Average Error: 0.0 → 0.0
Time: 6.6s
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 r637149 = x;
        double r637150 = y;
        double r637151 = r637149 + r637150;
        double r637152 = r637150 + r637150;
        double r637153 = r637151 / r637152;
        return r637153;
}
↓
double f(double x, double y) {
        double r637154 = 0.5;
        double r637155 = x;
        double r637156 = y;
        double r637157 = r637155 / r637156;
        double r637158 = r637154 * r637157;
        double r637159 = r637158 + r637154;
        return r637159;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.0

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

  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 2019326 
(FPCore (x y)
  :name "Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2"
  :precision binary64

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

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