Average Error: 0.1 → 0.0
Time: 2.1s
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 r40002709 = x;
        double r40002710 = y;
        double r40002711 = r40002709 + r40002710;
        double r40002712 = r40002710 + r40002710;
        double r40002713 = r40002711 / r40002712;
        return r40002713;
}
↓
double f(double x, double y) {
        double r40002714 = 0.5;
        double r40002715 = x;
        double r40002716 = y;
        double r40002717 = r40002715 / r40002716;
        double r40002718 = r40002717 * r40002714;
        double r40002719 = r40002714 + r40002718;
        return r40002719;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
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 2019165 
(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)))