Average Error: 0.0 → 0.0
Time: 5.5s
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 r161309 = x;
        double r161310 = r161309 * r161309;
        double r161311 = y;
        double r161312 = 4.0;
        double r161313 = r161311 * r161312;
        double r161314 = z;
        double r161315 = r161313 * r161314;
        double r161316 = r161310 - r161315;
        return r161316;
}
↓
double f(double x, double y, double z) {
        double r161317 = x;
        double r161318 = y;
        double r161319 = 4.0;
        double r161320 = r161318 * r161319;
        double r161321 = z;
        double r161322 = r161320 * r161321;
        double r161323 = -r161322;
        double r161324 = fma(r161317, r161317, r161323);
        return r161324;
}

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 2019303 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))