Average Error: 0.0 → 0.0
Time: 8.3s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot z\]
↓
\[\mathsf{fma}\left(z \cdot \left(-4\right), y, x \cdot x\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot z
↓
\mathsf{fma}\left(z \cdot \left(-4\right), y, x \cdot x\right)
double f(double x, double y, double z) {
        double r131880 = x;
        double r131881 = r131880 * r131880;
        double r131882 = y;
        double r131883 = 4.0;
        double r131884 = r131882 * r131883;
        double r131885 = z;
        double r131886 = r131884 * r131885;
        double r131887 = r131881 - r131886;
        return r131887;
}
↓
double f(double x, double y, double z) {
        double r131888 = z;
        double r131889 = 4.0;
        double r131890 = -r131889;
        double r131891 = r131888 * r131890;
        double r131892 = y;
        double r131893 = x;
        double r131894 = r131893 * r131893;
        double r131895 = fma(r131891, r131892, r131894);
        return r131895;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  (- (* x x) (* (* y 4.0) z)))