Average Error: 8.8 → 0.1
Time: 10.9s
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 r38484014 = x;
        double r38484015 = y;
        double r38484016 = r38484014 / r38484015;
        double r38484017 = 1.0;
        double r38484018 = r38484016 + r38484017;
        double r38484019 = r38484014 * r38484018;
        double r38484020 = r38484014 + r38484017;
        double r38484021 = r38484019 / r38484020;
        return r38484021;
}
↓
double f(double x, double y) {
        double r38484022 = x;
        double r38484023 = 1.0;
        double r38484024 = r38484023 + r38484022;
        double r38484025 = y;
        double r38484026 = r38484022 / r38484025;
        double r38484027 = r38484023 + r38484026;
        double r38484028 = r38484024 / r38484027;
        double r38484029 = r38484022 / r38484028;
        return r38484029;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original8.8
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1.0}{x + 1.0}\]

Derivation

  1. Initial program 8.8

    \[\frac{x \cdot \left(\frac{x}{y} + 1.0\right)}{x + 1.0}\]
  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 2019162 
(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)))