Average Error: 0.0 → 0.0
Time: 11.4s
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 r161758 = x;
        double r161759 = 1.0;
        double r161760 = r161758 + r161759;
        double r161761 = y;
        double r161762 = r161760 * r161761;
        double r161763 = r161762 - r161758;
        return r161763;
}
↓
double f(double x, double y) {
        double r161764 = x;
        double r161765 = 1.0;
        double r161766 = r161764 + r161765;
        double r161767 = y;
        double r161768 = -r161764;
        double r161769 = fma(r161766, r161767, r161768);
        return r161769;
}

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 2019325 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))