Average Error: 0.0 → 0.0
Time: 2.5s
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 r209732 = x;
        double r209733 = r209732 * r209732;
        double r209734 = y;
        double r209735 = 4.0;
        double r209736 = r209734 * r209735;
        double r209737 = z;
        double r209738 = r209736 * r209737;
        double r209739 = r209733 - r209738;
        return r209739;
}
↓
double f(double x, double y, double z) {
        double r209740 = x;
        double r209741 = z;
        double r209742 = y;
        double r209743 = 4.0;
        double r209744 = r209742 * r209743;
        double r209745 = r209741 * r209744;
        double r209746 = -r209745;
        double r209747 = fma(r209740, r209740, r209746);
        return r209747;
}

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 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)))