Average Error: 0.0 → 0.0
Time: 13.3s
Precision: 64
\[\left(x + 1.0\right) \cdot y - x\]
↓
\[\mathsf{fma}\left(1.0 + x, y, -x\right)\]
\left(x + 1.0\right) \cdot y - x
↓
\mathsf{fma}\left(1.0 + x, y, -x\right)
double f(double x, double y) {
        double r10288366 = x;
        double r10288367 = 1.0;
        double r10288368 = r10288366 + r10288367;
        double r10288369 = y;
        double r10288370 = r10288368 * r10288369;
        double r10288371 = r10288370 - r10288366;
        return r10288371;
}
↓
double f(double x, double y) {
        double r10288372 = 1.0;
        double r10288373 = x;
        double r10288374 = r10288372 + r10288373;
        double r10288375 = y;
        double r10288376 = -r10288373;
        double r10288377 = fma(r10288374, r10288375, r10288376);
        return r10288377;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x + 1.0\right) \cdot y - x\]
  2. Using strategy rm

  3. Applied fma-neg0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x + 1.0, y, -x\right)}\]

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(1.0 + x, y, -x\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  (- (* (+ x 1.0) y) x))