Average Error: 0.0 → 0.0
Time: 734.0ms
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 r285699 = x;
        double r285700 = 1.0;
        double r285701 = r285699 + r285700;
        double r285702 = y;
        double r285703 = r285701 * r285702;
        double r285704 = r285703 - r285699;
        return r285704;
}
↓
double f(double x, double y) {
        double r285705 = x;
        double r285706 = 1.0;
        double r285707 = r285705 + r285706;
        double r285708 = y;
        double r285709 = -r285705;
        double r285710 = fma(r285707, r285708, r285709);
        return r285710;
}

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 2019354 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))