Average Error: 0.1 → 0.0
Time: 5.3s
Precision: 64
\[\frac{x + y}{y + y}\]
↓
\[\frac{1}{2} + \frac{x}{y} \cdot \frac{1}{2}\]
\frac{x + y}{y + y}
↓
\frac{1}{2} + \frac{x}{y} \cdot \frac{1}{2}
double f(double x, double y) {
        double r37991050 = x;
        double r37991051 = y;
        double r37991052 = r37991050 + r37991051;
        double r37991053 = r37991051 + r37991051;
        double r37991054 = r37991052 / r37991053;
        return r37991054;
}
↓
double f(double x, double y) {
        double r37991055 = 0.5;
        double r37991056 = x;
        double r37991057 = y;
        double r37991058 = r37991056 / r37991057;
        double r37991059 = r37991058 * r37991055;
        double r37991060 = r37991055 + r37991059;
        return r37991060;
}

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

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

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x y)
  :name "Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2"

  :herbie-target
  (+ (* 1/2 (/ x y)) 1/2)

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