Average Error: 58.1 → 57.1
Time: 19.3s
Precision: 64
\[x = 77617 \land y = 33096\]
\[\left(\left(333.75 \cdot {y}^{6} + \left(x \cdot x\right) \cdot \left(\left(\left(\left(\left(\left(11 \cdot x\right) \cdot x\right) \cdot y\right) \cdot y - {y}^{6}\right) - 121 \cdot {y}^{4}\right) - 2\right)\right) + 5.5 \cdot {y}^{8}\right) + \frac{x}{2 \cdot y}\]
↓
\[\frac{0.5}{\frac{y}{x}} - \left(x \cdot 2\right) \cdot x\]
\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{0.5}{\frac{y}{x}} - \left(x \cdot 2\right) \cdot x
double f(double x, double y) {
        double r685873 = 333.75;
        double r685874 = y;
        double r685875 = 6.0;
        double r685876 = pow(r685874, r685875);
        double r685877 = r685873 * r685876;
        double r685878 = x;
        double r685879 = r685878 * r685878;
        double r685880 = 11.0;
        double r685881 = r685880 * r685878;
        double r685882 = r685881 * r685878;
        double r685883 = r685882 * r685874;
        double r685884 = r685883 * r685874;
        double r685885 = r685884 - r685876;
        double r685886 = 121.0;
        double r685887 = 4.0;
        double r685888 = pow(r685874, r685887);
        double r685889 = r685886 * r685888;
        double r685890 = r685885 - r685889;
        double r685891 = 2.0;
        double r685892 = r685890 - r685891;
        double r685893 = r685879 * r685892;
        double r685894 = r685877 + r685893;
        double r685895 = 5.5;
        double r685896 = 8.0;
        double r685897 = pow(r685874, r685896);
        double r685898 = r685895 * r685897;
        double r685899 = r685894 + r685898;
        double r685900 = r685891 * r685874;
        double r685901 = r685878 / r685900;
        double r685902 = r685899 + r685901;
        return r685902;
}
↓
double f(double x, double y) {
        double r685903 = 0.5;
        double r685904 = y;
        double r685905 = x;
        double r685906 = r685904 / r685905;
        double r685907 = r685903 / r685906;
        double r685908 = 2.0;
        double r685909 = r685905 * r685908;
        double r685910 = r685909 * r685905;
        double r685911 = r685907 - r685910;
        return r685911;
}

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

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

  4. Final simplification57.1

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

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(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))))