Average Error: 0.0 → 0.0
Time: 874.0ms
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 r228275 = x;
        double r228276 = y;
        double r228277 = r228275 + r228276;
        double r228278 = r228275 * r228276;
        double r228279 = r228277 - r228278;
        return r228279;
}
↓
double f(double x, double y) {
        double r228280 = 1.0;
        double r228281 = x;
        double r228282 = r228280 - r228281;
        double r228283 = y;
        double r228284 = fma(r228282, r228283, r228281);
        return r228284;
}

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 2020056 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))