Average Error: 0.0 → 0.0
Time: 16.5s
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 r8976903 = x;
        double r8976904 = 1.0;
        double r8976905 = r8976903 + r8976904;
        double r8976906 = y;
        double r8976907 = r8976905 * r8976906;
        double r8976908 = r8976907 - r8976903;
        return r8976908;
}
↓
double f(double x, double y) {
        double r8976909 = 1.0;
        double r8976910 = x;
        double r8976911 = r8976909 + r8976910;
        double r8976912 = y;
        double r8976913 = -r8976910;
        double r8976914 = fma(r8976911, r8976912, r8976913);
        return r8976914;
}

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 2019172 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  (- (* (+ x 1.0) y) x))