Average Error: 0.1 → 0.1
Time: 9.0s
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 r118550 = x;
        double r118551 = r118550 * r118550;
        double r118552 = y;
        double r118553 = 4.0;
        double r118554 = r118552 * r118553;
        double r118555 = z;
        double r118556 = r118554 * r118555;
        double r118557 = r118551 - r118556;
        return r118557;
}
↓
double f(double x, double y, double z) {
        double r118558 = x;
        double r118559 = y;
        double r118560 = 4.0;
        double r118561 = r118559 * r118560;
        double r118562 = z;
        double r118563 = r118561 * r118562;
        double r118564 = -r118563;
        double r118565 = fma(r118558, r118558, r118564);
        return r118565;
}

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 2019325 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))