Average Error: 15.8 → 0.0
Time: 1.5s
Precision: binary64
\[\frac{x + y}{\left(x \cdot 2\right) \cdot y}\]
↓
\[\frac{0.5}{y} + \frac{0.5}{x}\]
\frac{x + y}{\left(x \cdot 2\right) \cdot y}
↓
\frac{0.5}{y} + \frac{0.5}{x}
(FPCore (x y) :precision binary64 (/ (+ x y) (* (* x 2.0) y)))
↓
(FPCore (x y) :precision binary64 (+ (/ 0.5 y) (/ 0.5 x)))
double code(double x, double y) {
	return (((double) (x + y)) / ((double) (((double) (x * 2.0)) * y)));
}
↓
double code(double x, double y) {
	return ((double) ((0.5 / y) + (0.5 / x)));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original15.8
Target0.0
Herbie0.0
\[\frac{0.5}{x} + \frac{0.5}{y}\]

Derivation

  1. Initial program Error: 15.8 bits

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

  2. Taylor expanded around 0 Error: 0.0 bits

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

  3. SimplifiedError: 0.0 bits

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

  4. Final simplificationError: 0.0 bits

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

Reproduce

herbie shell --seed 2020204 
(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 2.0) y)))