Average Error: 0.0 → 0.0
Time: 807.0ms
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 r133140 = x;
        double r133141 = r133140 * r133140;
        double r133142 = y;
        double r133143 = 4.0;
        double r133144 = r133142 * r133143;
        double r133145 = z;
        double r133146 = r133144 * r133145;
        double r133147 = r133141 - r133146;
        return r133147;
}
↓
double f(double x, double y, double z) {
        double r133148 = x;
        double r133149 = y;
        double r133150 = 4.0;
        double r133151 = r133149 * r133150;
        double r133152 = z;
        double r133153 = r133151 * r133152;
        double r133154 = -r133153;
        double r133155 = fma(r133148, r133148, r133154);
        return r133155;
}

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 2020056 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))