Average Error: 0.0 → 0.0
Time: 9.8s
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 r118322 = x;
        double r118323 = r118322 * r118322;
        double r118324 = y;
        double r118325 = 4.0;
        double r118326 = r118324 * r118325;
        double r118327 = z;
        double r118328 = r118326 * r118327;
        double r118329 = r118323 - r118328;
        return r118329;
}
↓
double f(double x, double y, double z) {
        double r118330 = x;
        double r118331 = y;
        double r118332 = 4.0;
        double r118333 = r118331 * r118332;
        double r118334 = z;
        double r118335 = r118333 * r118334;
        double r118336 = -r118335;
        double r118337 = fma(r118330, r118330, r118336);
        return r118337;
}

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 2019322 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))