Average Error: 0.0 → 0.0
Time: 17.0s
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 r10084978 = x;
        double r10084979 = 1.0;
        double r10084980 = r10084978 + r10084979;
        double r10084981 = y;
        double r10084982 = r10084980 * r10084981;
        double r10084983 = r10084982 - r10084978;
        return r10084983;
}
↓
double f(double x, double y) {
        double r10084984 = 1.0;
        double r10084985 = x;
        double r10084986 = r10084984 + r10084985;
        double r10084987 = y;
        double r10084988 = -r10084985;
        double r10084989 = fma(r10084986, r10084987, r10084988);
        return r10084989;
}

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))