Average Error: 0.0 → 0.0
Time: 1.2s
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 r171628 = x;
        double r171629 = 1.0;
        double r171630 = r171628 + r171629;
        double r171631 = y;
        double r171632 = r171630 * r171631;
        double r171633 = r171632 - r171628;
        return r171633;
}
↓
double f(double x, double y) {
        double r171634 = x;
        double r171635 = 1.0;
        double r171636 = r171634 + r171635;
        double r171637 = y;
        double r171638 = -r171634;
        double r171639 = fma(r171636, r171637, r171638);
        return r171639;
}

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 2020025 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))