Average Error: 28.2 → 0.1
Time: 15.7s
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 r34311904 = x;
        double r34311905 = r34311904 * r34311904;
        double r34311906 = y;
        double r34311907 = r34311906 * r34311906;
        double r34311908 = r34311905 + r34311907;
        double r34311909 = z;
        double r34311910 = r34311909 * r34311909;
        double r34311911 = r34311908 - r34311910;
        double r34311912 = 2.0;
        double r34311913 = r34311906 * r34311912;
        double r34311914 = r34311911 / r34311913;
        return r34311914;
}
↓
double f(double x, double y, double z) {
        double r34311915 = y;
        double r34311916 = z;
        double r34311917 = x;
        double r34311918 = r34311916 - r34311917;
        double r34311919 = r34311916 + r34311917;
        double r34311920 = r34311915 / r34311919;
        double r34311921 = r34311918 / r34311920;
        double r34311922 = r34311915 - r34311921;
        double r34311923 = 2.0;
        double r34311924 = r34311922 / r34311923;
        return r34311924;
}

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

Original28.2
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 28.2

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

  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 2019179 
(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)))