Average Error: 8.9 → 0.1
Time: 13.7s
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 r571733 = x;
        double r571734 = y;
        double r571735 = r571733 / r571734;
        double r571736 = 1.0;
        double r571737 = r571735 + r571736;
        double r571738 = r571733 * r571737;
        double r571739 = r571733 + r571736;
        double r571740 = r571738 / r571739;
        return r571740;
}
↓
double f(double x, double y) {
        double r571741 = x;
        double r571742 = 1.0;
        double r571743 = r571741 + r571742;
        double r571744 = y;
        double r571745 = r571741 / r571744;
        double r571746 = r571745 + r571742;
        double r571747 = r571743 / r571746;
        double r571748 = r571741 / r571747;
        return r571748;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

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Target

Original8.9
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program 8.9

    \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
  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 2019326 
(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)))