Average Error: 0.0 → 0.0
Time: 45.3s
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 r14090607 = x;
        double r14090608 = 1.0;
        double r14090609 = r14090607 + r14090608;
        double r14090610 = y;
        double r14090611 = r14090609 * r14090610;
        double r14090612 = r14090611 - r14090607;
        return r14090612;
}
↓
double f(double x, double y) {
        double r14090613 = x;
        double r14090614 = 1.0;
        double r14090615 = r14090613 + r14090614;
        double r14090616 = y;
        double r14090617 = -r14090613;
        double r14090618 = fma(r14090615, r14090616, r14090617);
        return r14090618;
}

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 2019200 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  (- (* (+ x 1.0) y) x))