Average Error: 28.6 → 0.1
Time: 11.2s
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 r681302 = x;
        double r681303 = r681302 * r681302;
        double r681304 = y;
        double r681305 = r681304 * r681304;
        double r681306 = r681303 + r681305;
        double r681307 = z;
        double r681308 = r681307 * r681307;
        double r681309 = r681306 - r681308;
        double r681310 = 2.0;
        double r681311 = r681304 * r681310;
        double r681312 = r681309 / r681311;
        return r681312;
}
↓
double f(double x, double y, double z) {
        double r681313 = y;
        double r681314 = x;
        double r681315 = z;
        double r681316 = r681314 + r681315;
        double r681317 = r681314 - r681315;
        double r681318 = r681313 / r681317;
        double r681319 = r681316 / r681318;
        double r681320 = r681313 + r681319;
        double r681321 = 2.0;
        double r681322 = r681320 / r681321;
        return r681322;
}

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

Original28.6
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 28.6

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

  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 2020045 
(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)))