Average Error: 0.0 → 0.0
Time: 768.0ms
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 r260688 = x;
        double r260689 = 1.0;
        double r260690 = r260688 + r260689;
        double r260691 = y;
        double r260692 = r260690 * r260691;
        double r260693 = r260692 - r260688;
        return r260693;
}
↓
double f(double x, double y) {
        double r260694 = x;
        double r260695 = 1.0;
        double r260696 = r260694 + r260695;
        double r260697 = y;
        double r260698 = -r260694;
        double r260699 = fma(r260696, r260697, r260698);
        return r260699;
}

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 2020046 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))