Average Error: 28.2 → 0.2
Time: 16.7s
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 r479491 = x;
        double r479492 = r479491 * r479491;
        double r479493 = y;
        double r479494 = r479493 * r479493;
        double r479495 = r479492 + r479494;
        double r479496 = z;
        double r479497 = r479496 * r479496;
        double r479498 = r479495 - r479497;
        double r479499 = 2.0;
        double r479500 = r479493 * r479499;
        double r479501 = r479498 / r479500;
        return r479501;
}
↓
double f(double x, double y, double z) {
        double r479502 = y;
        double r479503 = z;
        double r479504 = x;
        double r479505 = r479503 + r479504;
        double r479506 = r479503 - r479504;
        double r479507 = r479502 / r479506;
        double r479508 = r479505 / r479507;
        double r479509 = r479502 - r479508;
        double r479510 = 2.0;
        double r479511 = r479509 / r479510;
        return r479511;
}

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)))