Average Error: 0.0 → 0.0
Time: 4.3s
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 r687787 = x;
        double r687788 = y;
        double r687789 = r687787 + r687788;
        double r687790 = r687788 + r687788;
        double r687791 = r687789 / r687790;
        return r687791;
}
↓
double f(double x, double y) {
        double r687792 = x;
        double r687793 = y;
        double r687794 = r687792 / r687793;
        double r687795 = 1.0;
        double r687796 = r687794 + r687795;
        double r687797 = 0.5;
        double r687798 = r687796 * r687797;
        return r687798;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[0.5 \cdot \frac{x}{y} + 0.5\]

Derivation

  1. Initial program 0.0

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

  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 2019194 
(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)))