Average Error: 0.0 → 0.0
Time: 1.3s
Precision: 64
\[200 \cdot \left(x - y\right)\]
↓
\[\mathsf{fma}\left(200, x, 200 \cdot \left(-y\right)\right)\]
200 \cdot \left(x - y\right)
↓
\mathsf{fma}\left(200, x, 200 \cdot \left(-y\right)\right)
double f(double x, double y) {
        double r222895 = 200.0;
        double r222896 = x;
        double r222897 = y;
        double r222898 = r222896 - r222897;
        double r222899 = r222895 * r222898;
        return r222899;
}
↓
double f(double x, double y) {
        double r222900 = 200.0;
        double r222901 = x;
        double r222902 = y;
        double r222903 = -r222902;
        double r222904 = r222900 * r222903;
        double r222905 = fma(r222900, r222901, r222904);
        return r222905;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[200 \cdot \left(x - y\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto 200 \cdot \color{blue}{\left(x + \left(-y\right)\right)}\]

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{200 \cdot x + 200 \cdot \left(-y\right)}\]
  5. Using strategy rm

  6. Applied fma-def0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(200, x, 200 \cdot \left(-y\right)\right)}\]

  7. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(200, x, 200 \cdot \left(-y\right)\right)\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200 (- x y)))