Average Error: 58.1 → 57.1
Time: 12.4s
Precision: 64
\[x = 77617 \land y = 33096\]
\[\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]
↓
\[0.5 \cdot \frac{x}{y} - 2 \cdot {x}^{2}\]
\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}
↓
0.5 \cdot \frac{x}{y} - 2 \cdot {x}^{2}
double f(double x, double y) {
        double r17073 = 333.75;
        double r17074 = y;
        double r17075 = 6.0;
        double r17076 = pow(r17074, r17075);
        double r17077 = r17073 * r17076;
        double r17078 = x;
        double r17079 = r17078 * r17078;
        double r17080 = 11.0;
        double r17081 = r17080 * r17078;
        double r17082 = r17081 * r17078;
        double r17083 = r17082 * r17074;
        double r17084 = r17083 * r17074;
        double r17085 = r17084 - r17076;
        double r17086 = 121.0;
        double r17087 = 4.0;
        double r17088 = pow(r17074, r17087);
        double r17089 = r17086 * r17088;
        double r17090 = r17085 - r17089;
        double r17091 = 2.0;
        double r17092 = r17090 - r17091;
        double r17093 = r17079 * r17092;
        double r17094 = r17077 + r17093;
        double r17095 = 5.5;
        double r17096 = 8.0;
        double r17097 = pow(r17074, r17096);
        double r17098 = r17095 * r17097;
        double r17099 = r17094 + r17098;
        double r17100 = r17091 * r17074;
        double r17101 = r17078 / r17100;
        double r17102 = r17099 + r17101;
        return r17102;
}
↓
double f(double x, double y) {
        double r17103 = 0.5;
        double r17104 = x;
        double r17105 = y;
        double r17106 = r17104 / r17105;
        double r17107 = r17103 * r17106;
        double r17108 = 2.0;
        double r17109 = 2.0;
        double r17110 = pow(r17104, r17109);
        double r17111 = r17108 * r17110;
        double r17112 = r17107 - r17111;
        return r17112;
}

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. Final simplification57.1

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

Reproduce

herbie shell --seed 2019195 
(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))))