Average Error: 0.0 → 0.0
Time: 7.3s
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 r164519 = x;
        double r164520 = 1.0;
        double r164521 = r164519 + r164520;
        double r164522 = y;
        double r164523 = r164521 * r164522;
        double r164524 = r164523 - r164519;
        return r164524;
}
↓
double f(double x, double y) {
        double r164525 = x;
        double r164526 = 1.0;
        double r164527 = r164525 + r164526;
        double r164528 = y;
        double r164529 = -r164525;
        double r164530 = fma(r164527, r164528, r164529);
        return r164530;
}

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 2019196 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  (- (* (+ x 1.0) y) x))