Average Error: 0.0 → 0.0
Time: 10.6s
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 r128622 = x;
        double r128623 = 1.0;
        double r128624 = r128622 + r128623;
        double r128625 = y;
        double r128626 = r128624 * r128625;
        double r128627 = r128626 - r128622;
        return r128627;
}
↓
double f(double x, double y) {
        double r128628 = x;
        double r128629 = 1.0;
        double r128630 = r128628 + r128629;
        double r128631 = y;
        double r128632 = -r128628;
        double r128633 = fma(r128630, r128631, r128632);
        return r128633;
}

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 2019325 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))