Average Error: 9.6 → 0.1
Time: 2.9s
Precision: 64
\[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
↓
\[\frac{x}{x + 1} \cdot \left(\frac{x}{y} + 1\right)\]
\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}
↓
\frac{x}{x + 1} \cdot \left(\frac{x}{y} + 1\right)
double f(double x, double y) {
        double r745675 = x;
        double r745676 = y;
        double r745677 = r745675 / r745676;
        double r745678 = 1.0;
        double r745679 = r745677 + r745678;
        double r745680 = r745675 * r745679;
        double r745681 = r745675 + r745678;
        double r745682 = r745680 / r745681;
        return r745682;
}
↓
double f(double x, double y) {
        double r745683 = x;
        double r745684 = 1.0;
        double r745685 = r745683 + r745684;
        double r745686 = r745683 / r745685;
        double r745687 = y;
        double r745688 = r745683 / r745687;
        double r745689 = r745688 + r745684;
        double r745690 = r745686 * r745689;
        return r745690;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.6
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program 9.6

    \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
  2. Using strategy rm

  3. Applied associate-/l*0.1

    \[\leadsto \color{blue}{\frac{x}{\frac{x + 1}{\frac{x}{y} + 1}}}\]
  4. Using strategy rm

  5. Applied associate-/r/0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020027 
(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)))