Average Error: 28.0 → 0.2
Time: 22.2s
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 r455864 = x;
        double r455865 = r455864 * r455864;
        double r455866 = y;
        double r455867 = r455866 * r455866;
        double r455868 = r455865 + r455867;
        double r455869 = z;
        double r455870 = r455869 * r455869;
        double r455871 = r455868 - r455870;
        double r455872 = 2.0;
        double r455873 = r455866 * r455872;
        double r455874 = r455871 / r455873;
        return r455874;
}
↓
double f(double x, double y, double z) {
        double r455875 = y;
        double r455876 = x;
        double r455877 = z;
        double r455878 = r455876 + r455877;
        double r455879 = r455876 - r455877;
        double r455880 = r455875 / r455879;
        double r455881 = r455878 / r455880;
        double r455882 = r455875 + r455881;
        double r455883 = 2.0;
        double r455884 = r455882 / r455883;
        return r455884;
}

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

Original28.0
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 28.0

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

  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 2019209 +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)))