Average Error: 0.0 → 0.0
Time: 5.2s
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 r102456 = x;
        double r102457 = r102456 * r102456;
        double r102458 = y;
        double r102459 = 4.0;
        double r102460 = r102458 * r102459;
        double r102461 = z;
        double r102462 = r102460 * r102461;
        double r102463 = r102457 - r102462;
        return r102463;
}
↓
double f(double x, double y, double z) {
        double r102464 = x;
        double r102465 = z;
        double r102466 = y;
        double r102467 = 4.0;
        double r102468 = r102466 * r102467;
        double r102469 = r102465 * r102468;
        double r102470 = -r102469;
        double r102471 = fma(r102464, r102464, r102470);
        return r102471;
}

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 2019208 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))