Average Error: 0.0 → 0.0
Time: 992.0ms
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, x, -\left(y \cdot 4\right) \cdot z\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot z
↓
\mathsf{fma}\left(x, x, -\left(y \cdot 4\right) \cdot z\right)
double f(double x, double y, double z) {
        double r135714 = x;
        double r135715 = r135714 * r135714;
        double r135716 = y;
        double r135717 = 4.0;
        double r135718 = r135716 * r135717;
        double r135719 = z;
        double r135720 = r135718 * r135719;
        double r135721 = r135715 - r135720;
        return r135721;
}
↓
double f(double x, double y, double z) {
        double r135722 = x;
        double r135723 = y;
        double r135724 = 4.0;
        double r135725 = r135723 * r135724;
        double r135726 = z;
        double r135727 = r135725 * r135726;
        double r135728 = -r135727;
        double r135729 = fma(r135722, r135722, r135728);
        return r135729;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))