Average Error: 0.0 → 0.0
Time: 3.7s
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 r167847 = x;
        double r167848 = r167847 * r167847;
        double r167849 = y;
        double r167850 = 4.0;
        double r167851 = r167849 * r167850;
        double r167852 = z;
        double r167853 = r167851 * r167852;
        double r167854 = r167848 - r167853;
        return r167854;
}
↓
double f(double x, double y, double z) {
        double r167855 = x;
        double r167856 = y;
        double r167857 = 4.0;
        double r167858 = r167856 * r167857;
        double r167859 = z;
        double r167860 = r167858 * r167859;
        double r167861 = -r167860;
        double r167862 = fma(r167855, r167855, r167861);
        return r167862;
}

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 2020045 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))