Average Error: 0.0 → 0.0
Time: 12.2s
Precision: 64
\[200 \cdot \left(x - y\right)\]
↓
\[\mathsf{fma}\left(200, x, \left(-y\right) \cdot 200\right)\]
200 \cdot \left(x - y\right)
↓
\mathsf{fma}\left(200, x, \left(-y\right) \cdot 200\right)
double f(double x, double y) {
        double r135212 = 200.0;
        double r135213 = x;
        double r135214 = y;
        double r135215 = r135213 - r135214;
        double r135216 = r135212 * r135215;
        return r135216;
}
↓
double f(double x, double y) {
        double r135217 = 200.0;
        double r135218 = x;
        double r135219 = y;
        double r135220 = -r135219;
        double r135221 = r135220 * r135217;
        double r135222 = fma(r135217, r135218, r135221);
        return r135222;
}

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. Simplified0.0

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

  7. Applied fma-def0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200 (- x y)))