Average Error: 58.1 → 57.1
Time: 3.3s
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 r10669 = 333.75;
        double r10670 = y;
        double r10671 = 6.0;
        double r10672 = pow(r10670, r10671);
        double r10673 = r10669 * r10672;
        double r10674 = x;
        double r10675 = r10674 * r10674;
        double r10676 = 11.0;
        double r10677 = r10676 * r10674;
        double r10678 = r10677 * r10674;
        double r10679 = r10678 * r10670;
        double r10680 = r10679 * r10670;
        double r10681 = r10680 - r10672;
        double r10682 = 121.0;
        double r10683 = 4.0;
        double r10684 = pow(r10670, r10683);
        double r10685 = r10682 * r10684;
        double r10686 = r10681 - r10685;
        double r10687 = 2.0;
        double r10688 = r10686 - r10687;
        double r10689 = r10675 * r10688;
        double r10690 = r10673 + r10689;
        double r10691 = 5.5;
        double r10692 = 8.0;
        double r10693 = pow(r10670, r10692);
        double r10694 = r10691 * r10693;
        double r10695 = r10690 + r10694;
        double r10696 = r10687 * r10670;
        double r10697 = r10674 / r10696;
        double r10698 = r10695 + r10697;
        return r10698;
}
↓
double f(double x, double y) {
        double r10699 = -2.0;
        double r10700 = x;
        double r10701 = 2.0;
        double r10702 = pow(r10700, r10701);
        double r10703 = r10699 * r10702;
        double r10704 = 2.0;
        double r10705 = y;
        double r10706 = r10704 * r10705;
        double r10707 = r10700 / r10706;
        double r10708 = r10703 + r10707;
        return r10708;
}

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 2020060 
(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))))