Average Error: 0.0 → 0.0
Time: 9.4s
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 r8164227 = x;
        double r8164228 = y;
        double r8164229 = r8164227 + r8164228;
        double r8164230 = r8164227 * r8164228;
        double r8164231 = r8164229 - r8164230;
        return r8164231;
}
↓
double f(double x, double y) {
        double r8164232 = 1.0;
        double r8164233 = x;
        double r8164234 = r8164232 - r8164233;
        double r8164235 = y;
        double r8164236 = fma(r8164234, r8164235, r8164233);
        return r8164236;
}

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 2019170 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  (- (+ x y) (* x y)))