Average Error: 0.0 → 0.0
Time: 6.2s
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 r194285 = x;
        double r194286 = 1.0;
        double r194287 = r194285 + r194286;
        double r194288 = y;
        double r194289 = r194287 * r194288;
        double r194290 = r194289 - r194285;
        return r194290;
}
↓
double f(double x, double y) {
        double r194291 = x;
        double r194292 = 1.0;
        double r194293 = r194291 + r194292;
        double r194294 = y;
        double r194295 = -r194291;
        double r194296 = fma(r194293, r194294, r194295);
        return r194296;
}

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 2019303 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))