Average Error: 0.0 → 0.0
Time: 9.1s
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 r221454 = 200.0;
        double r221455 = x;
        double r221456 = y;
        double r221457 = r221455 - r221456;
        double r221458 = r221454 * r221457;
        return r221458;
}
↓
double f(double x, double y) {
        double r221459 = x;
        double r221460 = 200.0;
        double r221461 = y;
        double r221462 = -r221461;
        double r221463 = r221462 * r221460;
        double r221464 = fma(r221459, r221460, r221463);
        return r221464;
}

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)))