Average Error: 0.0 → 0.0
Time: 581.0ms
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 r216183 = x;
        double r216184 = y;
        double r216185 = r216183 + r216184;
        double r216186 = r216183 * r216184;
        double r216187 = r216185 - r216186;
        return r216187;
}
↓
double f(double x, double y) {
        double r216188 = 1.0;
        double r216189 = x;
        double r216190 = r216188 - r216189;
        double r216191 = y;
        double r216192 = fma(r216190, r216191, r216189);
        return r216192;
}

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 2020039 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))