Average Error: 0.0 → 0.0
Time: 4.3s
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 r117590 = x;
        double r117591 = r117590 * r117590;
        double r117592 = y;
        double r117593 = 4.0;
        double r117594 = r117592 * r117593;
        double r117595 = z;
        double r117596 = r117594 * r117595;
        double r117597 = r117591 - r117596;
        return r117597;
}
↓
double f(double x, double y, double z) {
        double r117598 = x;
        double r117599 = y;
        double r117600 = 4.0;
        double r117601 = r117599 * r117600;
        double r117602 = z;
        double r117603 = r117601 * r117602;
        double r117604 = -r117603;
        double r117605 = fma(r117598, r117598, r117604);
        return r117605;
}

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 2019323 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))