Average Error: 0.1 → 0.1
Time: 1.1s
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 r131573 = x;
        double r131574 = r131573 * r131573;
        double r131575 = y;
        double r131576 = 4.0;
        double r131577 = r131575 * r131576;
        double r131578 = z;
        double r131579 = r131577 * r131578;
        double r131580 = r131574 - r131579;
        return r131580;
}
↓
double f(double x, double y, double z) {
        double r131581 = x;
        double r131582 = y;
        double r131583 = 4.0;
        double r131584 = r131582 * r131583;
        double r131585 = z;
        double r131586 = r131584 * r131585;
        double r131587 = -r131586;
        double r131588 = fma(r131581, r131581, r131587);
        return r131588;
}

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 2020083 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))