Average Error: 27.8 → 0.2
Time: 13.4s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y + \frac{x + z}{\frac{y}{x - z}}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y + \frac{x + z}{\frac{y}{x - z}}}{2}
double f(double x, double y, double z) {
        double r392974 = x;
        double r392975 = r392974 * r392974;
        double r392976 = y;
        double r392977 = r392976 * r392976;
        double r392978 = r392975 + r392977;
        double r392979 = z;
        double r392980 = r392979 * r392979;
        double r392981 = r392978 - r392980;
        double r392982 = 2.0;
        double r392983 = r392976 * r392982;
        double r392984 = r392981 / r392983;
        return r392984;
}
↓
double f(double x, double y, double z) {
        double r392985 = y;
        double r392986 = x;
        double r392987 = z;
        double r392988 = r392986 + r392987;
        double r392989 = r392986 - r392987;
        double r392990 = r392985 / r392989;
        double r392991 = r392988 / r392990;
        double r392992 = r392985 + r392991;
        double r392993 = 2.0;
        double r392994 = r392992 / r392993;
        return r392994;
}

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

Original27.8
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 27.8

    \[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]

  2. Simplified12.6

    \[\leadsto \color{blue}{\frac{y + \frac{x \cdot x - z \cdot z}{y}}{2}}\]
  3. Using strategy rm

  4. Applied difference-of-squares12.6

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

  5. Applied associate-/l*0.2

    \[\leadsto \frac{y + \color{blue}{\frac{x + z}{\frac{y}{x - z}}}}{2}\]

  6. Final simplification0.2

    \[\leadsto \frac{y + \frac{x + z}{\frac{y}{x - z}}}{2}\]

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, A"
  :precision binary64

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

  (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2)))