Average Error: 0.0 → 0.0
Time: 12.9s
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 r121219 = x;
        double r121220 = 1.0;
        double r121221 = r121219 + r121220;
        double r121222 = y;
        double r121223 = r121221 * r121222;
        double r121224 = r121223 - r121219;
        return r121224;
}
↓
double f(double x, double y) {
        double r121225 = x;
        double r121226 = 1.0;
        double r121227 = r121225 + r121226;
        double r121228 = y;
        double r121229 = -r121225;
        double r121230 = fma(r121227, r121228, r121229);
        return r121230;
}

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 2019323 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))