Average Error: 0.0 → 0.0
Time: 14.3s
Precision: 64
\[\left(x + 1\right) \cdot y - x\]
↓
\[\mathsf{fma}\left(1 + x, y, -x\right)\]
\left(x + 1\right) \cdot y - x
↓
\mathsf{fma}\left(1 + x, y, -x\right)
double f(double x, double y) {
        double r10152794 = x;
        double r10152795 = 1.0;
        double r10152796 = r10152794 + r10152795;
        double r10152797 = y;
        double r10152798 = r10152796 * r10152797;
        double r10152799 = r10152798 - r10152794;
        return r10152799;
}
↓
double f(double x, double y) {
        double r10152800 = 1.0;
        double r10152801 = x;
        double r10152802 = r10152800 + r10152801;
        double r10152803 = y;
        double r10152804 = -r10152801;
        double r10152805 = fma(r10152802, r10152803, r10152804);
        return r10152805;
}

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

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  (- (* (+ x 1.0) y) x))