Average Error: 58.1 → 57.1
Time: 16.1s
Precision: 64
\[x = 77617 \land y = 33096\]
\[\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]
↓
\[\frac{x}{y} \cdot 0.5 - \left(2 \cdot x\right) \cdot x\]
\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}
↓
\frac{x}{y} \cdot 0.5 - \left(2 \cdot x\right) \cdot x
double f(double x, double y) {
        double r785524 = 333.75;
        double r785525 = y;
        double r785526 = 6.0;
        double r785527 = pow(r785525, r785526);
        double r785528 = r785524 * r785527;
        double r785529 = x;
        double r785530 = r785529 * r785529;
        double r785531 = 11.0;
        double r785532 = r785531 * r785529;
        double r785533 = r785532 * r785529;
        double r785534 = r785533 * r785525;
        double r785535 = r785534 * r785525;
        double r785536 = r785535 - r785527;
        double r785537 = 121.0;
        double r785538 = 4.0;
        double r785539 = pow(r785525, r785538);
        double r785540 = r785537 * r785539;
        double r785541 = r785536 - r785540;
        double r785542 = 2.0;
        double r785543 = r785541 - r785542;
        double r785544 = r785530 * r785543;
        double r785545 = r785528 + r785544;
        double r785546 = 5.5;
        double r785547 = 8.0;
        double r785548 = pow(r785525, r785547);
        double r785549 = r785546 * r785548;
        double r785550 = r785545 + r785549;
        double r785551 = r785542 * r785525;
        double r785552 = r785529 / r785551;
        double r785553 = r785550 + r785552;
        return r785553;
}
↓
double f(double x, double y) {
        double r785554 = x;
        double r785555 = y;
        double r785556 = r785554 / r785555;
        double r785557 = 0.5;
        double r785558 = r785556 * r785557;
        double r785559 = 2.0;
        double r785560 = r785559 * r785554;
        double r785561 = r785560 * r785554;
        double r785562 = r785558 - r785561;
        return r785562;
}

Error

Try it out

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

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

  3. Taylor expanded around 0 57.1

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

  4. Simplified57.1

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

  5. Final simplification57.1

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

Reproduce

herbie shell --seed 2019171 
(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))))