Average Error: 0.0 → 0.0
Time: 12.7s
Precision: 64
\[500 \cdot \left(x - y\right)\]
↓
\[\mathsf{fma}\left(500, x, \left(-y\right) \cdot 500\right)\]
500 \cdot \left(x - y\right)
↓
\mathsf{fma}\left(500, x, \left(-y\right) \cdot 500\right)
double f(double x, double y) {
        double r145873 = 500.0;
        double r145874 = x;
        double r145875 = y;
        double r145876 = r145874 - r145875;
        double r145877 = r145873 * r145876;
        return r145877;
}
↓
double f(double x, double y) {
        double r145878 = 500.0;
        double r145879 = x;
        double r145880 = y;
        double r145881 = -r145880;
        double r145882 = r145881 * r145878;
        double r145883 = fma(r145878, r145879, r145882);
        return r145883;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[500 \cdot \left(x - y\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto 500 \cdot \color{blue}{\left(x + \left(-y\right)\right)}\]

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{500 \cdot x + 500 \cdot \left(-y\right)}\]

  5. Simplified0.0

    \[\leadsto 500 \cdot x + \color{blue}{\left(-y\right) \cdot 500}\]
  6. Using strategy rm

  7. Applied fma-def0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(500, x, \left(-y\right) \cdot 500\right)}\]

  8. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(500, x, \left(-y\right) \cdot 500\right)\]

Reproduce

herbie shell --seed 2019304 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500 (- x y)))