Average Error: 8.5 → 0.1
Time: 12.6s
Precision: 64
\[\frac{x \cdot \left(\frac{x}{y} + 1.0\right)}{x + 1.0}\]
↓
\[\frac{x}{\frac{1.0 + x}{1.0 + \frac{x}{y}}}\]
\frac{x \cdot \left(\frac{x}{y} + 1.0\right)}{x + 1.0}
↓
\frac{x}{\frac{1.0 + x}{1.0 + \frac{x}{y}}}
double f(double x, double y) {
        double r49520243 = x;
        double r49520244 = y;
        double r49520245 = r49520243 / r49520244;
        double r49520246 = 1.0;
        double r49520247 = r49520245 + r49520246;
        double r49520248 = r49520243 * r49520247;
        double r49520249 = r49520243 + r49520246;
        double r49520250 = r49520248 / r49520249;
        return r49520250;
}
↓
double f(double x, double y) {
        double r49520251 = x;
        double r49520252 = 1.0;
        double r49520253 = r49520252 + r49520251;
        double r49520254 = y;
        double r49520255 = r49520251 / r49520254;
        double r49520256 = r49520252 + r49520255;
        double r49520257 = r49520253 / r49520256;
        double r49520258 = r49520251 / r49520257;
        return r49520258;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original8.5
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1.0}{x + 1.0}\]

Derivation

  1. Initial program 8.5

    \[\frac{x \cdot \left(\frac{x}{y} + 1.0\right)}{x + 1.0}\]
  2. Using strategy rm

  3. Applied associate-/l*0.1

    \[\leadsto \color{blue}{\frac{x}{\frac{x + 1.0}{\frac{x}{y} + 1.0}}}\]

  4. Final simplification0.1

    \[\leadsto \frac{x}{\frac{1.0 + x}{1.0 + \frac{x}{y}}}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y)
  :name "Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1"

  :herbie-target
  (* (/ x 1) (/ (+ (/ x y) 1.0) (+ x 1.0)))

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