Average Error: 0.0 → 0.0
Time: 2.9s
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 r165273 = x;
        double r165274 = r165273 * r165273;
        double r165275 = y;
        double r165276 = 4.0;
        double r165277 = r165275 * r165276;
        double r165278 = z;
        double r165279 = r165277 * r165278;
        double r165280 = r165274 - r165279;
        return r165280;
}
↓
double f(double x, double y, double z) {
        double r165281 = x;
        double r165282 = y;
        double r165283 = 4.0;
        double r165284 = r165282 * r165283;
        double r165285 = z;
        double r165286 = r165284 * r165285;
        double r165287 = -r165286;
        double r165288 = fma(r165281, r165281, r165287);
        return r165288;
}

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 2020047 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))