Average Error: 0.1 → 0.1
Time: 1.9s
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 r143460 = x;
        double r143461 = r143460 * r143460;
        double r143462 = y;
        double r143463 = 4.0;
        double r143464 = r143462 * r143463;
        double r143465 = z;
        double r143466 = r143464 * r143465;
        double r143467 = r143461 - r143466;
        return r143467;
}
↓
double f(double x, double y, double z) {
        double r143468 = x;
        double r143469 = y;
        double r143470 = 4.0;
        double r143471 = r143469 * r143470;
        double r143472 = z;
        double r143473 = r143471 * r143472;
        double r143474 = -r143473;
        double r143475 = fma(r143468, r143468, r143474);
        return r143475;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[x \cdot x - \left(y \cdot 4\right) \cdot z\]
  2. Using strategy rm

  3. Applied fma-neg0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, -\left(y \cdot 4\right) \cdot z\right)}\]

  4. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(x, x, -\left(y \cdot 4\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))