Average Error: 28.7 → 0.1
Time: 15.3s
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 r495700 = x;
        double r495701 = r495700 * r495700;
        double r495702 = y;
        double r495703 = r495702 * r495702;
        double r495704 = r495701 + r495703;
        double r495705 = z;
        double r495706 = r495705 * r495705;
        double r495707 = r495704 - r495706;
        double r495708 = 2.0;
        double r495709 = r495702 * r495708;
        double r495710 = r495707 / r495709;
        return r495710;
}
↓
double f(double x, double y, double z) {
        double r495711 = y;
        double r495712 = x;
        double r495713 = z;
        double r495714 = r495712 + r495713;
        double r495715 = r495712 - r495713;
        double r495716 = r495711 / r495715;
        double r495717 = r495714 / r495716;
        double r495718 = r495711 + r495717;
        double r495719 = 2.0;
        double r495720 = r495718 / r495719;
        return r495720;
}

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

Original28.7
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 28.7

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

  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*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019305 
(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)))