Average Error: 58.1 → 57.1
Time: 5.0s
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 r10680 = 333.75;
        double r10681 = y;
        double r10682 = 6.0;
        double r10683 = pow(r10681, r10682);
        double r10684 = r10680 * r10683;
        double r10685 = x;
        double r10686 = r10685 * r10685;
        double r10687 = 11.0;
        double r10688 = r10687 * r10685;
        double r10689 = r10688 * r10685;
        double r10690 = r10689 * r10681;
        double r10691 = r10690 * r10681;
        double r10692 = r10691 - r10683;
        double r10693 = 121.0;
        double r10694 = 4.0;
        double r10695 = pow(r10681, r10694);
        double r10696 = r10693 * r10695;
        double r10697 = r10692 - r10696;
        double r10698 = 2.0;
        double r10699 = r10697 - r10698;
        double r10700 = r10686 * r10699;
        double r10701 = r10684 + r10700;
        double r10702 = 5.5;
        double r10703 = 8.0;
        double r10704 = pow(r10681, r10703);
        double r10705 = r10702 * r10704;
        double r10706 = r10701 + r10705;
        double r10707 = r10698 * r10681;
        double r10708 = r10685 / r10707;
        double r10709 = r10706 + r10708;
        return r10709;
}
↓
double f(double x, double y) {
        double r10710 = -2.0;
        double r10711 = x;
        double r10712 = 2.0;
        double r10713 = pow(r10711, r10712);
        double r10714 = r10710 * r10713;
        double r10715 = 2.0;
        double r10716 = y;
        double r10717 = r10715 * r10716;
        double r10718 = r10711 / r10717;
        double r10719 = r10714 + r10718;
        return r10719;
}

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 2019354 
(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))))