Average Error: 58.1 → 57.1
Time: 12.0s
Precision: 64
\[x = 77617 \land y = 33096\]
\[\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]
↓
\[\frac{x \cdot 0.5}{y} - x \cdot \left(2 \cdot x\right)\]
\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}
↓
\frac{x \cdot 0.5}{y} - x \cdot \left(2 \cdot x\right)
double f(double x, double y) {
        double r17051 = 333.75;
        double r17052 = y;
        double r17053 = 6.0;
        double r17054 = pow(r17052, r17053);
        double r17055 = r17051 * r17054;
        double r17056 = x;
        double r17057 = r17056 * r17056;
        double r17058 = 11.0;
        double r17059 = r17058 * r17056;
        double r17060 = r17059 * r17056;
        double r17061 = r17060 * r17052;
        double r17062 = r17061 * r17052;
        double r17063 = r17062 - r17054;
        double r17064 = 121.0;
        double r17065 = 4.0;
        double r17066 = pow(r17052, r17065);
        double r17067 = r17064 * r17066;
        double r17068 = r17063 - r17067;
        double r17069 = 2.0;
        double r17070 = r17068 - r17069;
        double r17071 = r17057 * r17070;
        double r17072 = r17055 + r17071;
        double r17073 = 5.5;
        double r17074 = 8.0;
        double r17075 = pow(r17052, r17074);
        double r17076 = r17073 * r17075;
        double r17077 = r17072 + r17076;
        double r17078 = r17069 * r17052;
        double r17079 = r17056 / r17078;
        double r17080 = r17077 + r17079;
        return r17080;
}
↓
double f(double x, double y) {
        double r17081 = x;
        double r17082 = 0.5;
        double r17083 = r17081 * r17082;
        double r17084 = y;
        double r17085 = r17083 / r17084;
        double r17086 = 2.0;
        double r17087 = r17086 * r17081;
        double r17088 = r17081 * r17087;
        double r17089 = r17085 - r17088;
        return r17089;
}

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

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

  3. Simplified57.1

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

  4. Final simplification57.1

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

Reproduce

herbie shell --seed 2019194 
(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))))