Average Error: 58.1 → 57.1
Time: 6.7s
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 r10755 = 333.75;
        double r10756 = y;
        double r10757 = 6.0;
        double r10758 = pow(r10756, r10757);
        double r10759 = r10755 * r10758;
        double r10760 = x;
        double r10761 = r10760 * r10760;
        double r10762 = 11.0;
        double r10763 = r10762 * r10760;
        double r10764 = r10763 * r10760;
        double r10765 = r10764 * r10756;
        double r10766 = r10765 * r10756;
        double r10767 = r10766 - r10758;
        double r10768 = 121.0;
        double r10769 = 4.0;
        double r10770 = pow(r10756, r10769);
        double r10771 = r10768 * r10770;
        double r10772 = r10767 - r10771;
        double r10773 = 2.0;
        double r10774 = r10772 - r10773;
        double r10775 = r10761 * r10774;
        double r10776 = r10759 + r10775;
        double r10777 = 5.5;
        double r10778 = 8.0;
        double r10779 = pow(r10756, r10778);
        double r10780 = r10777 * r10779;
        double r10781 = r10776 + r10780;
        double r10782 = r10773 * r10756;
        double r10783 = r10760 / r10782;
        double r10784 = r10781 + r10783;
        return r10784;
}
↓
double f(double x, double y) {
        double r10785 = -2.0;
        double r10786 = x;
        double r10787 = 2.0;
        double r10788 = pow(r10786, r10787);
        double r10789 = r10785 * r10788;
        double r10790 = 2.0;
        double r10791 = y;
        double r10792 = r10790 * r10791;
        double r10793 = r10786 / r10792;
        double r10794 = r10789 + r10793;
        return r10794;
}

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))))