Average Error: 0.1 → 0.1
Time: 9.0s
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 r115899 = x;
        double r115900 = r115899 * r115899;
        double r115901 = y;
        double r115902 = 4.0;
        double r115903 = r115901 * r115902;
        double r115904 = z;
        double r115905 = r115903 * r115904;
        double r115906 = r115900 - r115905;
        return r115906;
}
↓
double f(double x, double y, double z) {
        double r115907 = x;
        double r115908 = y;
        double r115909 = 4.0;
        double r115910 = r115908 * r115909;
        double r115911 = z;
        double r115912 = r115910 * r115911;
        double r115913 = -r115912;
        double r115914 = fma(r115907, r115907, r115913);
        return r115914;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[x \cdot x - \left(y \cdot 4\right) \cdot z\]
  2. Using strategy rm

  3. Applied fma-neg0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))