Average Error: 0.0 → 0.0
Time: 1.0s
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 r173591 = x;
        double r173592 = r173591 * r173591;
        double r173593 = y;
        double r173594 = 4.0;
        double r173595 = r173593 * r173594;
        double r173596 = z;
        double r173597 = r173595 * r173596;
        double r173598 = r173592 - r173597;
        return r173598;
}
↓
double f(double x, double y, double z) {
        double r173599 = x;
        double r173600 = y;
        double r173601 = 4.0;
        double r173602 = r173600 * r173601;
        double r173603 = z;
        double r173604 = r173602 * r173603;
        double r173605 = -r173604;
        double r173606 = fma(r173599, r173599, r173605);
        return r173606;
}

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 2020064 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))