Average Error: 9.5 → 0.1
Time: 12.0s
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 r648837 = x;
        double r648838 = y;
        double r648839 = r648837 / r648838;
        double r648840 = 1.0;
        double r648841 = r648839 + r648840;
        double r648842 = r648837 * r648841;
        double r648843 = r648837 + r648840;
        double r648844 = r648842 / r648843;
        return r648844;
}
↓
double f(double x, double y) {
        double r648845 = x;
        double r648846 = 1.0;
        double r648847 = r648845 + r648846;
        double r648848 = y;
        double r648849 = r648845 / r648848;
        double r648850 = r648849 + r648846;
        double r648851 = r648847 / r648850;
        double r648852 = r648845 / r648851;
        return r648852;
}

Error

Bits error versus x

Bits error versus y

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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 2019306 
(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)))