Average Error: 0.0 → 0.0
Time: 8.0s
Precision: 64
\[200 \cdot \left(x - y\right)\]
↓
\[\mathsf{fma}\left(x, 200, \left(-y\right) \cdot 200\right)\]
200 \cdot \left(x - y\right)
↓
\mathsf{fma}\left(x, 200, \left(-y\right) \cdot 200\right)
double f(double x, double y) {
        double r175336 = 200.0;
        double r175337 = x;
        double r175338 = y;
        double r175339 = r175337 - r175338;
        double r175340 = r175336 * r175339;
        return r175340;
}
↓
double f(double x, double y) {
        double r175341 = x;
        double r175342 = 200.0;
        double r175343 = y;
        double r175344 = -r175343;
        double r175345 = r175344 * r175342;
        double r175346 = fma(r175341, r175342, r175345);
        return r175346;
}

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

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

  6. Simplified0.0

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

  8. Applied fma-def0.0

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

  9. Final simplification0.0

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

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)))