Average Error: 0.0 → 0.0
Time: 2.8s
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 r34409667 = x;
        double r34409668 = y;
        double r34409669 = r34409667 + r34409668;
        double r34409670 = r34409668 + r34409668;
        double r34409671 = r34409669 / r34409670;
        return r34409671;
}
↓
double f(double x, double y) {
        double r34409672 = 0.5;
        double r34409673 = x;
        double r34409674 = y;
        double r34409675 = r34409673 / r34409674;
        double r34409676 = r34409675 * r34409672;
        double r34409677 = r34409672 + r34409676;
        return r34409677;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\frac{1}{2} \cdot \frac{x}{y} + \frac{1}{2}\]

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

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

Reproduce

herbie shell --seed 2019162 
(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)))