Average Error: 28.5 → 0.2
Time: 15.9s
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 r434101 = x;
        double r434102 = r434101 * r434101;
        double r434103 = y;
        double r434104 = r434103 * r434103;
        double r434105 = r434102 + r434104;
        double r434106 = z;
        double r434107 = r434106 * r434106;
        double r434108 = r434105 - r434107;
        double r434109 = 2.0;
        double r434110 = r434103 * r434109;
        double r434111 = r434108 / r434110;
        return r434111;
}
↓
double f(double x, double y, double z) {
        double r434112 = y;
        double r434113 = z;
        double r434114 = x;
        double r434115 = r434113 + r434114;
        double r434116 = r434113 - r434114;
        double r434117 = r434112 / r434116;
        double r434118 = r434115 / r434117;
        double r434119 = r434112 - r434118;
        double r434120 = 2.0;
        double r434121 = r434119 / r434120;
        return r434121;
}

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
Herbie0.2
\[y \cdot 0.5 - \left(\frac{0.5}{y} \cdot \left(z + x\right)\right) \cdot \left(z - x\right)\]

Derivation

  1. Initial program 28.5

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

  2. Simplified12.9

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

  4. Applied difference-of-squares12.9

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

  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 2019322 
(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)))