Average Error: 9.0 → 0.1
Time: 6.6s
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 r912859 = x;
        double r912860 = y;
        double r912861 = r912859 / r912860;
        double r912862 = 1.0;
        double r912863 = r912861 + r912862;
        double r912864 = r912859 * r912863;
        double r912865 = r912859 + r912862;
        double r912866 = r912864 / r912865;
        return r912866;
}
↓
double f(double x, double y) {
        double r912867 = x;
        double r912868 = 1.0;
        double r912869 = r912867 + r912868;
        double r912870 = y;
        double r912871 = r912867 / r912870;
        double r912872 = r912871 + r912868;
        double r912873 = r912869 / r912872;
        double r912874 = r912867 / r912873;
        return r912874;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.0
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program 9.0

    \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
  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 2019354 
(FPCore (x y)
  :name "Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1"
  :precision binary64

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

  (/ (* x (+ (/ x y) 1)) (+ x 1)))