Average Error: 0.0 → 0.0
Time: 1.3s
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 r255621 = x;
        double r255622 = 1.0;
        double r255623 = r255621 + r255622;
        double r255624 = y;
        double r255625 = r255623 * r255624;
        double r255626 = r255625 - r255621;
        return r255626;
}
↓
double f(double x, double y) {
        double r255627 = x;
        double r255628 = 1.0;
        double r255629 = r255627 + r255628;
        double r255630 = y;
        double r255631 = -r255627;
        double r255632 = fma(r255629, r255630, r255631);
        return r255632;
}

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 2020064 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))