Average Error: 0.0 → 0.0
Time: 1.5s
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 r230714 = x;
        double r230715 = r230714 * r230714;
        double r230716 = y;
        double r230717 = 4.0;
        double r230718 = r230716 * r230717;
        double r230719 = z;
        double r230720 = r230718 * r230719;
        double r230721 = r230715 - r230720;
        return r230721;
}
↓
double f(double x, double y, double z) {
        double r230722 = x;
        double r230723 = y;
        double r230724 = 4.0;
        double r230725 = r230723 * r230724;
        double r230726 = z;
        double r230727 = r230725 * r230726;
        double r230728 = -r230727;
        double r230729 = fma(r230722, r230722, r230728);
        return r230729;
}

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 2020024 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))