Average Error: 28.9 → 0.2
Time: 7.4s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y + \left(z + x\right) \cdot \frac{x - z}{y}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y + \left(z + x\right) \cdot \frac{x - z}{y}}{2}
double f(double x, double y, double z) {
        double r841029 = x;
        double r841030 = r841029 * r841029;
        double r841031 = y;
        double r841032 = r841031 * r841031;
        double r841033 = r841030 + r841032;
        double r841034 = z;
        double r841035 = r841034 * r841034;
        double r841036 = r841033 - r841035;
        double r841037 = 2.0;
        double r841038 = r841031 * r841037;
        double r841039 = r841036 / r841038;
        return r841039;
}
↓
double f(double x, double y, double z) {
        double r841040 = y;
        double r841041 = z;
        double r841042 = x;
        double r841043 = r841041 + r841042;
        double r841044 = r841042 - r841041;
        double r841045 = r841044 / r841040;
        double r841046 = r841043 * r841045;
        double r841047 = r841040 + r841046;
        double r841048 = 2.0;
        double r841049 = r841047 / r841048;
        return r841049;
}

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

Original28.9
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 28.9

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

  2. Simplified12.9

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

  4. Applied *-un-lft-identity12.9

    \[\leadsto \frac{y + \frac{x \cdot x - z \cdot z}{\color{blue}{1 \cdot y}}}{2}\]

  5. Applied difference-of-squares12.9

    \[\leadsto \frac{y + \frac{\color{blue}{\left(x + z\right) \cdot \left(x - z\right)}}{1 \cdot y}}{2}\]

  6. Applied times-frac0.2

    \[\leadsto \frac{y + \color{blue}{\frac{x + z}{1} \cdot \frac{x - z}{y}}}{2}\]

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 
(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)))