Average Error: 0.0 → 0.0
Time: 1.2s
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 r213018 = x;
        double r213019 = y;
        double r213020 = r213018 + r213019;
        double r213021 = r213018 * r213019;
        double r213022 = r213020 - r213021;
        return r213022;
}
↓
double f(double x, double y) {
        double r213023 = 1.0;
        double r213024 = x;
        double r213025 = r213023 - r213024;
        double r213026 = y;
        double r213027 = fma(r213025, r213026, r213024);
        return r213027;
}

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 2020081 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))