Average Error: 28.0 → 0.2
Time: 18.3s
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 r1074040 = x;
        double r1074041 = r1074040 * r1074040;
        double r1074042 = y;
        double r1074043 = r1074042 * r1074042;
        double r1074044 = r1074041 + r1074043;
        double r1074045 = z;
        double r1074046 = r1074045 * r1074045;
        double r1074047 = r1074044 - r1074046;
        double r1074048 = 2.0;
        double r1074049 = r1074042 * r1074048;
        double r1074050 = r1074047 / r1074049;
        return r1074050;
}
↓
double f(double x, double y, double z) {
        double r1074051 = y;
        double r1074052 = x;
        double r1074053 = z;
        double r1074054 = r1074052 + r1074053;
        double r1074055 = r1074052 - r1074053;
        double r1074056 = r1074051 / r1074055;
        double r1074057 = r1074054 / r1074056;
        double r1074058 = r1074051 + r1074057;
        double r1074059 = 2.0;
        double r1074060 = r1074058 / r1074059;
        return r1074060;
}

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 
(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)))