Average Error: 0.0 → 0.0
Time: 10.4s
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 r165350 = x;
        double r165351 = 1.0;
        double r165352 = r165350 + r165351;
        double r165353 = y;
        double r165354 = r165352 * r165353;
        double r165355 = r165354 - r165350;
        return r165355;
}
↓
double f(double x, double y) {
        double r165356 = x;
        double r165357 = 1.0;
        double r165358 = r165356 + r165357;
        double r165359 = y;
        double r165360 = -r165356;
        double r165361 = fma(r165358, r165359, r165360);
        return r165361;
}

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 2019198 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  (- (* (+ x 1.0) y) x))