Average Error: 28.4 → 0.1
Time: 21.0s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y - \frac{z + x}{\frac{y}{z - x}}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y - \frac{z + x}{\frac{y}{z - x}}}{2}
double f(double x, double y, double z) {
        double r421886 = x;
        double r421887 = r421886 * r421886;
        double r421888 = y;
        double r421889 = r421888 * r421888;
        double r421890 = r421887 + r421889;
        double r421891 = z;
        double r421892 = r421891 * r421891;
        double r421893 = r421890 - r421892;
        double r421894 = 2.0;
        double r421895 = r421888 * r421894;
        double r421896 = r421893 / r421895;
        return r421896;
}
↓
double f(double x, double y, double z) {
        double r421897 = y;
        double r421898 = z;
        double r421899 = x;
        double r421900 = r421898 + r421899;
        double r421901 = r421898 - r421899;
        double r421902 = r421897 / r421901;
        double r421903 = r421900 / r421902;
        double r421904 = r421897 - r421903;
        double r421905 = 2.0;
        double r421906 = r421904 / r421905;
        return r421906;
}

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

Original28.4
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 28.4

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

  2. Simplified12.9

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

  4. Applied difference-of-squares12.9

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

  5. Applied associate-/l*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019304 
(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)))