Average Error: 8.7 → 0.1
Time: 9.1s
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 r581760 = x;
        double r581761 = y;
        double r581762 = r581760 / r581761;
        double r581763 = 1.0;
        double r581764 = r581762 + r581763;
        double r581765 = r581760 * r581764;
        double r581766 = r581760 + r581763;
        double r581767 = r581765 / r581766;
        return r581767;
}
↓
double f(double x, double y) {
        double r581768 = x;
        double r581769 = 1.0;
        double r581770 = r581768 + r581769;
        double r581771 = y;
        double r581772 = r581768 / r581771;
        double r581773 = r581772 + r581769;
        double r581774 = r581770 / r581773;
        double r581775 = r581768 / r581774;
        return r581775;
}

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

Original8.7
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program 8.7

    \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
  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 2019209 
(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)))