Average Error: 0.1 → 0.0
Time: 3.4s
Precision: 64
\[\frac{x + y}{y + y}\]
↓
\[\frac{1}{2} \cdot \frac{x}{y} + \frac{1}{2}\]
\frac{x + y}{y + y}
↓
\frac{1}{2} \cdot \frac{x}{y} + \frac{1}{2}
double f(double x, double y) {
        double r134620895 = x;
        double r134620896 = y;
        double r134620897 = r134620895 + r134620896;
        double r134620898 = r134620896 + r134620896;
        double r134620899 = r134620897 / r134620898;
        return r134620899;
}
↓
double f(double x, double y) {
        double r134620900 = 0.5;
        double r134620901 = x;
        double r134620902 = y;
        double r134620903 = r134620901 / r134620902;
        double r134620904 = r134620900 * r134620903;
        double r134620905 = r134620904 + r134620900;
        return r134620905;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.0
Herbie0.0
\[0.5 \cdot \frac{x}{y} + 0.5\]

Derivation

  1. Initial program 0.1

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

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{x}{y} + \frac{1}{2}}\]

  3. Final simplification0.0

    \[\leadsto \frac{1}{2} \cdot \frac{x}{y} + \frac{1}{2}\]

Reproduce

herbie shell --seed 2019173 
(FPCore (x y)
  :name "Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2"

  :herbie-target
  (+ (* 0.5 (/ x y)) 0.5)

  (/ (+ x y) (+ y y)))