Average Error: 0.0 → 0.0
Time: 4.3s
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 r96694 = x;
        double r96695 = r96694 * r96694;
        double r96696 = y;
        double r96697 = 4.0;
        double r96698 = r96696 * r96697;
        double r96699 = z;
        double r96700 = r96698 * r96699;
        double r96701 = r96695 - r96700;
        return r96701;
}
↓
double f(double x, double y, double z) {
        double r96702 = x;
        double r96703 = y;
        double r96704 = 4.0;
        double r96705 = r96703 * r96704;
        double r96706 = z;
        double r96707 = r96705 * r96706;
        double r96708 = -r96707;
        double r96709 = fma(r96702, r96702, r96708);
        return r96709;
}

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 2019323 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))