Average Error: 58.1 → 57.1
Time: 22.5s
Precision: 64
\[x = 77617 \land y = 33096\]
\[\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]
↓
\[\frac{x}{y} \cdot 0.5 - \left(x \cdot x\right) \cdot 2\]
\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(x \cdot x\right) \cdot 2
double f(double x, double y) {
        double r971476 = 333.75;
        double r971477 = y;
        double r971478 = 6.0;
        double r971479 = pow(r971477, r971478);
        double r971480 = r971476 * r971479;
        double r971481 = x;
        double r971482 = r971481 * r971481;
        double r971483 = 11.0;
        double r971484 = r971483 * r971481;
        double r971485 = r971484 * r971481;
        double r971486 = r971485 * r971477;
        double r971487 = r971486 * r971477;
        double r971488 = r971487 - r971479;
        double r971489 = 121.0;
        double r971490 = 4.0;
        double r971491 = pow(r971477, r971490);
        double r971492 = r971489 * r971491;
        double r971493 = r971488 - r971492;
        double r971494 = 2.0;
        double r971495 = r971493 - r971494;
        double r971496 = r971482 * r971495;
        double r971497 = r971480 + r971496;
        double r971498 = 5.5;
        double r971499 = 8.0;
        double r971500 = pow(r971477, r971499);
        double r971501 = r971498 * r971500;
        double r971502 = r971497 + r971501;
        double r971503 = r971494 * r971477;
        double r971504 = r971481 / r971503;
        double r971505 = r971502 + r971504;
        return r971505;
}
↓
double f(double x, double y) {
        double r971506 = x;
        double r971507 = y;
        double r971508 = r971506 / r971507;
        double r971509 = 0.5;
        double r971510 = r971508 * r971509;
        double r971511 = r971506 * r971506;
        double r971512 = 2.0;
        double r971513 = r971511 * r971512;
        double r971514 = r971510 - r971513;
        return r971514;
}

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. Simplified58.1

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

  3. Taylor expanded around 0 57.1

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

  4. Simplified57.1

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

  5. Final simplification57.1

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

Reproduce

herbie shell --seed 2019170 
(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))))