Average Error: 58.1 → 57.1
Time: 7.5s
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 r10820 = 333.75;
        double r10821 = y;
        double r10822 = 6.0;
        double r10823 = pow(r10821, r10822);
        double r10824 = r10820 * r10823;
        double r10825 = x;
        double r10826 = r10825 * r10825;
        double r10827 = 11.0;
        double r10828 = r10827 * r10825;
        double r10829 = r10828 * r10825;
        double r10830 = r10829 * r10821;
        double r10831 = r10830 * r10821;
        double r10832 = r10831 - r10823;
        double r10833 = 121.0;
        double r10834 = 4.0;
        double r10835 = pow(r10821, r10834);
        double r10836 = r10833 * r10835;
        double r10837 = r10832 - r10836;
        double r10838 = 2.0;
        double r10839 = r10837 - r10838;
        double r10840 = r10826 * r10839;
        double r10841 = r10824 + r10840;
        double r10842 = 5.5;
        double r10843 = 8.0;
        double r10844 = pow(r10821, r10843);
        double r10845 = r10842 * r10844;
        double r10846 = r10841 + r10845;
        double r10847 = r10838 * r10821;
        double r10848 = r10825 / r10847;
        double r10849 = r10846 + r10848;
        return r10849;
}
↓
double f(double x, double y) {
        double r10850 = -2.0;
        double r10851 = x;
        double r10852 = 2.0;
        double r10853 = pow(r10851, r10852);
        double r10854 = r10850 * r10853;
        double r10855 = 2.0;
        double r10856 = y;
        double r10857 = r10855 * r10856;
        double r10858 = r10851 / r10857;
        double r10859 = r10854 + r10858;
        return r10859;
}

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 2020045 
(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))))