Average Error: 15.5 → 0.0
Time: 9.2s
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 r628482 = x;
        double r628483 = y;
        double r628484 = r628482 + r628483;
        double r628485 = 2.0;
        double r628486 = r628482 * r628485;
        double r628487 = r628486 * r628483;
        double r628488 = r628484 / r628487;
        return r628488;
}
↓
double f(double x, double y) {
        double r628489 = 0.5;
        double r628490 = y;
        double r628491 = r628489 / r628490;
        double r628492 = x;
        double r628493 = r628489 / r628492;
        double r628494 = r628491 + r628493;
        return r628494;
}

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

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

  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 2019303 +o rules:numerics
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, C"
  :precision binary64

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

  (/ (+ x y) (* (* x 2) y)))