Average Error: 0.0 → 0.0
Time: 848.0ms
Precision: 64
\[\left(x + 1\right) \cdot y - x\]
↓
\[\mathsf{fma}\left(x + 1, y, -x\right)\]
\left(x + 1\right) \cdot y - x
↓
\mathsf{fma}\left(x + 1, y, -x\right)
double f(double x, double y) {
        double r205704 = x;
        double r205705 = 1.0;
        double r205706 = r205704 + r205705;
        double r205707 = y;
        double r205708 = r205706 * r205707;
        double r205709 = r205708 - r205704;
        return r205709;
}
↓
double f(double x, double y) {
        double r205710 = x;
        double r205711 = 1.0;
        double r205712 = r205710 + r205711;
        double r205713 = y;
        double r205714 = -r205710;
        double r205715 = fma(r205712, r205713, r205714);
        return r205715;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x + 1\right) \cdot y - x\]
  2. Using strategy rm

  3. Applied fma-neg0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))