Average Error: 0.0 → 0.0
Time: 4.0s
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 r160692 = x;
        double r160693 = r160692 * r160692;
        double r160694 = y;
        double r160695 = 4.0;
        double r160696 = r160694 * r160695;
        double r160697 = z;
        double r160698 = r160696 * r160697;
        double r160699 = r160693 - r160698;
        return r160699;
}
↓
double f(double x, double y, double z) {
        double r160700 = x;
        double r160701 = y;
        double r160702 = 4.0;
        double r160703 = r160701 * r160702;
        double r160704 = z;
        double r160705 = r160703 * r160704;
        double r160706 = -r160705;
        double r160707 = fma(r160700, r160700, r160706);
        return r160707;
}

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 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)))