Average Error: 0.1 → 0.0
Time: 1.5s
Precision: binary64
\[\frac{x + y}{y + y}\]
↓
\[0.5 + 0.5 \cdot \frac{x}{y}\]
\frac{x + y}{y + y}
↓
0.5 + 0.5 \cdot \frac{x}{y}
(FPCore (x y) :precision binary64 (/ (+ x y) (+ y y)))
↓
(FPCore (x y) :precision binary64 (+ 0.5 (* 0.5 (/ x y))))
double code(double x, double y) {
	return (x + y) / (y + y);
}
↓
double code(double x, double y) {
	return 0.5 + (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. Using strategy rm

  3. Applied clear-num_binary640.2

    \[\leadsto \color{blue}{\frac{1}{\frac{y + y}{x + y}}}\]

  4. Simplified0.1

    \[\leadsto \frac{1}{\color{blue}{\frac{y}{\frac{x + y}{2}}}}\]

  5. Taylor expanded around 0 0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020219 
(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)))