Average Error: 0.0 → 0.0
Time: 820.0ms
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 r221294 = x;
        double r221295 = 1.0;
        double r221296 = r221294 + r221295;
        double r221297 = y;
        double r221298 = r221296 * r221297;
        double r221299 = r221298 - r221294;
        return r221299;
}
↓
double f(double x, double y) {
        double r221300 = x;
        double r221301 = 1.0;
        double r221302 = r221300 + r221301;
        double r221303 = y;
        double r221304 = -r221300;
        double r221305 = fma(r221302, r221303, r221304);
        return r221305;
}

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 2020021 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1) y) x))