Average Error: 9.0 → 0.1
Time: 10.9s
Precision: 64
\[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
↓
\[\frac{x}{1 + x} \cdot \left(1 + \frac{x}{y}\right)\]
\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}
↓
\frac{x}{1 + x} \cdot \left(1 + \frac{x}{y}\right)
double f(double x, double y) {
        double r775631 = x;
        double r775632 = y;
        double r775633 = r775631 / r775632;
        double r775634 = 1.0;
        double r775635 = r775633 + r775634;
        double r775636 = r775631 * r775635;
        double r775637 = r775631 + r775634;
        double r775638 = r775636 / r775637;
        return r775638;
}
↓
double f(double x, double y) {
        double r775639 = x;
        double r775640 = 1.0;
        double r775641 = r775640 + r775639;
        double r775642 = r775639 / r775641;
        double r775643 = y;
        double r775644 = r775639 / r775643;
        double r775645 = r775640 + r775644;
        double r775646 = r775642 * r775645;
        return r775646;
}

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. Simplified0.1

    \[\leadsto \color{blue}{\left(\frac{x}{y} + 1\right) \cdot \frac{x}{1 + x}}\]

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y)
  :name "Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1"

  :herbie-target
  (* (/ x 1.0) (/ (+ (/ x y) 1.0) (+ x 1.0)))

  (/ (* x (+ (/ x y) 1.0)) (+ x 1.0)))