Average Error: 0.0 → 0.0
Time: 10.8s
Precision: 64
\[\left(x + y\right) - x \cdot y\]
↓
\[\mathsf{fma}\left(y, 1 - x, x\right)\]
\left(x + y\right) - x \cdot y
↓
\mathsf{fma}\left(y, 1 - x, x\right)
double f(double x, double y) {
        double r263952 = x;
        double r263953 = y;
        double r263954 = r263952 + r263953;
        double r263955 = r263952 * r263953;
        double r263956 = r263954 - r263955;
        return r263956;
}
↓
double f(double x, double y) {
        double r263957 = y;
        double r263958 = 1.0;
        double r263959 = x;
        double r263960 = r263958 - r263959;
        double r263961 = fma(r263957, r263960, r263959);
        return r263961;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))