Average Error: 0.0 → 0.0
Time: 7.8s
Precision: 64
\[\left(x + 1\right) \cdot y - x\]
↓
\[\mathsf{fma}\left(1 + x, y, -x\right)\]
\left(x + 1\right) \cdot y - x
↓
\mathsf{fma}\left(1 + x, y, -x\right)
double f(double x, double y) {
        double r8329412 = x;
        double r8329413 = 1.0;
        double r8329414 = r8329412 + r8329413;
        double r8329415 = y;
        double r8329416 = r8329414 * r8329415;
        double r8329417 = r8329416 - r8329412;
        return r8329417;
}
↓
double f(double x, double y) {
        double r8329418 = 1.0;
        double r8329419 = x;
        double r8329420 = r8329418 + r8329419;
        double r8329421 = y;
        double r8329422 = -r8329419;
        double r8329423 = fma(r8329420, r8329421, r8329422);
        return r8329423;
}

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

    \[\leadsto \mathsf{fma}\left(1 + x, y, -x\right)\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  (- (* (+ x 1.0) y) x))