Average Error: 0.0 → 0.0
Time: 6.2s
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 r95707 = x;
        double r95708 = r95707 * r95707;
        double r95709 = y;
        double r95710 = 4.0;
        double r95711 = r95709 * r95710;
        double r95712 = z;
        double r95713 = r95711 * r95712;
        double r95714 = r95708 - r95713;
        return r95714;
}
↓
double f(double x, double y, double z) {
        double r95715 = x;
        double r95716 = y;
        double r95717 = 4.0;
        double r95718 = r95716 * r95717;
        double r95719 = z;
        double r95720 = r95718 * r95719;
        double r95721 = -r95720;
        double r95722 = fma(r95715, r95715, r95721);
        return r95722;
}

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 2019306 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))