Average Error: 0.0 → 0.0
Time: 1.6s
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 r651 = x;
        double r652 = r651 * r651;
        double r653 = y;
        double r654 = 4.0;
        double r655 = r653 * r654;
        double r656 = z;
        double r657 = r655 * r656;
        double r658 = r652 - r657;
        return r658;
}
↓
double f(double x, double y, double z) {
        double r659 = x;
        double r660 = y;
        double r661 = 4.0;
        double r662 = r660 * r661;
        double r663 = z;
        double r664 = r662 * r663;
        double r665 = -r664;
        double r666 = fma(r659, r659, r665);
        return r666;
}

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 2020025 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))