Average Error: 0.0 → 0.0
Time: 876.0ms
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 r165896 = x;
        double r165897 = 1.0;
        double r165898 = r165896 + r165897;
        double r165899 = y;
        double r165900 = r165898 * r165899;
        double r165901 = r165900 - r165896;
        return r165901;
}
↓
double f(double x, double y) {
        double r165902 = x;
        double r165903 = 1.0;
        double r165904 = r165902 + r165903;
        double r165905 = y;
        double r165906 = -r165902;
        double r165907 = fma(r165904, r165905, r165906);
        return r165907;
}

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 2020001 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))