Average Error: 0.0 → 0.0
Time: 6.3s
Precision: 64
\[x \cdot x - \left(y \cdot 4.0\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, x, \left(-z\right) \cdot \left(4.0 \cdot y\right)\right)\]
x \cdot x - \left(y \cdot 4.0\right) \cdot z
↓
\mathsf{fma}\left(x, x, \left(-z\right) \cdot \left(4.0 \cdot y\right)\right)
double f(double x, double y, double z) {
        double r11163976 = x;
        double r11163977 = r11163976 * r11163976;
        double r11163978 = y;
        double r11163979 = 4.0;
        double r11163980 = r11163978 * r11163979;
        double r11163981 = z;
        double r11163982 = r11163980 * r11163981;
        double r11163983 = r11163977 - r11163982;
        return r11163983;
}
↓
double f(double x, double y, double z) {
        double r11163984 = x;
        double r11163985 = z;
        double r11163986 = -r11163985;
        double r11163987 = 4.0;
        double r11163988 = y;
        double r11163989 = r11163987 * r11163988;
        double r11163990 = r11163986 * r11163989;
        double r11163991 = fma(r11163984, r11163984, r11163990);
        return r11163991;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot x - \left(y \cdot 4.0\right) \cdot z\]
  2. Using strategy rm

  3. Applied fma-neg0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, -\left(y \cdot 4.0\right) \cdot z\right)}\]

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, x, \left(-z\right) \cdot \left(4.0 \cdot y\right)\right)\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  (- (* x x) (* (* y 4.0) z)))