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 r216716 = x;
        double r216717 = 1.0;
        double r216718 = r216716 + r216717;
        double r216719 = y;
        double r216720 = r216718 * r216719;
        double r216721 = r216720 - r216716;
        return r216721;
}
↓
double f(double x, double y) {
        double r216722 = x;
        double r216723 = 1.0;
        double r216724 = r216722 + r216723;
        double r216725 = y;
        double r216726 = -r216722;
        double r216727 = fma(r216724, r216725, r216726);
        return r216727;
}

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 2020062 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))