Average Error: 9.2 → 0.1
Time: 2.6s
Precision: 64
\[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
↓
\[x \cdot \frac{\frac{x}{y} + 1}{x + 1}\]
\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}
↓
x \cdot \frac{\frac{x}{y} + 1}{x + 1}
double code(double x, double y) {
	return ((x * ((x / y) + 1.0)) / (x + 1.0));
}
↓
double code(double x, double y) {
	return (x * (((x / y) + 1.0) / (x + 1.0)));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.2
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program 9.2

    \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity9.2

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

  4. Applied times-frac0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020106 
(FPCore (x y)
  :name "Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1"
  :precision binary64

  :herbie-target
  (* (/ x 1) (/ (+ (/ x y) 1) (+ x 1)))

  (/ (* x (+ (/ x y) 1)) (+ x 1)))