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 r10753 = 333.75;
        double r10754 = y;
        double r10755 = 6.0;
        double r10756 = pow(r10754, r10755);
        double r10757 = r10753 * r10756;
        double r10758 = x;
        double r10759 = r10758 * r10758;
        double r10760 = 11.0;
        double r10761 = r10760 * r10758;
        double r10762 = r10761 * r10758;
        double r10763 = r10762 * r10754;
        double r10764 = r10763 * r10754;
        double r10765 = r10764 - r10756;
        double r10766 = 121.0;
        double r10767 = 4.0;
        double r10768 = pow(r10754, r10767);
        double r10769 = r10766 * r10768;
        double r10770 = r10765 - r10769;
        double r10771 = 2.0;
        double r10772 = r10770 - r10771;
        double r10773 = r10759 * r10772;
        double r10774 = r10757 + r10773;
        double r10775 = 5.5;
        double r10776 = 8.0;
        double r10777 = pow(r10754, r10776);
        double r10778 = r10775 * r10777;
        double r10779 = r10774 + r10778;
        double r10780 = r10771 * r10754;
        double r10781 = r10758 / r10780;
        double r10782 = r10779 + r10781;
        return r10782;
}
↓
double f(double x, double y) {
        double r10783 = -2.0;
        double r10784 = x;
        double r10785 = 2.0;
        double r10786 = pow(r10784, r10785);
        double r10787 = r10783 * r10786;
        double r10788 = 2.0;
        double r10789 = y;
        double r10790 = r10788 * r10789;
        double r10791 = r10784 / r10790;
        double r10792 = r10787 + r10791;
        return r10792;
}

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))))