Average Error: 28.3 → 0.1
Time: 16.9s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y - \frac{z - x}{y} \cdot \left(z + x\right)}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y - \frac{z - x}{y} \cdot \left(z + x\right)}{2}
double f(double x, double y, double z) {
        double r33356978 = x;
        double r33356979 = r33356978 * r33356978;
        double r33356980 = y;
        double r33356981 = r33356980 * r33356980;
        double r33356982 = r33356979 + r33356981;
        double r33356983 = z;
        double r33356984 = r33356983 * r33356983;
        double r33356985 = r33356982 - r33356984;
        double r33356986 = 2.0;
        double r33356987 = r33356980 * r33356986;
        double r33356988 = r33356985 / r33356987;
        return r33356988;
}
↓
double f(double x, double y, double z) {
        double r33356989 = y;
        double r33356990 = z;
        double r33356991 = x;
        double r33356992 = r33356990 - r33356991;
        double r33356993 = r33356992 / r33356989;
        double r33356994 = r33356990 + r33356991;
        double r33356995 = r33356993 * r33356994;
        double r33356996 = r33356989 - r33356995;
        double r33356997 = 2.0;
        double r33356998 = r33356996 / r33356997;
        return r33356998;
}

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

Original28.3
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 28.3

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

  2. Simplified0.1

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

  4. Applied associate-/r/0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019192 
(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)))