Average Error: 0.0 → 0.0
Time: 4.2s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, x, -z \cdot \left(y \cdot 4\right)\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot z
↓
\mathsf{fma}\left(x, x, -z \cdot \left(y \cdot 4\right)\right)
double f(double x, double y, double z) {
        double r182323 = x;
        double r182324 = r182323 * r182323;
        double r182325 = y;
        double r182326 = 4.0;
        double r182327 = r182325 * r182326;
        double r182328 = z;
        double r182329 = r182327 * r182328;
        double r182330 = r182324 - r182329;
        return r182330;
}
↓
double f(double x, double y, double z) {
        double r182331 = x;
        double r182332 = z;
        double r182333 = y;
        double r182334 = 4.0;
        double r182335 = r182333 * r182334;
        double r182336 = r182332 * r182335;
        double r182337 = -r182336;
        double r182338 = fma(r182331, r182331, r182337);
        return r182338;
}

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. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))