Average Error: 0.0 → 0.0
Time: 2.7s
Precision: binary64
\[\frac{x + y}{y + y}\]
↓
\[0.5 + \frac{x}{y + y}\]
\frac{x + y}{y + y}
↓
0.5 + \frac{x}{y + y}
(FPCore (x y) :precision binary64 (/ (+ x y) (+ y y)))
↓
(FPCore (x y) :precision binary64 (+ 0.5 (/ x (+ y y))))
double code(double x, double y) {
	return (((double) (x + y)) / ((double) (y + y)));
}
↓
double code(double x, double y) {
	return ((double) (0.5 + (x / ((double) (y + 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

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

Derivation

  1. Initial program 0.0

    \[\frac{x + y}{y + y}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt_binary6432.0

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

  4. Applied associate-/r*_binary6432.0

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

  5. Taylor expanded around 0 1.4

    \[\leadsto \color{blue}{\frac{1}{{\left(\sqrt{2}\right)}^{2}} + \frac{x}{{\left(\sqrt{2}\right)}^{2} \cdot y}}\]

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020210 
(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)))