Average Error: 0.0 → 0.0
Time: 11.3s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, x, \left(-z\right) \cdot \left(4 \cdot y\right)\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot z
↓
\mathsf{fma}\left(x, x, \left(-z\right) \cdot \left(4 \cdot y\right)\right)
double f(double x, double y, double z) {
        double r7912912 = x;
        double r7912913 = r7912912 * r7912912;
        double r7912914 = y;
        double r7912915 = 4.0;
        double r7912916 = r7912914 * r7912915;
        double r7912917 = z;
        double r7912918 = r7912916 * r7912917;
        double r7912919 = r7912913 - r7912918;
        return r7912919;
}
↓
double f(double x, double y, double z) {
        double r7912920 = x;
        double r7912921 = z;
        double r7912922 = -r7912921;
        double r7912923 = 4.0;
        double r7912924 = y;
        double r7912925 = r7912923 * r7912924;
        double r7912926 = r7912922 * r7912925;
        double r7912927 = fma(r7912920, r7912920, r7912926);
        return r7912927;
}

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

    \[\leadsto \mathsf{fma}\left(x, x, \left(-z\right) \cdot \left(4 \cdot y\right)\right)\]

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  (- (* x x) (* (* y 4.0) z)))