Average Error: 0.0 → 0.0
Time: 867.0ms
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 r192445 = x;
        double r192446 = r192445 * r192445;
        double r192447 = y;
        double r192448 = 4.0;
        double r192449 = r192447 * r192448;
        double r192450 = z;
        double r192451 = r192449 * r192450;
        double r192452 = r192446 - r192451;
        return r192452;
}
↓
double f(double x, double y, double z) {
        double r192453 = x;
        double r192454 = y;
        double r192455 = 4.0;
        double r192456 = r192454 * r192455;
        double r192457 = z;
        double r192458 = r192456 * r192457;
        double r192459 = -r192458;
        double r192460 = fma(r192453, r192453, r192459);
        return r192460;
}

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 2019352 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))