Average Error: 9.5 → 0.1
Time: 3.4s
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 r862052 = x;
        double r862053 = y;
        double r862054 = r862052 / r862053;
        double r862055 = 1.0;
        double r862056 = r862054 + r862055;
        double r862057 = r862052 * r862056;
        double r862058 = r862052 + r862055;
        double r862059 = r862057 / r862058;
        return r862059;
}
↓
double f(double x, double y) {
        double r862060 = x;
        double r862061 = 1.0;
        double r862062 = r862060 + r862061;
        double r862063 = r862060 / r862062;
        double r862064 = y;
        double r862065 = r862060 / r862064;
        double r862066 = r862065 + r862061;
        double r862067 = r862063 * r862066;
        return r862067;
}

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. 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 2020036 
(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)))