Average Error: 0.0 → 0.0
Time: 4.1s
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 r147930 = x;
        double r147931 = r147930 * r147930;
        double r147932 = y;
        double r147933 = 4.0;
        double r147934 = r147932 * r147933;
        double r147935 = z;
        double r147936 = r147934 * r147935;
        double r147937 = r147931 - r147936;
        return r147937;
}
↓
double f(double x, double y, double z) {
        double r147938 = x;
        double r147939 = y;
        double r147940 = 4.0;
        double r147941 = r147939 * r147940;
        double r147942 = z;
        double r147943 = r147941 * r147942;
        double r147944 = -r147943;
        double r147945 = fma(r147938, r147938, r147944);
        return r147945;
}

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)))