Average Error: 0.0 → 0.0
Time: 8.4s
Precision: 64
\[\left(x + y\right) - x \cdot y\]
↓
\[\mathsf{fma}\left(1 - x, y, x\right)\]
\left(x + y\right) - x \cdot y
↓
\mathsf{fma}\left(1 - x, y, x\right)
double f(double x, double y) {
        double r9036996 = x;
        double r9036997 = y;
        double r9036998 = r9036996 + r9036997;
        double r9036999 = r9036996 * r9036997;
        double r9037000 = r9036998 - r9036999;
        return r9037000;
}
↓
double f(double x, double y) {
        double r9037001 = 1.0;
        double r9037002 = x;
        double r9037003 = r9037001 - r9037002;
        double r9037004 = y;
        double r9037005 = fma(r9037003, r9037004, r9037002);
        return r9037005;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x + y\right) - x \cdot y\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  (- (+ x y) (* x y)))