Average Error: 0.0 → 0.0
Time: 776.0ms
Precision: 64
\[\left(x + 1\right) \cdot y - x\]
↓
\[\mathsf{fma}\left(x + 1, y, -x\right)\]
\left(x + 1\right) \cdot y - x
↓
\mathsf{fma}\left(x + 1, y, -x\right)
double f(double x, double y) {
        double r236702 = x;
        double r236703 = 1.0;
        double r236704 = r236702 + r236703;
        double r236705 = y;
        double r236706 = r236704 * r236705;
        double r236707 = r236706 - r236702;
        return r236707;
}
↓
double f(double x, double y) {
        double r236708 = x;
        double r236709 = 1.0;
        double r236710 = r236708 + r236709;
        double r236711 = y;
        double r236712 = -r236708;
        double r236713 = fma(r236710, r236711, r236712);
        return r236713;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x + 1\right) \cdot y - x\]
  2. Using strategy rm

  3. Applied fma-neg0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x + 1, y, -x\right)}\]

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x + 1, y, -x\right)\]

Reproduce

herbie shell --seed 2020056 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))