Average Error: 0.1 → 0.1
Time: 4.2s
Precision: binary64
\[x + \frac{\left|y - x\right|}{2} \]
↓
\[\mathsf{fma}\left(\left|y - x\right|, 0.5, x\right) \]
x + \frac{\left|y - x\right|}{2}
↓
\mathsf{fma}\left(\left|y - x\right|, 0.5, x\right)

(FPCore (x y) :precision binary64 (+ x (/ (fabs (- y x)) 2.0)))
↓
(FPCore (x y) :precision binary64 (fma (fabs (- y x)) 0.5 x))
double code(double x, double y) {
	return x + (fabs(y - x) / 2.0);
}
↓
double code(double x, double y) {
	return fma(fabs(y - x), 0.5, x);
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.1

    \[x + \frac{\left|y - x\right|}{2} \]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\left|y - x\right|, 0.5, x\right)} \]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\left|y - x\right|, 0.5, x\right) \]

Reproduce

herbie shell --seed 2022077 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderSpotLegend from Chart-1.5.3"
  :precision binary64
  (+ x (/ (fabs (- y x)) 2.0)))