Average Error: 28.2 → 0.2
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 r484221 = x;
        double r484222 = r484221 * r484221;
        double r484223 = y;
        double r484224 = r484223 * r484223;
        double r484225 = r484222 + r484224;
        double r484226 = z;
        double r484227 = r484226 * r484226;
        double r484228 = r484225 - r484227;
        double r484229 = 2.0;
        double r484230 = r484223 * r484229;
        double r484231 = r484228 / r484230;
        return r484231;
}
↓
double f(double x, double y, double z) {
        double r484232 = y;
        double r484233 = z;
        double r484234 = x;
        double r484235 = r484233 + r484234;
        double r484236 = r484233 - r484234;
        double r484237 = r484232 / r484236;
        double r484238 = r484235 / r484237;
        double r484239 = r484232 - r484238;
        double r484240 = 2.0;
        double r484241 = r484239 / r484240;
        return r484241;
}

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

Derivation

  1. Initial program 28.2

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

  2. Simplified12.1

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

  4. Applied difference-of-squares12.1

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

  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 2019325 
(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)))