Average Error: 28.6 → 0.2
Time: 21.4s
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 r426731 = x;
        double r426732 = r426731 * r426731;
        double r426733 = y;
        double r426734 = r426733 * r426733;
        double r426735 = r426732 + r426734;
        double r426736 = z;
        double r426737 = r426736 * r426736;
        double r426738 = r426735 - r426737;
        double r426739 = 2.0;
        double r426740 = r426733 * r426739;
        double r426741 = r426738 / r426740;
        return r426741;
}
↓
double f(double x, double y, double z) {
        double r426742 = y;
        double r426743 = z;
        double r426744 = x;
        double r426745 = r426743 + r426744;
        double r426746 = r426743 - r426744;
        double r426747 = r426742 / r426746;
        double r426748 = r426745 / r426747;
        double r426749 = r426742 - r426748;
        double r426750 = 2.0;
        double r426751 = r426749 / r426750;
        return r426751;
}

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

Original28.6
Target0.1
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 28.6

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

  2. Simplified12.5

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

  4. Applied difference-of-squares12.5

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

  5. Applied associate-/l*0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 
(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)))