Average Error: 58.1 → 57.1
Time: 13.5s
Precision: 64
\[x = 77617 \land y = 33096\]
\[\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]
↓
\[-2 \cdot \left(x \cdot x\right) + \frac{x}{2 \cdot y}\]
\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 \left(x \cdot x\right) + \frac{x}{2 \cdot y}
double f(double x, double y) {
        double r17671 = 333.75;
        double r17672 = y;
        double r17673 = 6.0;
        double r17674 = pow(r17672, r17673);
        double r17675 = r17671 * r17674;
        double r17676 = x;
        double r17677 = r17676 * r17676;
        double r17678 = 11.0;
        double r17679 = r17678 * r17676;
        double r17680 = r17679 * r17676;
        double r17681 = r17680 * r17672;
        double r17682 = r17681 * r17672;
        double r17683 = r17682 - r17674;
        double r17684 = 121.0;
        double r17685 = 4.0;
        double r17686 = pow(r17672, r17685);
        double r17687 = r17684 * r17686;
        double r17688 = r17683 - r17687;
        double r17689 = 2.0;
        double r17690 = r17688 - r17689;
        double r17691 = r17677 * r17690;
        double r17692 = r17675 + r17691;
        double r17693 = 5.5;
        double r17694 = 8.0;
        double r17695 = pow(r17672, r17694);
        double r17696 = r17693 * r17695;
        double r17697 = r17692 + r17696;
        double r17698 = r17689 * r17672;
        double r17699 = r17676 / r17698;
        double r17700 = r17697 + r17699;
        return r17700;
}
↓
double f(double x, double y) {
        double r17701 = -2.0;
        double r17702 = x;
        double r17703 = r17702 * r17702;
        double r17704 = r17701 * r17703;
        double r17705 = 2.0;
        double r17706 = y;
        double r17707 = r17705 * r17706;
        double r17708 = r17702 / r17707;
        double r17709 = r17704 + r17708;
        return r17709;
}

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. Simplified57.1

    \[\leadsto \color{blue}{-2 \cdot \left(x \cdot x\right)} + \frac{x}{2 \cdot y}\]

  4. Final simplification57.1

    \[\leadsto -2 \cdot \left(x \cdot x\right) + \frac{x}{2 \cdot y}\]

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (x y)
  :name "Rump's expression from Stadtherr's award speech"
  :pre (and (== x 77617.0) (== y 33096.0))
  (+ (+ (+ (* 333.75 (pow y 6.0)) (* (* x x) (- (- (- (* (* (* (* 11.0 x) x) y) y) (pow y 6.0)) (* 121.0 (pow y 4.0))) 2.0))) (* 5.5 (pow y 8.0))) (/ x (* 2.0 y))))