Average Error: 15.5 → 0.0
Time: 21.3s
Precision: 64
\[\frac{x + y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{0.5}{y} + \frac{0.5}{x}\]
\frac{x + y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{0.5}{y} + \frac{0.5}{x}
double f(double x, double y) {
        double r443077 = x;
        double r443078 = y;
        double r443079 = r443077 + r443078;
        double r443080 = 2.0;
        double r443081 = r443077 * r443080;
        double r443082 = r443081 * r443078;
        double r443083 = r443079 / r443082;
        return r443083;
}
↓
double f(double x, double y) {
        double r443084 = 0.5;
        double r443085 = y;
        double r443086 = r443084 / r443085;
        double r443087 = x;
        double r443088 = r443084 / r443087;
        double r443089 = r443086 + r443088;
        return r443089;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.5
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program 15.5

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

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{0.5 \cdot \frac{1}{x} + 0.5 \cdot \frac{1}{y}}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{\frac{0.5}{y} + \frac{0.5}{x}}\]

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, C"

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

  (/ (+ x y) (* (* x 2.0) y)))