Average Error: 8.2 → 0.1
Time: 11.8s
Precision: 64
\[\frac{x \cdot \left(\frac{x}{y} + 1.0\right)}{x + 1.0}\]
↓
\[\frac{x}{\frac{1.0 + x}{1.0 + \frac{x}{y}}}\]
\frac{x \cdot \left(\frac{x}{y} + 1.0\right)}{x + 1.0}
↓
\frac{x}{\frac{1.0 + x}{1.0 + \frac{x}{y}}}
double f(double x, double y) {
        double r45043657 = x;
        double r45043658 = y;
        double r45043659 = r45043657 / r45043658;
        double r45043660 = 1.0;
        double r45043661 = r45043659 + r45043660;
        double r45043662 = r45043657 * r45043661;
        double r45043663 = r45043657 + r45043660;
        double r45043664 = r45043662 / r45043663;
        return r45043664;
}
↓
double f(double x, double y) {
        double r45043665 = x;
        double r45043666 = 1.0;
        double r45043667 = r45043666 + r45043665;
        double r45043668 = y;
        double r45043669 = r45043665 / r45043668;
        double r45043670 = r45043666 + r45043669;
        double r45043671 = r45043667 / r45043670;
        double r45043672 = r45043665 / r45043671;
        return r45043672;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original8.2
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1.0}{x + 1.0}\]

Derivation

  1. Initial program 8.2

    \[\frac{x \cdot \left(\frac{x}{y} + 1.0\right)}{x + 1.0}\]
  2. Using strategy rm

  3. Applied associate-/l*0.1

    \[\leadsto \color{blue}{\frac{x}{\frac{x + 1.0}{\frac{x}{y} + 1.0}}}\]

  4. Final simplification0.1

    \[\leadsto \frac{x}{\frac{1.0 + x}{1.0 + \frac{x}{y}}}\]

Reproduce

herbie shell --seed 2019158 
(FPCore (x y)
  :name "Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1"

  :herbie-target
  (* (/ x 1) (/ (+ (/ x y) 1.0) (+ x 1.0)))

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