Average Error: 0.0 → 0.0
Time: 2.7s
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 r168540 = x;
        double r168541 = r168540 * r168540;
        double r168542 = y;
        double r168543 = 4.0;
        double r168544 = r168542 * r168543;
        double r168545 = z;
        double r168546 = r168544 * r168545;
        double r168547 = r168541 - r168546;
        return r168547;
}
↓
double f(double x, double y, double z) {
        double r168548 = x;
        double r168549 = y;
        double r168550 = 4.0;
        double r168551 = r168549 * r168550;
        double r168552 = z;
        double r168553 = r168551 * r168552;
        double r168554 = -r168553;
        double r168555 = fma(r168548, r168548, r168554);
        return r168555;
}

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 2019353 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))