Average Error: 28.4 → 0.2
Time: 17.9s
Precision: 64
\[\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}\]
↓
\[\frac{y - \left(z + x\right) \cdot \frac{z - x}{y}}{2}\]
\frac{\left(x \cdot x + y \cdot y\right) - z \cdot z}{y \cdot 2}
↓
\frac{y - \left(z + x\right) \cdot \frac{z - x}{y}}{2}
double f(double x, double y, double z) {
        double r537609 = x;
        double r537610 = r537609 * r537609;
        double r537611 = y;
        double r537612 = r537611 * r537611;
        double r537613 = r537610 + r537612;
        double r537614 = z;
        double r537615 = r537614 * r537614;
        double r537616 = r537613 - r537615;
        double r537617 = 2.0;
        double r537618 = r537611 * r537617;
        double r537619 = r537616 / r537618;
        return r537619;
}
↓
double f(double x, double y, double z) {
        double r537620 = y;
        double r537621 = z;
        double r537622 = x;
        double r537623 = r537621 + r537622;
        double r537624 = r537621 - r537622;
        double r537625 = r537624 / r537620;
        double r537626 = r537623 * r537625;
        double r537627 = r537620 - r537626;
        double r537628 = 2.0;
        double r537629 = r537627 / r537628;
        return r537629;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

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Target

Original28.4
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 28.4

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

  2. Simplified12.6

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

  4. Applied *-un-lft-identity12.6

    \[\leadsto \frac{y - \frac{z \cdot z - x \cdot x}{\color{blue}{1 \cdot y}}}{2}\]

  5. Applied difference-of-squares12.6

    \[\leadsto \frac{y - \frac{\color{blue}{\left(z + x\right) \cdot \left(z - x\right)}}{1 \cdot y}}{2}\]

  6. Applied times-frac0.2

    \[\leadsto \frac{y - \color{blue}{\frac{z + x}{1} \cdot \frac{z - x}{y}}}{2}\]

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019303 
(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)))