Average Error: 0.0 → 0.0
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 r138400 = x;
        double r138401 = r138400 * r138400;
        double r138402 = y;
        double r138403 = 4.0;
        double r138404 = r138402 * r138403;
        double r138405 = z;
        double r138406 = r138404 * r138405;
        double r138407 = r138401 - r138406;
        return r138407;
}
↓
double f(double x, double y, double z) {
        double r138408 = x;
        double r138409 = y;
        double r138410 = 4.0;
        double r138411 = r138409 * r138410;
        double r138412 = z;
        double r138413 = r138411 * r138412;
        double r138414 = -r138413;
        double r138415 = fma(r138408, r138408, r138414);
        return r138415;
}

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 2020100 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))