Average Error: 9.5 → 0.1
Time: 15.3s
Precision: 64
\[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
↓
\[\frac{x}{\frac{x + 1}{\frac{x}{y} + 1}}\]
\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}
↓
\frac{x}{\frac{x + 1}{\frac{x}{y} + 1}}
double f(double x, double y) {
        double r56150322 = x;
        double r56150323 = y;
        double r56150324 = r56150322 / r56150323;
        double r56150325 = 1.0;
        double r56150326 = r56150324 + r56150325;
        double r56150327 = r56150322 * r56150326;
        double r56150328 = r56150322 + r56150325;
        double r56150329 = r56150327 / r56150328;
        return r56150329;
}
↓
double f(double x, double y) {
        double r56150330 = x;
        double r56150331 = 1.0;
        double r56150332 = r56150330 + r56150331;
        double r56150333 = y;
        double r56150334 = r56150330 / r56150333;
        double r56150335 = r56150334 + r56150331;
        double r56150336 = r56150332 / r56150335;
        double r56150337 = r56150330 / r56150336;
        return r56150337;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.5
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program 9.5

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

  3. Applied associate-/l*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y)
  :name "Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1"

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

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