Average Error: 0.1 → 0.1
Time: 1.9s
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 r153047 = x;
        double r153048 = r153047 * r153047;
        double r153049 = y;
        double r153050 = 4.0;
        double r153051 = r153049 * r153050;
        double r153052 = z;
        double r153053 = r153051 * r153052;
        double r153054 = r153048 - r153053;
        return r153054;
}
↓
double f(double x, double y, double z) {
        double r153055 = x;
        double r153056 = y;
        double r153057 = 4.0;
        double r153058 = r153056 * r153057;
        double r153059 = z;
        double r153060 = r153058 * r153059;
        double r153061 = -r153060;
        double r153062 = fma(r153055, r153055, r153061);
        return r153062;
}

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 2020027 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))