Average Error: 0.0 → 0.0
Time: 2.8s
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 r128648 = x;
        double r128649 = r128648 * r128648;
        double r128650 = y;
        double r128651 = 4.0;
        double r128652 = r128650 * r128651;
        double r128653 = z;
        double r128654 = r128652 * r128653;
        double r128655 = r128649 - r128654;
        return r128655;
}
↓
double f(double x, double y, double z) {
        double r128656 = x;
        double r128657 = y;
        double r128658 = 4.0;
        double r128659 = r128657 * r128658;
        double r128660 = z;
        double r128661 = r128659 * r128660;
        double r128662 = -r128661;
        double r128663 = fma(r128656, r128656, r128662);
        return r128663;
}

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 2019354 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))