Average Error: 0.0 → 0.0
Time: 1.2s
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 r206747 = x;
        double r206748 = 1.0;
        double r206749 = r206747 + r206748;
        double r206750 = y;
        double r206751 = r206749 * r206750;
        double r206752 = r206751 - r206747;
        return r206752;
}
↓
double f(double x, double y) {
        double r206753 = x;
        double r206754 = 1.0;
        double r206755 = r206753 + r206754;
        double r206756 = y;
        double r206757 = -r206753;
        double r206758 = fma(r206755, r206756, r206757);
        return r206758;
}

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 2020062 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))