Average Error: 0.0 → 0.0
Time: 885.0ms
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 r160212 = x;
        double r160213 = r160212 * r160212;
        double r160214 = y;
        double r160215 = 4.0;
        double r160216 = r160214 * r160215;
        double r160217 = z;
        double r160218 = r160216 * r160217;
        double r160219 = r160213 - r160218;
        return r160219;
}
↓
double f(double x, double y, double z) {
        double r160220 = x;
        double r160221 = y;
        double r160222 = 4.0;
        double r160223 = r160221 * r160222;
        double r160224 = z;
        double r160225 = r160223 * r160224;
        double r160226 = -r160225;
        double r160227 = fma(r160220, r160220, r160226);
        return r160227;
}

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 2020021 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))