Average Error: 28.2 → 0.1
Time: 1.8m
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y + \frac{z + x}{y} \cdot \left(x - z\right)}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y + \frac{z + x}{y} \cdot \left(x - z\right)}{2}
double f(double x, double y, double z) {
        double r30633623 = x;
        double r30633624 = r30633623 * r30633623;
        double r30633625 = y;
        double r30633626 = r30633625 * r30633625;
        double r30633627 = r30633624 + r30633626;
        double r30633628 = z;
        double r30633629 = r30633628 * r30633628;
        double r30633630 = r30633627 - r30633629;
        double r30633631 = 2.0;
        double r30633632 = r30633625 * r30633631;
        double r30633633 = r30633630 / r30633632;
        return r30633633;
}
↓
double f(double x, double y, double z) {
        double r30633634 = y;
        double r30633635 = z;
        double r30633636 = x;
        double r30633637 = r30633635 + r30633636;
        double r30633638 = r30633637 / r30633634;
        double r30633639 = r30633636 - r30633635;
        double r30633640 = r30633638 * r30633639;
        double r30633641 = r30633634 + r30633640;
        double r30633642 = 2.0;
        double r30633643 = r30633641 / r30633642;
        return r30633643;
}

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
Herbie0.1
\[y \cdot 0.5 - \left(\frac{0.5}{y} \cdot \left(z + x\right)\right) \cdot \left(z - x\right)\]

Derivation

  1. Initial program 28.2

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(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)))