Average Error: 0.0 → 0.0
Time: 791.0ms
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 r263447 = 200.0;
        double r263448 = x;
        double r263449 = y;
        double r263450 = r263448 - r263449;
        double r263451 = r263447 * r263450;
        return r263451;
}
↓
double f(double x, double y) {
        double r263452 = 200.0;
        double r263453 = x;
        double r263454 = y;
        double r263455 = -r263454;
        double r263456 = r263452 * r263455;
        double r263457 = fma(r263452, r263453, r263456);
        return r263457;
}

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 2020018 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200 (- x y)))