Average Error: 0.0 → 0.0
Time: 4.9s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, x, -z \cdot \left(y \cdot 4\right)\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot z
↓
\mathsf{fma}\left(x, x, -z \cdot \left(y \cdot 4\right)\right)
double f(double x, double y, double z) {
        double r127725 = x;
        double r127726 = r127725 * r127725;
        double r127727 = y;
        double r127728 = 4.0;
        double r127729 = r127727 * r127728;
        double r127730 = z;
        double r127731 = r127729 * r127730;
        double r127732 = r127726 - r127731;
        return r127732;
}
↓
double f(double x, double y, double z) {
        double r127733 = x;
        double r127734 = z;
        double r127735 = y;
        double r127736 = 4.0;
        double r127737 = r127735 * r127736;
        double r127738 = r127734 * r127737;
        double r127739 = -r127738;
        double r127740 = fma(r127733, r127733, r127739);
        return r127740;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot x - \left(y \cdot 4\right) \cdot z\]
  2. Using strategy rm

  3. Applied fma-neg0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, -\left(y \cdot 4\right) \cdot z\right)}\]

  4. Simplified0.0

    \[\leadsto \mathsf{fma}\left(x, x, \color{blue}{-z \cdot \left(y \cdot 4\right)}\right)\]

  5. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, x, -z \cdot \left(y \cdot 4\right)\right)\]

Reproduce

herbie shell --seed 2019235 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))