Average Error: 9.4 → 0.1
Time: 2.3s
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 r756481 = x;
        double r756482 = y;
        double r756483 = r756481 / r756482;
        double r756484 = 1.0;
        double r756485 = r756483 + r756484;
        double r756486 = r756481 * r756485;
        double r756487 = r756481 + r756484;
        double r756488 = r756486 / r756487;
        return r756488;
}
↓
double f(double x, double y) {
        double r756489 = x;
        double r756490 = 1.0;
        double r756491 = r756489 + r756490;
        double r756492 = y;
        double r756493 = r756489 / r756492;
        double r756494 = r756493 + r756490;
        double r756495 = r756491 / r756494;
        double r756496 = r756489 / r756495;
        return r756496;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.4
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program 9.4

    \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
  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 2020002 
(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)))