10829 = r10824 - r10828;
        double r10830 = 2.0;
        double r10831 = r10829 - r10830;
        double r10832 = r10818 * r10831;
        double r10833 = r10816 + r10832;
        double r10834 = 5.5;
        double r10835 = 8.0;
        double r10836 = pow(r10813, r10835);
        double r10837 = r10834 * r10836;
        double r10838 = r10833 + r10837;
        double r10839 = r10830 * r10813;
        double r10840 = r10817 / r10839;
        double r10841 = r10838 + r10840;
        return r10841;
}
↓
double f(double x, double y) {
        double r10842 = -2.0;
        double r10843 = x;
        double r10844 = 2.0;
        double r10845 = pow(r10843, r10844);
        double r10846 = r10842 * r10845;
        double r10847 = 2.0;
        double r10848 = y;
        double r10849 = r10847 * r10848;
        double r10850 = r10843 / r10849;
        double r10851 = r10846 + r10850;
        return r10851;
}

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 2020047 
(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))))