Average Error: 0.1 → 0.0
Time: 5.0s
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 r39740813 = x;
        double r39740814 = y;
        double r39740815 = r39740813 + r39740814;
        double r39740816 = r39740814 + r39740814;
        double r39740817 = r39740815 / r39740816;
        return r39740817;
}
↓
double f(double x, double y) {
        double r39740818 = 0.5;
        double r39740819 = x;
        double r39740820 = y;
        double r39740821 = r39740819 / r39740820;
        double r39740822 = r39740821 * r39740818;
        double r39740823 = r39740818 + r39740822;
        return r39740823;
}

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

Original0.1
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 2019158 
(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)))