Average Error: 0.0 → 0.0
Time: 824.0ms
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 r889737 = x;
        double r889738 = y;
        double r889739 = r889737 + r889738;
        double r889740 = r889738 + r889738;
        double r889741 = r889739 / r889740;
        return r889741;
}
↓
double f(double x, double y) {
        double r889742 = 0.5;
        double r889743 = x;
        double r889744 = y;
        double r889745 = r889743 / r889744;
        double r889746 = r889742 * r889745;
        double r889747 = r889746 + r889742;
        return r889747;
}

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 2020047 
(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)))