Average Error: 58.1 → 57.1
Time: 15.0s
Precision: 64
\[x = 77617 \land y = 33096\]
\[\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]
↓
\[0.5 \cdot \frac{x}{y} - 2 \cdot \left(x \cdot x\right)\]
\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}
↓
0.5 \cdot \frac{x}{y} - 2 \cdot \left(x \cdot x\right)
double f(double x, double y) {
        double r1341707 = 333.75;
        double r1341708 = y;
        double r1341709 = 6.0;
        double r1341710 = pow(r1341708, r1341709);
        double r1341711 = r1341707 * r1341710;
        double r1341712 = x;
        double r1341713 = r1341712 * r1341712;
        double r1341714 = 11.0;
        double r1341715 = r1341714 * r1341712;
        double r1341716 = r1341715 * r1341712;
        double r1341717 = r1341716 * r1341708;
        double r1341718 = r1341717 * r1341708;
        double r1341719 = r1341718 - r1341710;
        double r1341720 = 121.0;
        double r1341721 = 4.0;
        double r1341722 = pow(r1341708, r1341721);
        double r1341723 = r1341720 * r1341722;
        double r1341724 = r1341719 - r1341723;
        double r1341725 = 2.0;
        double r1341726 = r1341724 - r1341725;
        double r1341727 = r1341713 * r1341726;
        double r1341728 = r1341711 + r1341727;
        double r1341729 = 5.5;
        double r1341730 = 8.0;
        double r1341731 = pow(r1341708, r1341730);
        double r1341732 = r1341729 * r1341731;
        double r1341733 = r1341728 + r1341732;
        double r1341734 = r1341725 * r1341708;
        double r1341735 = r1341712 / r1341734;
        double r1341736 = r1341733 + r1341735;
        return r1341736;
}
↓
double f(double x, double y) {
        double r1341737 = 0.5;
        double r1341738 = x;
        double r1341739 = y;
        double r1341740 = r1341738 / r1341739;
        double r1341741 = r1341737 * r1341740;
        double r1341742 = 2.0;
        double r1341743 = r1341738 * r1341738;
        double r1341744 = r1341742 * r1341743;
        double r1341745 = r1341741 - r1341744;
        return r1341745;
}

Error

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Simplified58.1

    \[\leadsto \color{blue}{\left(333.75 \cdot {y}^{6} + \left(5.5 \cdot {y}^{8} + \frac{x}{2 \cdot y}\right)\right) + \left(x \cdot x\right) \cdot \left(11 \cdot \left(\left(x \cdot y\right) \cdot \left(x \cdot y\right)\right) - \left(\left({y}^{6} + 121 \cdot {y}^{4}\right) + 2\right)\right)}\]

  3. Taylor expanded around 0 57.1

    \[\leadsto \color{blue}{0.5 \cdot \frac{x}{y} - 2 \cdot {x}^{2}}\]

  4. Simplified57.1

    \[\leadsto \color{blue}{0.5 \cdot \frac{x}{y} - 2 \cdot \left(x \cdot x\right)}\]

  5. Final simplification57.1

    \[\leadsto 0.5 \cdot \frac{x}{y} - 2 \cdot \left(x \cdot x\right)\]

Reproduce

herbie shell --seed 2019174 
(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))))