Average Error: 0.1 → 0.0
Time: 1.2s
Precision: binary64
\[\frac{x + y}{y + y}\]
↓
\[0.5 + \frac{0.5 \cdot x}{y}\]
\frac{x + y}{y + y}
↓
0.5 + \frac{0.5 \cdot x}{y}
double code(double x, double y) {
	return (((double) (x + y)) / ((double) (y + y)));
}
↓
double code(double x, double y) {
	return ((double) (0.5 + (((double) (0.5 * x)) / y)));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.0
Herbie0.0
\[0.5 \cdot \frac{x}{y} + 0.5\]

Derivation

  1. Initial program 0.1

    \[\frac{x + y}{y + y}\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{0.5 \cdot \frac{x}{y} + 0.5}\]

  3. Simplified0.1

    \[\leadsto \color{blue}{0.5 + x \cdot \frac{0.5}{y}}\]
  4. Using strategy rm

  5. Applied associate-*r/0.0

    \[\leadsto 0.5 + \color{blue}{\frac{x \cdot 0.5}{y}}\]

  6. Final simplification0.0

    \[\leadsto 0.5 + \frac{0.5 \cdot x}{y}\]

Reproduce

herbie shell --seed 2020196 
(FPCore (x y)
  :name "Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2"
  :precision binary64

  :herbie-target
  (+ (* 0.5 (/ x y)) 0.5)

  (/ (+ x y) (+ y y)))