Average Error: 27.8 → 0.2
Time: 9.5s
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 r404677 = x;
        double r404678 = r404677 * r404677;
        double r404679 = y;
        double r404680 = r404679 * r404679;
        double r404681 = r404678 + r404680;
        double r404682 = z;
        double r404683 = r404682 * r404682;
        double r404684 = r404681 - r404683;
        double r404685 = 2.0;
        double r404686 = r404679 * r404685;
        double r404687 = r404684 / r404686;
        return r404687;
}
↓
double f(double x, double y, double z) {
        double r404688 = y;
        double r404689 = x;
        double r404690 = z;
        double r404691 = r404689 + r404690;
        double r404692 = r404689 - r404690;
        double r404693 = r404688 / r404692;
        double r404694 = r404691 / r404693;
        double r404695 = r404688 + r404694;
        double r404696 = 2.0;
        double r404697 = r404695 / r404696;
        return r404697;
}

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 
(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)))