Average Error: 0.1 → 0.1
Time: 1.6s
Precision: binary64
\[\frac{x + y}{y + y}\]
↓
\[\frac{1}{2} + \frac{1}{2} \cdot \frac{x}{y}\]
\frac{x + y}{y + y}
↓
\frac{1}{2} + \frac{1}{2} \cdot \frac{x}{y}
double code(double x, double y) {
	return ((double) (((double) (x + y)) / ((double) (y + y))));
}
↓
double code(double x, double y) {
	return ((double) (0.5 + ((double) (0.5 * ((double) (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
Target0.1
Herbie0.1
\[0.5 \cdot \frac{x}{y} + 0.5\]

Derivation

  1. Initial program 0.1

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

  3. Applied add-sqr-sqrt32.1

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

  4. Applied add-sqr-sqrt32.2

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

  5. Applied distribute-lft-out32.2

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

  6. Applied associate-/r*32.2

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

  7. Taylor expanded around 0 0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020185 
(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)))