Average Error: 9.2 → 0.1
Time: 13.5s
Precision: 64
\[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
↓
\[\frac{x}{\frac{1 + x}{1 + \frac{x}{y}}}\]
\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}
↓
\frac{x}{\frac{1 + x}{1 + \frac{x}{y}}}
double f(double x, double y) {
        double r42406423 = x;
        double r42406424 = y;
        double r42406425 = r42406423 / r42406424;
        double r42406426 = 1.0;
        double r42406427 = r42406425 + r42406426;
        double r42406428 = r42406423 * r42406427;
        double r42406429 = r42406423 + r42406426;
        double r42406430 = r42406428 / r42406429;
        return r42406430;
}
↓
double f(double x, double y) {
        double r42406431 = x;
        double r42406432 = 1.0;
        double r42406433 = r42406432 + r42406431;
        double r42406434 = y;
        double r42406435 = r42406431 / r42406434;
        double r42406436 = r42406432 + r42406435;
        double r42406437 = r42406433 / r42406436;
        double r42406438 = r42406431 / r42406437;
        return r42406438;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.2
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program 9.2

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

    \[\leadsto \frac{x}{\frac{1 + x}{1 + \frac{x}{y}}}\]

Reproduce

herbie shell --seed 2019169 
(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)))