Average Error: 0.1 → 0.1
Time: 1.1s
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 r147785 = x;
        double r147786 = r147785 * r147785;
        double r147787 = y;
        double r147788 = 4.0;
        double r147789 = r147787 * r147788;
        double r147790 = z;
        double r147791 = r147789 * r147790;
        double r147792 = r147786 - r147791;
        return r147792;
}
↓
double f(double x, double y, double z) {
        double r147793 = x;
        double r147794 = y;
        double r147795 = 4.0;
        double r147796 = r147794 * r147795;
        double r147797 = z;
        double r147798 = r147796 * r147797;
        double r147799 = -r147798;
        double r147800 = fma(r147793, r147793, r147799);
        return r147800;
}

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 2020033 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))