Average Error: 0.0 → 0.0
Time: 4.3s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, x, \left(-z\right) \cdot \left(4 \cdot y\right)\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot z
↓
\mathsf{fma}\left(x, x, \left(-z\right) \cdot \left(4 \cdot y\right)\right)
double f(double x, double y, double z) {
        double r5556132 = x;
        double r5556133 = r5556132 * r5556132;
        double r5556134 = y;
        double r5556135 = 4.0;
        double r5556136 = r5556134 * r5556135;
        double r5556137 = z;
        double r5556138 = r5556136 * r5556137;
        double r5556139 = r5556133 - r5556138;
        return r5556139;
}
↓
double f(double x, double y, double z) {
        double r5556140 = x;
        double r5556141 = z;
        double r5556142 = -r5556141;
        double r5556143 = 4.0;
        double r5556144 = y;
        double r5556145 = r5556143 * r5556144;
        double r5556146 = r5556142 * r5556145;
        double r5556147 = fma(r5556140, r5556140, r5556146);
        return r5556147;
}

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

    \[\leadsto \mathsf{fma}\left(x, x, \left(-z\right) \cdot \left(4 \cdot y\right)\right)\]

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  (- (* x x) (* (* y 4.0) z)))