Average Error: 0.0 → 0.0
Time: 6.6s
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 r9025945 = x;
        double r9025946 = y;
        double r9025947 = r9025945 + r9025946;
        double r9025948 = r9025945 * r9025946;
        double r9025949 = r9025947 - r9025948;
        return r9025949;
}
↓
double f(double x, double y) {
        double r9025950 = 1.0;
        double r9025951 = x;
        double r9025952 = r9025950 - r9025951;
        double r9025953 = y;
        double r9025954 = fma(r9025952, r9025953, r9025951);
        return r9025954;
}

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 2019163 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  (- (+ x y) (* x y)))