Average Error: 9.8 → 0.1
Time: 3.1s
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}
(FPCore (x y) :precision binary64 (/ (* x (+ (/ x y) 1.0)) (+ x 1.0)))
↓
(FPCore (x y) :precision binary64 (* x (/ (+ (/ x y) 1.0) (+ x 1.0))))
double code(double x, double y) {
	return (((double) (x * ((double) ((x / y) + 1.0)))) / ((double) (x + 1.0)));
}
↓
double code(double x, double y) {
	return ((double) (x * (((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

Original9.8
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program Error: 9.8 bits

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

  2. SimplifiedError: 0.1 bits

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

  3. Final simplificationError: 0.1 bits

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

Reproduce

herbie shell --seed 2020204 
(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)))