Average Error: 0.1 → 0.1
Time: 1.1s
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 r147235 = x;
        double r147236 = r147235 * r147235;
        double r147237 = y;
        double r147238 = 4.0;
        double r147239 = r147237 * r147238;
        double r147240 = z;
        double r147241 = r147239 * r147240;
        double r147242 = r147236 - r147241;
        return r147242;
}
↓
double f(double x, double y, double z) {
        double r147243 = x;
        double r147244 = y;
        double r147245 = 4.0;
        double r147246 = r147244 * r147245;
        double r147247 = z;
        double r147248 = r147246 * r147247;
        double r147249 = -r147248;
        double r147250 = fma(r147243, r147243, r147249);
        return r147250;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[x \cdot x - \left(y \cdot 4\right) \cdot z\]
  2. Using strategy rm

  3. Applied fma-neg0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020089 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))