Average Error: 0.0 → 0.0
Time: 12.8s
Precision: 64
\[\frac{x + y}{y + y}\]
↓
\[\frac{x}{y} \cdot \frac{1}{2} + \frac{1}{2}\]
\frac{x + y}{y + y}
↓
\frac{x}{y} \cdot \frac{1}{2} + \frac{1}{2}
double f(double x, double y) {
        double r34837072 = x;
        double r34837073 = y;
        double r34837074 = r34837072 + r34837073;
        double r34837075 = r34837073 + r34837073;
        double r34837076 = r34837074 / r34837075;
        return r34837076;
}
↓
double f(double x, double y) {
        double r34837077 = x;
        double r34837078 = y;
        double r34837079 = r34837077 / r34837078;
        double r34837080 = 0.5;
        double r34837081 = r34837079 * r34837080;
        double r34837082 = r34837081 + r34837080;
        return r34837082;
}

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

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

Reproduce

herbie shell --seed 2019200 
(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)))