Average Error: 26.3 → 0.1
Time: 13.3s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}\]
↓
\[\frac{y + \frac{x - z}{\frac{y}{x + z}}}{2.0}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}
↓
\frac{y + \frac{x - z}{\frac{y}{x + z}}}{2.0}
double f(double x, double y, double z) {
        double r36429930 = x;
        double r36429931 = r36429930 * r36429930;
        double r36429932 = y;
        double r36429933 = r36429932 * r36429932;
        double r36429934 = r36429931 + r36429933;
        double r36429935 = z;
        double r36429936 = r36429935 * r36429935;
        double r36429937 = r36429934 - r36429936;
        double r36429938 = 2.0;
        double r36429939 = r36429932 * r36429938;
        double r36429940 = r36429937 / r36429939;
        return r36429940;
}
↓
double f(double x, double y, double z) {
        double r36429941 = y;
        double r36429942 = x;
        double r36429943 = z;
        double r36429944 = r36429942 - r36429943;
        double r36429945 = r36429942 + r36429943;
        double r36429946 = r36429941 / r36429945;
        double r36429947 = r36429944 / r36429946;
        double r36429948 = r36429941 + r36429947;
        double r36429949 = 2.0;
        double r36429950 = r36429948 / r36429949;
        return r36429950;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original26.3
Target0.2
Herbie0.1
\[y \cdot 0.5 - \left(\frac{0.5}{y} \cdot \left(z + x\right)\right) \cdot \left(z - x\right)\]

Derivation

  1. Initial program 26.3

    \[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\frac{y + \frac{x - z}{\frac{y}{z + x}}}{2.0}}\]

  3. Final simplification0.1

    \[\leadsto \frac{y + \frac{x - z}{\frac{y}{x + z}}}{2.0}\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, A"

  :herbie-target
  (- (* y 0.5) (* (* (/ 0.5 y) (+ z x)) (- z x)))

  (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0)))