Average Error: 9.3 → 0.1
Time: 8.4s
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 r982091 = x;
        double r982092 = y;
        double r982093 = r982091 / r982092;
        double r982094 = 1.0;
        double r982095 = r982093 + r982094;
        double r982096 = r982091 * r982095;
        double r982097 = r982091 + r982094;
        double r982098 = r982096 / r982097;
        return r982098;
}
↓
double f(double x, double y) {
        double r982099 = x;
        double r982100 = 1.0;
        double r982101 = r982099 + r982100;
        double r982102 = y;
        double r982103 = r982099 / r982102;
        double r982104 = r982103 + r982100;
        double r982105 = r982101 / r982104;
        double r982106 = r982099 / r982105;
        return r982106;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.3
Target0.1
Herbie0.1
\[\frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1}\]

Derivation

  1. Initial program 9.3

    \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\]
  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 2020057 
(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)))