Average Error: 28.6 → 0.2
Time: 23.1s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y + \frac{x + z}{\frac{y}{x - z}}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y + \frac{x + z}{\frac{y}{x - z}}}{2}
double f(double x, double y, double z) {
        double r468566 = x;
        double r468567 = r468566 * r468566;
        double r468568 = y;
        double r468569 = r468568 * r468568;
        double r468570 = r468567 + r468569;
        double r468571 = z;
        double r468572 = r468571 * r468571;
        double r468573 = r468570 - r468572;
        double r468574 = 2.0;
        double r468575 = r468568 * r468574;
        double r468576 = r468573 / r468575;
        return r468576;
}
↓
double f(double x, double y, double z) {
        double r468577 = y;
        double r468578 = x;
        double r468579 = z;
        double r468580 = r468578 + r468579;
        double r468581 = r468578 - r468579;
        double r468582 = r468577 / r468581;
        double r468583 = r468580 / r468582;
        double r468584 = r468577 + r468583;
        double r468585 = 2.0;
        double r468586 = r468584 / r468585;
        return r468586;
}

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
Target0.2
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 28.6

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

  2. Simplified12.7

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

  4. Applied difference-of-squares12.7

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

  5. Applied associate-/l*0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, A"

  :herbie-target
  (- (* y 0.5) (* (* (/ 0.5 y) (+ z x)) (- z x)))

  (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0)))