Average Error: 0.1 → 0.1
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 r802370 = x;
        double r802371 = y;
        double r802372 = r802370 + r802371;
        double r802373 = r802371 + r802371;
        double r802374 = r802372 / r802373;
        return r802374;
}
↓
double f(double x, double y) {
        double r802375 = 0.5;
        double r802376 = x;
        double r802377 = y;
        double r802378 = r802376 / r802377;
        double r802379 = r802375 * r802378;
        double r802380 = r802379 + r802375;
        return r802380;
}

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
Target0.1
Herbie0.1
\[0.5 \cdot \frac{x}{y} + 0.5\]

Derivation

  1. Initial program 0.1

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

  2. Taylor expanded around 0 0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2020035 
(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)))