Average Error: 0.1 → 0.0
Time: 690.0ms
Precision: 64
\[\frac{x + y}{y + y}\]
↓
\[\frac{1}{2} \cdot \frac{x}{y} + \frac{1}{2}\]
\frac{x + y}{y + y}
↓
\frac{1}{2} \cdot \frac{x}{y} + \frac{1}{2}
double f(double x, double y) {
        double r703849 = x;
        double r703850 = y;
        double r703851 = r703849 + r703850;
        double r703852 = r703850 + r703850;
        double r703853 = r703851 / r703852;
        return r703853;
}
↓
double f(double x, double y) {
        double r703854 = 0.5;
        double r703855 = x;
        double r703856 = y;
        double r703857 = r703855 / r703856;
        double r703858 = r703854 * r703857;
        double r703859 = r703858 + r703854;
        return r703859;
}

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
\[0.5 \cdot \frac{x}{y} + 0.5\]

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

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

Reproduce

herbie shell --seed 2020024 
(FPCore (x y)
  :name "Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2"
  :precision binary64

  :herbie-target
  (+ (* 0.5 (/ x y)) 0.5)

  (/ (+ x y) (+ y y)))