Average Error: 0.0 → 0.0
Time: 6.4s
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 r131359 = x;
        double r131360 = 1.0;
        double r131361 = r131359 + r131360;
        double r131362 = y;
        double r131363 = r131361 * r131362;
        double r131364 = r131363 - r131359;
        return r131364;
}
↓
double f(double x, double y) {
        double r131365 = x;
        double r131366 = 1.0;
        double r131367 = r131365 + r131366;
        double r131368 = y;
        double r131369 = -r131365;
        double r131370 = fma(r131367, r131368, r131369);
        return r131370;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x + 1\right) \cdot y - x\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  (- (* (+ x 1.0) y) x))