Average Error: 9.3 → 0.1
Time: 4.3s
Precision: binary64
\[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
↓
\[x \cdot \frac{\frac{x}{y} + 1}{x + 1}\]
\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 ((double) (((double) (x * ((double) (((double) (x / y)) + 1.0)))) / ((double) (x + 1.0))));
}
↓
double code(double x, double y) {
	return ((double) (x * ((double) (((double) (((double) (x / y)) + 1.0)) / ((double) (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

Original9.3
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program 9.3

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

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

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

  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 2020163 
(FPCore (x y)
  :name "Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1"
  :precision binary64

  :herbie-target
  (* (/ x 1.0) (/ (+ (/ x y) 1.0) (+ x 1.0)))

  (/ (* x (+ (/ x y) 1.0)) (+ x 1.0)))