Average Error: 9.5 → 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 r852580 = x;
        double r852581 = y;
        double r852582 = r852580 / r852581;
        double r852583 = 1.0;
        double r852584 = r852582 + r852583;
        double r852585 = r852580 * r852584;
        double r852586 = r852580 + r852583;
        double r852587 = r852585 / r852586;
        return r852587;
}
↓
double f(double x, double y) {
        double r852588 = x;
        double r852589 = 1.0;
        double r852590 = r852588 + r852589;
        double r852591 = y;
        double r852592 = r852588 / r852591;
        double r852593 = r852592 + r852589;
        double r852594 = r852590 / r852593;
        double r852595 = r852588 / r852594;
        return r852595;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.5
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program 9.5

    \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
  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 2019353 
(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)))