Average Error: 25.9 → 0.2
Time: 18.3s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}\]
↓
\[\frac{y + \frac{x - z}{y} \cdot \left(x + z\right)}{2.0}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2.0}
↓
\frac{y + \frac{x - z}{y} \cdot \left(x + z\right)}{2.0}
double f(double x, double y, double z) {
        double r48464890 = x;
        double r48464891 = r48464890 * r48464890;
        double r48464892 = y;
        double r48464893 = r48464892 * r48464892;
        double r48464894 = r48464891 + r48464893;
        double r48464895 = z;
        double r48464896 = r48464895 * r48464895;
        double r48464897 = r48464894 - r48464896;
        double r48464898 = 2.0;
        double r48464899 = r48464892 * r48464898;
        double r48464900 = r48464897 / r48464899;
        return r48464900;
}
↓
double f(double x, double y, double z) {
        double r48464901 = y;
        double r48464902 = x;
        double r48464903 = z;
        double r48464904 = r48464902 - r48464903;
        double r48464905 = r48464904 / r48464901;
        double r48464906 = r48464902 + r48464903;
        double r48464907 = r48464905 * r48464906;
        double r48464908 = r48464901 + r48464907;
        double r48464909 = 2.0;
        double r48464910 = r48464908 / r48464909;
        return r48464910;
}

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

Original25.9
Target0.2
Herbie0.2
\[y \cdot 0.5 - \left(\frac{0.5}{y} \cdot \left(z + x\right)\right) \cdot \left(z - x\right)\]

Derivation

  1. Initial program 25.9

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

  2. Simplified0.2

    \[\leadsto \color{blue}{\frac{y + \frac{x - z}{\frac{y}{z + x}}}{2.0}}\]
  3. Using strategy rm

  4. Applied associate-/r/0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019158 
(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)))