Average Error: 0.1 → 0.0
Time: 5.4s
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 r36366561 = x;
        double r36366562 = y;
        double r36366563 = r36366561 + r36366562;
        double r36366564 = r36366562 + r36366562;
        double r36366565 = r36366563 / r36366564;
        return r36366565;
}
↓
double f(double x, double y) {
        double r36366566 = 0.5;
        double r36366567 = x;
        double r36366568 = y;
        double r36366569 = r36366567 / r36366568;
        double r36366570 = r36366569 * r36366566;
        double r36366571 = r36366566 + r36366570;
        return r36366571;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

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

Derivation

  1. Initial program 0.1

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

  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 2019163 
(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)))