Average Error: 0.0 → 0.0
Time: 944.0ms
Precision: 64
\[500 \cdot \left(x - y\right)\]
↓
\[\mathsf{fma}\left(500, x, 500 \cdot \left(-y\right)\right)\]
500 \cdot \left(x - y\right)
↓
\mathsf{fma}\left(500, x, 500 \cdot \left(-y\right)\right)
double f(double x, double y) {
        double r236436 = 500.0;
        double r236437 = x;
        double r236438 = y;
        double r236439 = r236437 - r236438;
        double r236440 = r236436 * r236439;
        return r236440;
}
↓
double f(double x, double y) {
        double r236441 = 500.0;
        double r236442 = x;
        double r236443 = y;
        double r236444 = -r236443;
        double r236445 = r236441 * r236444;
        double r236446 = fma(r236441, r236442, r236445);
        return r236446;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[500 \cdot \left(x - y\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.0

    \[\leadsto 500 \cdot \color{blue}{\left(x + \left(-y\right)\right)}\]

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{500 \cdot x + 500 \cdot \left(-y\right)}\]
  5. Using strategy rm

  6. Applied fma-def0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(500, x, 500 \cdot \left(-y\right)\right)}\]

  7. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(500, x, 500 \cdot \left(-y\right)\right)\]

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500 (- x y)))