Average Error: 28.5 → 0.1
Time: 15.4s
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 r555041 = x;
        double r555042 = r555041 * r555041;
        double r555043 = y;
        double r555044 = r555043 * r555043;
        double r555045 = r555042 + r555044;
        double r555046 = z;
        double r555047 = r555046 * r555046;
        double r555048 = r555045 - r555047;
        double r555049 = 2.0;
        double r555050 = r555043 * r555049;
        double r555051 = r555048 / r555050;
        return r555051;
}
↓
double f(double x, double y, double z) {
        double r555052 = y;
        double r555053 = z;
        double r555054 = x;
        double r555055 = r555053 - r555054;
        double r555056 = r555053 + r555054;
        double r555057 = r555052 / r555056;
        double r555058 = r555055 / r555057;
        double r555059 = r555052 - r555058;
        double r555060 = 2.0;
        double r555061 = r555059 / r555060;
        return r555061;
}

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

Original28.5
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 28.5

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, A"

  :herbie-target
  (- (* y 0.5) (* (* (/ 0.5 y) (+ z x)) (- z x)))

  (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0)))