Average Error: 0.0 → 0.0
Time: 4.1s
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 r38781655 = x;
        double r38781656 = y;
        double r38781657 = r38781655 + r38781656;
        double r38781658 = r38781656 + r38781656;
        double r38781659 = r38781657 / r38781658;
        return r38781659;
}
↓
double f(double x, double y) {
        double r38781660 = 0.5;
        double r38781661 = x;
        double r38781662 = y;
        double r38781663 = r38781661 / r38781662;
        double r38781664 = r38781663 * r38781660;
        double r38781665 = r38781660 + r38781664;
        return r38781665;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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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 2019168 
(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)))