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 r191683 = x;
        double r191684 = r191683 * r191683;
        double r191685 = y;
        double r191686 = 4.0;
        double r191687 = r191685 * r191686;
        double r191688 = z;
        double r191689 = r191687 * r191688;
        double r191690 = r191684 - r191689;
        return r191690;
}
↓
double f(double x, double y, double z) {
        double r191691 = x;
        double r191692 = z;
        double r191693 = y;
        double r191694 = 4.0;
        double r191695 = r191693 * r191694;
        double r191696 = r191692 * r191695;
        double r191697 = -r191696;
        double r191698 = fma(r191691, r191691, r191697);
        return r191698;
}

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 2019209 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))