Average Error: 0.1 → 0.0
Time: 6.9s
Precision: 64
\[\frac{x + y}{y + y}\]
↓
\[\left(\frac{x}{y} + 1\right) \cdot \frac{1}{2}\]
\frac{x + y}{y + y}
↓
\left(\frac{x}{y} + 1\right) \cdot \frac{1}{2}
double f(double x, double y) {
        double r629215 = x;
        double r629216 = y;
        double r629217 = r629215 + r629216;
        double r629218 = r629216 + r629216;
        double r629219 = r629217 / r629218;
        return r629219;
}
↓
double f(double x, double y) {
        double r629220 = x;
        double r629221 = y;
        double r629222 = r629220 / r629221;
        double r629223 = 1.0;
        double r629224 = r629222 + r629223;
        double r629225 = 0.5;
        double r629226 = r629224 * r629225;
        return r629226;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\left(1 + \frac{x}{y}\right) \cdot \frac{1}{2}}\]

  4. Final simplification0.0

    \[\leadsto \left(\frac{x}{y} + 1\right) \cdot \frac{1}{2}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y)
  :name "Data.Random.Distribution.T:$ccdf from random-fu-0.2.6.2"

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

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