Average Error: 0.0 → 0.0
Time: 9.8s
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 r115786 = x;
        double r115787 = r115786 * r115786;
        double r115788 = y;
        double r115789 = 4.0;
        double r115790 = r115788 * r115789;
        double r115791 = z;
        double r115792 = r115790 * r115791;
        double r115793 = r115787 - r115792;
        return r115793;
}
↓
double f(double x, double y, double z) {
        double r115794 = x;
        double r115795 = y;
        double r115796 = 4.0;
        double r115797 = r115795 * r115796;
        double r115798 = z;
        double r115799 = r115797 * r115798;
        double r115800 = -r115799;
        double r115801 = fma(r115794, r115794, r115800);
        return r115801;
}

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 2019304 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))