Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1

Average Error: 9.1 → 0.1

Time: 5.4s

Precision: binary64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

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 (x / (((double) (x + 1.0)) / ((double) ((x / y) + 1.0))));
}

Error

Bits error versus x

Bits error versus y

Target

Original	9.1
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 9.1

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

3. Applied associate-/l* 0.1

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

4. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020182 
(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)))