Average Error: 9.0 → 0.1
Time: 2.6s
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 r871742 = x;
        double r871743 = y;
        double r871744 = r871742 / r871743;
        double r871745 = 1.0;
        double r871746 = r871744 + r871745;
        double r871747 = r871742 * r871746;
        double r871748 = r871742 + r871745;
        double r871749 = r871747 / r871748;
        return r871749;
}
↓
double f(double x, double y) {
        double r871750 = x;
        double r871751 = 1.0;
        double r871752 = r871750 + r871751;
        double r871753 = y;
        double r871754 = r871750 / r871753;
        double r871755 = r871754 + r871751;
        double r871756 = r871752 / r871755;
        double r871757 = r871750 / r871756;
        return r871757;
}

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 2019362 
(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)))