Average Error: 0.1 → 0.0
Time: 1.0s
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 r443430 = x;
        double r443431 = y;
        double r443432 = r443430 + r443431;
        double r443433 = r443431 + r443431;
        double r443434 = r443432 / r443433;
        return r443434;
}
↓
double f(double x, double y) {
        double r443435 = 0.5;
        double r443436 = x;
        double r443437 = y;
        double r443438 = r443436 / r443437;
        double r443439 = r443435 * r443438;
        double r443440 = r443439 + r443435;
        return r443440;
}

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 2019304 
(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)))